KfK 3652
Februar 1984
Neutron Capture Cross Sections
of the Krypton Isotopes and the
s-Process Branching at 79Se
G. Walter, B. Leugers, F. Käppeler, Z. Y. Bao, D. Erbe,
G. Rupp, G. Reffo, F. Fabbri
Institut fÜr Kernphysik
Kernforschungszentrum Karlsruhe
KERNFORSCHUNGSZENTRUM KARLSRUHE
Institut für Kernphysik
KfK 3652
NEUTRON CAPTURE CROSS SECTIONS OF THE
KRYPTON ISOTOPES AND THE
79
s-PROCESS BRANCHING AT
se
G. Walter, B. Leugers, F. Käppeler, Z.Y. Bao+, D. Erbe, G. Rupp,
++
.++
G. Reffo , F. Fabbrl
Kernforschungszentrum Karlsruhe GmbH, Karlsruhe
+
++
on leave frorn the Institute of Atornic Energy,
Acadernia Sinica, Peking, China
E.N.E.A. Bologna, Italy
Als Manuskript vervielfältigt
Für diesen Bericht behalten wir uns alle Rechte vor
Kernforschungszentrum Karlsruhe GmbH
ISSN 0303-4003
Abstract
The input data for an analysis of the s-process branching at 79 se
have been significantly improved. The neutron capture cross
86
sections for the stable krypton isotopes (except
Kr) were
measured between 3 and 24G keV neutron energy.
In addition,
statistical model calculations of the (n,r)-cross sections for
all isotopes involved in this branching were performed. With these
data and with other experimental results from literature a recommended set of Maxwellian average cross sections was established
in the mass region 77<A<85. The relevant decay parameters of the
involved unstable nuclei and the parameters for the s-process
model are discussed as well. On this basis the following aspects
are investigated: the temperature during s-process, the decomposition into s- and r-process contributions and the
sola~
krypton
abundance.
Die Neutroneneinfangquerschnitte der Kryptonisotope und die
s-Prozess Verzweigung am 79 se
Zusammenfassung
Die Datenbasis für die Analyse der s-P~ozeß Verzweigung beim
79
se wurde signifikant verbessert. Für die stabilen Krypton86
isotope (mit Ausnahme von
Kr) wurde der Neutroneneinfangquerschnitt zwischen 3 und 240 keV gemessen. Weiterhin wurden die
(n,r)-Querschnitte aller Isotope,die in dieser Verzweigung
eine Rolle spielen,mit dem statistischen Modell berechnet. Aus
diesen Daten und mit experimentellen Ergebnissen aus der Literatur
wurde ein empfohlener Satz von Maxwell-gemittelten Querschnitten
im Massenbereich 77<A<85 erstellt. Die für die Verzweigung
relevanten Zerfallsparameter der instabilen Kerne sowie die Parameter des s-Prozess Modells werden ebenfalls diskutiert. Auf
dieser Grundlage werden folgende Aspekte untersucht: die Temperatur beim s-Prozeß, Aufteilung der Häufigkeiten in s- und rProzeß Anteile und die solare Kryptonhäufigkeit.
CONTENTS
1.
Introduction
2.
Experiments
2
2.1
Experimental Set-Up
2
2.2
Electronics and Data Acquisition
4
2.3
Data Analysis
4
3.
4.
5.
Experimental Results and Uncertainties
7
3.1
Experimental Capture Cross Sections
7
3.2
Maxwellian Averaged Cross Sections
7
3.3
Uncertainties
8
Model Calculations
11
4.1
Outline of the Model
12
4.2
Model Parameters
13
4.3
Results and Discussion
19
Astrophysical Interpretation
5.2
79
s-Process Model and the
se-Branching
79
80
Decay Parameters of
Se and
Br
5.3
The Solar Krypton Abundance
27
5.4
r-Process Abundances in the Se, Br, Kr Region
28
5.5
The s-Process Temperature
30
5. 1
6.
21
21
25
Conclusions
34
Tables and Figures
35
Literature
65
Appendix I
68
"
II
73
"
"
III
77
IV
81
II
V
86
"
VI
91
-
1.
1 -
INTRODUCTION
In this paper we discuss the s-process branching at 79 se in the
light of new experimental and theoretical neutron capture cross
sections. This branching is best suited to yield an estimate for
the s-process temperature due to the accelerated beta decay from
the isomeric state at 95.7 keV in 79 se. Up to now only preliminary analyses were possible due to the lack of data (Ward,
Newman and Clayton 1 1976).
For that reason we have measured the neutron capture cross
sections of the stable krypton isotopes and have calculated the
cross sections of all nuclei involved in the branching. The
theoretical calculations were performed with great care including as much experimental information on the respective nuclei
as possible (e.g. experimental level densities, low lying level
schemes or extrapolations from neighbouring nuclei). Contrary
to the usual global description of parameters we find it essential for a more accurate treatment that local parameter
systema-
tics are included. From this local behaviour it is possible to
deduce even uncertainties for the calculated cross sections which
are useful for estimating their impact on the resulting s-process
temperature. Besides the measured and calculated cross sections
we also evaluated existing cross section measurements and condensed all this information to a set of recommended Maxwellian
averages for kT
= 30
keV in the mass range 78<A<84.
In addition to the capture cross sections we consider the
required information on s-process parameters (seed abundance,
fluence distribution) as well as the decay parameters of the
relevant unstable nuclei ( 79 se and 80 Br).
- 2 -
2.
EXPERIMENTS
The neutron capture cross sections of the krypton isotopes
were measured relative to the standard gold cross section of
ENDF/B-IV (Garber 1975). Capture events were registered by detecting the gamma-ray cascade from the deexciting compound nucleus
with two c 6 n6 -scintillators. Neutron energies were determined
by time-of-flight (TOF) . A set of six isotopic mixtures was
used to determine the neutron capture cross sections of 78 Kr,
80K r, 82K r, 83K r, 84K r an d , as a cons1stency
.
c h ec k , a 1 so
the capture cross sections of natural krypton. The isotopic
compositions of the samples are given in Table 1.
2.1
Experimental Set-Up
The experiments were performed at the Karlsruhe 3.75 MV
Van de Graaff accelerator. Important parameters of the neutron
source and the accelerator are listed in Table 2. The target
consisted of a metallic lithium layer of 3
~m
thickness and 6 mm
diameter evaporated on a 0.3 mm thick tantalum backing. As the
protons are slowed down in penetrating the lithium, the target
yields neutrons with a continuous energy spectrum. The target
backing was cooled from the outside by a thin film of flowing
water, thus increasing the neutron flux at low energies by elastic
hydrogen scattering.
Elaborate background reduction and careful beam collimation
6
resulted in the experimental set-up shown in Fig. 1. Li 2 co 3
was chosen as coating material of the inner collimator to minimize gamma background. The surrounding shielding consists of a
B4 c-araldite mixture which is an effective neutron absorber
due to the high 10 B density. The 478 keV gamma line from neutron
capture in 10 B is suppressed by the 20 cm thick lead shielding
of the
c 6 n6 -scintillators.
Only a small fraction of neutrons
10
penetrates the
B shielding and is finally absorbed by capture
in the outer shielding of Li-loaded paraffin. Some of these
neutrons might be captured in hydrogen, but the associated
4
2.2 MeV gamma-rays are suppressed by a factor 10 in the lead
-
3 -
shielding and are therefore negligible. Another background component originating from neutron capture in the antimony admixture
to ordinary lead could be eliminated by using pure lead for the
shielding. A non-negligible fraction of the background was caused
by neutrons scattered in the sample, thermalized in the
c 6 o6 -
scintillators and subsequently captured in the lead shielding
c 6 o6
or the residual hydrogen of the
scintillator (ratio D/H
~
0.72 ). This backgroundwas reduced by a factor of two by coating
6
the scintillator volume with a 4 mm thick layer of Li co . With
2 3
this set-up capture cross sections of the order of 1 mb have
been measured successfully (Almeida and Käppeler 1983).
Our sample cannings consisted of low mass stainless steel
spheres with an inner diameter of 20 mm and a wall thickness of
0.5 mm. The krypton gas was brought into the containers by
cooling them to liquid nitrogen temperature. The spheres could
withstand pressures of
~
the measurements at only
500 atmospheres but were operated during
~
300 atmospheres. The samples were
located at a flight path of 60.5 cm. With the overall time resolution of
~
1 ns obtained in these time-of-flight measure-
ments, an energy resolution of
~
0.5 keV at 30 keV neutron
energy was obtained, most of this being due to the 20 mm diameter of the sample cannings.
Up to seven samples were mounted on a sample chanqer supc:rvised by the data acquisition computer. One position was occupied
by a canning containing a 1 mm thick gold disk for measuring the
neutron flux. An empty canning and a canning filled with graphite
served for experimental background determination so that four
positions remained for the cannings filled with the various krypton isotopes. The samples were successively moved into the measuring position. A full cycle was chosen to take about 1 hour; in
this way long term variations in the neutron yield affected all
samples equally. This was verified by means of an additional
neutron monitor located at 90 deg to the beam axis (see Fig. 1),
the spectrum of which was recorded for all samples separately.
- 4 -
2.2
Electronics and Data Acquisition
Fig. 2 shows a block diagram of the electronics. Dynode
signals from the photomultipliers, E
and E , were used for
2
1
pulse height analysis whereas the anode signals served to define the TOF. Capture events were stored in a two dimensional
array of 16 pulse height and 1024 TOF channels for each of the
two detectors. In this way, the full experimental information
was recorded and pulse height weighting could be applied off
line. Coincident events were stored separately in a 1024 channel
TOF spectrum. These data were served for later correction of
pile-up events. Another 1024 channels were used to record the
neutron monitor spectrum. All these spectra were accumulated
for each sample position; during a sample change the data were
sequentially written to magnetic tape and, in addition, added
to a sum spectrum on magnetic disc for continuous inspection
throughout the measurement. Digital ratemeters allowed for a
permanent control of all relevant count rates.
2.3
Data Analysis
of the scintillation detectors is a nonThe efficiency
linear function of the gamma-ray energy. In order to determine
the nurober of captures independently of the multiplicity of the
gamma-ray cascade, we applied the Maier-Leibnitz weighting technique (Rau 1963, Macklin and Gibbons 1967) to our spectra.
The procedure of data analysis is illustrated as follows:
First, all individual, sequential spectra were read from magnetic tape, inspected by computer routines for equal neutron
flux and correct time resolution, eventually normalized to
equal flight path and then added to sum spectra. As an example,
the summed TOF spectra for the first pulse height channel of
8
8
the °Kr run are shown in Fig. 3 where the "empty" and °Krspectra are given for the two detectors. These spectra are
shifted arbitrarily to illustrate that they agree within counting
statistics.
-
5 -
Let now GOLD, CARBON and KRYPTON be the TOF spectra of the
gold, carbon and krypton sarnple after subtraction of the spectrurn
of the ernpty canning. These spectra are plotted in Fig. 4.
It
can clearly be seen frorn CARBON that neutron scattering in the
sarnple caused a tirne-dependent background. In turn, this effect
can be corrected for just by rneans of this spectrurn because
carbon does not capture neutrons at a detectable rate. For this
purpose, the CARBON spectrurn is norrnalized in a TOF region right
of the garnrna peak at channel 900 which contains no genuine capture
events.
(The garnrna peak rnarks the zero point of the TOF scale
when the proton pulses hit the Li-target). After subtraction of
the norrnalized CARBON spectrurn frorn GOLD and KRYPTON the spectra
of Fig. 5 are obtained which finally were subjected to the MaierLeibnitz procedure. Then, the so corrected count rates C can be
expressed by
c
= E
N •
•
~
• o with
E
=
( 1)
kB.
B denotes the binding energy of the captured neutron plus its
kinetic energy E ,a
n
is the capture cross section,
~
the neutron
flux and N the nurnber of nuclei in the sarnple and k is a constant.
Cornbining the count rates of the investigated sarnple and the gold
sarnple, the unknown cross section is then given by
aK r (E n ) =
NAu BAu CKr (E n )
(E )
n
a
Au
(En)
( 2)
When isotopic rnixtures are used B has to be replaced by an
effective value
L:
'
~
N. a. B.
~
~
L:
N
i
i
~
( 3)
a
i
with the surn running over all isotopes.
The final GOLD and CARBON spectra are used only for norrnalization; these spectra were smoothed artificially during data
analysis to irnprove statistics. This procedure is discussed in
detail by Leugers
(1979) and Alrneida (1982) and rnust, of course,
- 6 -
take into account that at least for the gold sample, the
smoothing is performed consistently for the experimental
spectrum and for the standard gold cross section.
Finally, corrections have been applied to the cross
sections accounting for neutron multiple scattering and selfshielding and for gamma-ray self-absorption in the samples, for
pile-up events and for the lost fraction of low-energy gammarays which were cut off by the electronic pulse-height threshold
(see Leugers 1979 and Almeida 1982 for a detailed discussion).
-
7 -
3.
EXPERIMENTAL RESULTS AND UNCERTAINTIES
3.1
Experimental capture cross sections
The deduced cross sections are plotted as a function of
neutron energy in Figs. 6, 7 and 8 for Kr-nat, 84 Kr and
8 °K
' 1 y. Isotop1c
' corrections were neglig1'b le on 1 y
r, respect1ve
84
for
Kr. The cross sections of all other isotopes had to be
determined from the cross sections measured for the various
isotopic mixtures by solving the corresponding set of linear
equations. In Figs. 9, 10 and 11 the respective cross sectians of the mixtures, denoted by quotation marks are shown. The
unfolded isotopic cross sections are given in numerical form in
the appendix.
3.2
Maxwellian averaged cross sections
The neutron capture rates for a nuclear species, i, is given
by
dN.
l
dt
= -
( 4)
Ni n n vo
for monoenergetic neutrons. Here N. and n
1
n
are the density of
nuclei and neutrons, v denotes the neutron velocity and o the
capture cross section at fixed neutron energy.
During the formation of the heavy elements inside a star,
however, we have to consider a non-relativistic, non-degenerate
plasrna.
In case of thermal equilibrium, characterized by a temperature T, the velocity v has to be replaced by vT and o by the Maxwellian average <ov> (Clayton 1968)
VT
00
f
=
2
dE o(E) E
exp(-~T)
0
( 5)
;,;:-
Now v represents the relative velocity between neutrons and
nuclei and vT the most probable neutron velocity
2kT
VT = / -~(~
reduced mass, k Boltzmann constant).
( 6)
- 8 -
From our data we calculated
between kT
=
20 and 50 keV.
These Maxwellian averaged cross sections are surnrnarized in
Table 3. In the following we consider only Maxwellian average
cross sections and denote these by a for simplicity.
The simultaneaus measurement of the capture cross section of
natural krypton provides a consistency check for our isotopic
results. For kT
=
30 keV we cornbined our individual isotopic
cross sections weighted with their relative abundances and
obtained a composed cross section of 67
~
5 rnb which is in good
agreement with the experimental result of 63 + 4 rnb for Kr-nat.
84
At this point we note that the new
Kr cross section
85
determines the isomeric ratio, IR, in
Kr which is defined
84
as the ratio of the partial capture cross section of
Kr lead85
ing to the isomeric state in
Kr and the total capture cross
section of 84 Kr. The partial cross section was measured for
84
kT = 25 keV by Beer and Käppeler (1982) who report aP( Kr)
=
24 !
3 rnb. With the total capture cross section for the same
thermal energy o( 84 Kr) = 42.2 ~ 4.8 rnb we obtain
IR(
85
Kr)
=
0.57 + 0.10
This value is an important parameter for a forthcoming analysis
85
of the
Kr-branching by Walter et al. (1983).
3.3
Uncertainties
In this section we discuss the uncertainties related to
the various steps of data analysis. Principally, there are two
classes of uncertainties: those which are about equal for all
isotopes
(e.g. reference cross section, sample related effects)
and others which are determined by the size of the respective
cross sections (background, statistics). As can be seen from
Figs. 3 to 5 the latter uncertainties depend also strongly
on neutron energy. Here, we restriet the discussion to the
uncertainties of the Maxwellian average cross section.
- 9 -
Note that in calculating the total uncertainty we have
neglected possible correlations between individual components.
All considered uncertainties are summarized in Table 4.
a)
Standard cross section:
For the Maxwellian average of the
197
ENDF/B-IV cross section of
Au we estimated an uncertainty of 3 %. Meanwhile, a new version ENDF/B-V is available1 which on an average is higher by
~
2.3 % compared
to ENDF/B-IV. However, this version might change as the
data of Macklin et al.
(1975)_,
on which it is primarily
based, have been revised recently (Macklin 1982).
b)
Gamma-ray self-absorption in the sample: This effect was
investigated experimentally for a set of gold samples
with different thicknesses and diameters (Wisshak, Walter
and Käppeler 1983). From these results extrapolations
to other sample materials could be made. These corrections
which introduce an uncertainty of 1 % were not applied
to our first results (Leugers 1979 and Leugers et al. 1979).
c)
Neutron multiple scattering
and self-absorption: For
the gold sample these correction factors were calculated
by the SESH-eode (Fröhner 1968). For the Krypton samples
the spherical geometry implied that no correction was required for neutron multiple scattering and therefore only
the self-shielding effect was corrected for.
d)
Pile-up events: Given the large solid angle of the detectors seen by the sample, there is a nonnegligible probability for two (or more) gamma-rays of the same cascade to be
simultaneously detected in the same detector. These events
are incorrectly weighted by the Maier-Leibnitz method.
The correction is derived from the experimentally measured
coincidence rate between the two
sulting uncertainty is
e)
~
c6 n6
detectors. The re-
1 %.
Lower threshold correction: Events with a pulse height less
than 90 keV fall below the electronic threshold and are
lost. Because the pulse height weighting function is very
small for these events, the resulting correction as also
srnall leading to an uncertainty of 0.5 %.
- 10 -
f)
Sample mass: The weight of the empty and filled sample
cannings was determined before and after the measurements.
Losses of krypton gas through leaks in the cannings were
negligible in most cases. The related uncertainties are
84
1 % except for
Kr where 2 % had to be tolerated.
g)
Time dependent background: The relative size of this correction depends on the observed signal-to-background ratio in
the TOF spectra. This uncertainty is typically 1 % but 2 %
84
for
Kr because of its smaller cross section.
h)
Weighting function: The uncertainty introduced by the pulse
height weighting function was checked by variation of the
adopted function (Hensley 1980) within reasonable limits
(30 %) . The impact on the cross sections is relatively small
giving rise to an uncertainty of 0.5 - 1 %.
i)
Effective neutron binding energy: This uncertainty is the
smaller the higher the sample is enriched. It is largest
for " 78 Kr" and "Kr-nat" (3 %) and zero for 84 Kr.
j)
Isotopic impurities: The isotopic cross sections were
determined from the experimentally investigated "mixtures"
solving the corresponding set of linear equations. The
related uncertainties are correlated to the enrichment
78
of the samples. They are largest for
Kr (10 %) and again
84
zero for
Kr.
k)
Statistics: The statistical uncertainties are t~pically
84
2 % but are larger for
Kr (3 %) because of the less
favourable signal-to-background ratio.
-
4.
11 -
MODEL CALCULATIONS
Theoretical calculations of neutron capture cross sec-
tians in the keV energy range are usually based on the HauserFeshbach formalism. For astrophysical purposes extensive calculations of Maxwellian average cross sections for kT = 30 keV
have been performed (Holmes et al. 1976, Woosley et al. 1978)
on a variety of isotopes using global parameter systematics
in order to cover a large range of atomic masses. However, such
global treatments imply that local details (e.g. due to deformation or to shell effects) are not sufficiently accounted for,
and the results so obtained differ from experimental cross sectians by 30-50 % on the average.
The reliability of theoretical cross sections can be improved by refined techniques as they were developed for evaluation of neutron cross sections in the technological field.
The idea is to use as much experimental information as is available in the literature to determine the relevant Hauser-Feshbach
parameters and to build local parameter systematics for the
investigated isotopes and for their neighbours as well (Reffo
1980a). In this procedure special attention was paid to achieve
internal consistency of all parameter sets. The so determined
parameter sets enable us to deduce the capture cross sections
with typical uncertainties of
~
25 % even for those isotopes
~or
which no experimental information is available at all. The
capability of the local approach may be verified by comparison
of theoretical data obtained by this technique (Benzi et al.
1973, Harris, 1981) and by global parametrization (Holmes
et al. 1976) with experimental cross sections as quoted in
the compilation of Käppeler et al.
(1982). From Table 1 in
this latter reference one finds average deviations from the
experimental values of 20-25 % for local and 30-40 % for global
parameter sets. It should be noted that the systematic treatment of parameters as well as the theoretical formalism has
been improved recently in several aspects (Reffo 1980b,
Reffo et al. 1982, Reffo 1981 now even allowing for calculation of capture gamma-ray spectra and isomeric ratios)
-
12 -
In the present investigation our interest is focused
on the mass region 78 < A < 84 and, in particular, on the
81
radioactive isotopes on the s-process path, 79 se and
Kr,
which cannot be investigated experimentally. We also try
to quantify the uncertainties in the calculations for some
important cases in order to estimate how they affect the related astrophysical interpretations.
4.1
Outline of the Model
Our investigations are carried out with the modular system
of computer codes, IDA,
(Reffo and Fabbri 1981). The present
cross section calculations were made with the module POLIFEMO
based on the Hauser-Feshbach theory including correction for
width fluctuations. It was used in the spherical optical model
approximation to calculate the neutron transmission coefficients in the entrance and exit channel. The probability for
gamma decay of the compound nucleus states of any given J and
n
is then determined for each step of each possible gamma-ray
cascade.
After summation over all J and n and by considering
E1, E2 and M1 electromagnetic selection rules, the various
single step contributions are lumped tagether into energy
bins according to the energies of the emitted gamma rays so
that partial and total gamma-ray spectra can be obtained on
option. The code also traces gamma-ray stories which feed
some particular levels. In this way, it is possible to calculate the cross sections for the population of isomeric
states and the corresponding gamma-ray spectra as well. For
the transitions between discrete levels, gamma-ray decay schemes
and branching ratios were either given as input or were internally calculated according to different options.
- 13 -
The gamma-decay widths of E1 transitions are estimated
according to the Brink-Axel model as used by Reffo (1980a)
where
fy
(E,J,TI) =
c
p(E,J,TI)
*6
( 7)
lE-E ) 2 o (E-E )
TI ,-n
n
L
n
n
gives the width for gamma decay from continuum levels (E,J,TI)
to the nth discrete level (E , J , TI ) and
n
n
n
c
llr:; (E,J,TI) =
P
(E,J,TI)
2
E
OL(E)
J+ 1
t
J'=TJ-11
p (E-E:,J' ,-TI)liE
( 8)
the width for gamma decay from continuum levels (E,J,TI) to
continuum levels (E-E,J' ,-TI).
( 9)
is the adopted Lorentzian form for the splitted photon-absorption cross section and C = 2/3 (Tihc) 2 .
4.2
Model Parameters
'l'he most important quantities needed for the determina-
tion of gamma decay widths of the compound system are the
level density p and the photon absorption cross section oL.
In spite of many attempts, there is no level density model
which may provide absolute values over a wide range of atomic
masses. Therefore, we adopt the approach outlined below which
offers the advantage of being characterized by only two parameters
(a,U ) both of which exhibit a well established systemx
atic behaviour (Reffo 1980 b). For evaluation of the level
density the range of accessible excitation energies is subdivided into three intervals:
-
(i)
14 -
The region of known discrete levels where no theoretical
model is needed; the respective quantum characteristics
(E,J,~)
are taken from Ledererand Shirley (1978)
(ii) At high excitation energies a total level density
=
ln
exp[21~(E-6)]
T2 a 1 74 (E-6) 5 / 4 12~a 2 TEf
( 1 0)
is assumed, 6 being the pairing correction and a the
level density parameter. This expression results essentially
from the Fermi gas model.
The corresponding spin distribution is
f (E ,J)
=
(2J+1)exp[-(J+1/2) 2 /2o 2 (E)]
with a spin cut-off factor a 2 (E)
level density parameter
( 11 )
(E)
2
~
=
2
0.146 la(E-6) A 1 3 . The
that characterizes the level
density and the spin distribution has been treated as
a free parameter which was obtained at the neutron separation energy by normalization of p
2
to mean spacings D
of s-wave neutron resonances.
(iil)In the intermediate region between the last known
discrete level and the region where the Fermi gas model
is valid, .a semiempirical exponential form suggested by
Gilbert and Cameron (1965) was used for interpolation
( 1 2)
Both parameters in this equation, T and E0
pressed by the level density parameter
tive energy U
X
E
X
=
~
,
can be ex-
and by an effec-
E -6, 6 being the pairing energy, and
X
that excitation energy where the level densities
and p match smoothly. Eventually, it may be helpful
1
2
in ambiguous cases to consider the nuclear. temperature as
p
a supplementary information, because it exhibits a very
stable behaviour with mass nurober (Reffo 1980a).
-
15 -
For the parities usually an equal distribution is assumed
in the entire continuum energy range. But for certain cases
specified below a distribution
P(n,E)
=
e
AE+B
( 1 3)
is used (Reffo 1980a) in order to account for the experimental
parity distribution of the discrete levels.
4.2
Evaluation of Model Parameters
The discussion of how we determined the parameters and the
parameter systematics for the investigated isotopes is presented
in the same order as they were introduced in the preceding section.
Optical model parameters (OMP) :
In the energy range considered
here we know that the OMP may influence even strongly the
calculated neutron capture cross sections. To reduce this uncertainty we have chosen OMP sets which reproduce s- and p-wave
strength functions
s0
,
s1
and the scattering radii R because
these quantities completely determine the cornpound nucleus cross
Beetion and the shape elastic cross section, respectively, for
neutron energies below 100 keV. For the Kr and Se isotopes this
requirement was sufficiently satisfied by the OMPs of Wilmore
and Hodgson (1964) and for the Br isotopes by those. of Perey
and Buck
(1962). These adopted OMP sets were tested by comparison
of our calculated total cross sections with experimental resu]ts.
In Table5 the scattering radii
8
0
1
s1
~
and strength functions
which we calculated with the above OMP sets are shown
tagether with the respective values taken frorn systernatics
and from analysis of neutron resonances. The good agreement
between calculated and ernpirical values indicates that no
significant uncertainty is to be expected in this part of the
cross section calculations.
Level density pararneters:
The level density pararneter
~,
that
characterizes p , is usually deduced frorn statistical analy2
ses of neutron resonance schemes but where no such infor-
-
mation is available,
~
16 -
can be deduced either from systematics
(Reffo 1980a) or from experimental capture cross sections,
provided that all other model parameters are sufficiently known.
For the Se and Br isotopes the existing resonance schemes are
rather poor (Mughabghab et al. 1981). Therefore, no sophisticated
resonance analysis could be performed but mean resonance spacings
D
088
were deduced by simple staircase statistics and the associated
uncertainties were derived using Student's t-distribution. The
resulting values for DOBS are listed in Table 6.
They show sig-
nificant discrepancies compared to the values given by Mughabghab
et al.
(1981) and also more conservative uncertainties.
In case of the Kr isotopes, resonance schemes were not
86
available except for
Kr. Therefore in our first calculations
(Leugers et al. 1979) level density parameters were deduced
from overall systematics. But with the now available experimental
cross sections the mean level spacings could be improved. In the
range of the Maxwellian energy distribution (kT
=
30 keV) one
may write (Reffo 1980a)
a ny
=
r
K _.1.
( 14)
D
K being a known factor. Provided that the average radiative
width is known, D can thus be determined from the cross section.
Uncertainties were estimated via error propagation from the
uncertainties of a ny and r y as given in Table 6.
The results for
~
are plotted in the upper part of Fig. 12
for all investigated isotopes, and members of the individual
families are connected by eye guide curves. Two features can
be distinguished in this plot which justify the local treatment
of a: There is a significant difference in
and non even-even target nuclei
~
for even-even
(open and black symbols) and
there appears to be a displacement between the even Se and Kr
isotopes as well. However, in this particular case the uncertainties
- 17 -
are too large to allow for a conclusive statement and so the
effect of different proton numbers was neglected here. This is
in accord with Reffo (1980a) who finds that this effect starts
to be sizeable only for A > 100. Assuming a smooth dependence
of a on neutron nurnber, the scatter of the a values deduced
from experimental data could be used to estimate the uncertainty
of the systematics. In view of the large uncertainties,
especially for the Se isotopes, we assumed ~a ~ 0.5 Mev- 1 as
being realistic. The finally adopted level density parameters
are listed in Table 9; values interpolated from the systematics are marked by an asterisk.
In the intermediate energy range the level schemes of
all
compound nuclei (Lederer and Shirley 1978) were considered to deduce the parameters UX and T. For some examples Fig. 13 shows
the cumulated nurober of the known discrete levels (staircase
plots) and the respective fits
(solid lines). The inserts give
the spin distributions of the known levels which have been fitted
by the maximum likelihood method to obtain the spin cut-off
2
factors o . The resulting values for U and o 2 are also
X
shown in Table 9. As one may see from Fig. 13, sometimes
there is no good agreement between t.he experimental and the
fitted spin distribution. In these cases two values for o 2 are
given in Table 9, the first being derived from the theoretical
and the second from the experimental distribution, and the
adopted value is marked (§). The differences between theoretical
2
and experimental o -results are assumed as an estimate for the
uncertainty in the spin distribution.
,
1
t which is indicated
The continuum approximation for the level density,
was used above the excitation energy E
CU
by arrows in Fig. 13. The position of E
CU
p
t is determined
either by the energy of the first level of unknown J,TI or
where the fitted curve starts to deviate from the staircase
plot due to missing levels. The results for E
CU
in Table 9.
t are given
- 18 -
In the mid part of Fig. 12 the matehing energy U
X
is
plotted versus neutron number for all investigated isotopes.
The smooth behaviour of U
X
provides not only information for
those cases where only poor level schemes are available but
can also be used as a test for the analyzed level sc~emes
and for the respective values of
~·
If, for a particular iso-
tope, Ux does not fit in the systematics of Fig. 12, this
would indicate ambiguities and would require reconsideration
of the entire parameter set. Overall, the consistent systematics for a and U
-
X
as shown in Fig. 12 ensure the reliability
of the basic experimental information and of the analysis as
well.
For calculation of the isomeric ratio
IR
for
79
= Eartial
capture cross section to the isomer
total capture cross section
se the gamma decay scheme and branching ratio in the
compound nucleus are also required as input. This information
was taken from Lederer and Shirley (1978). Gaps in these data
were filled by the assumption that E1, M1 single particle transitions dominate. The finally adopted level scheme with all
spectroscopic information is summarized in Table 7.
Radiative Widths: The giant resonance parameters (GRP) for
the calculation of the radiative widths are taken from the
systematics of Reffo (1980a). The corresponding nuclear
deformations ß were determined from the tentative systernatics
at the bottom of Fig. 12. The deformation parameters used
for the systematics are taken from Stelson and Grodzins (1965)
or are deduced from quadrupole moments
(Fuller and Cohen 1969).
The adopted GRP and deformations are listed in Table 9.
Table 8 shows the radiative widths for s- and p-wave resonances calculated with the above parameters in comparison to
experimental values. In general, the agreement is remarkably
good, at least in view of the experimental uncertainties.
- 19 -
4.3
Results and Discussion
Our calculated neutron capture cross section are summarized
in Table 10. The astrophysically important Maxwellian averaged
cross sections for kT = 30 keV are listed in Table 11 tagether
with the experimental values. This table provides also results
from other calculations and the experimental data from the
literature.
Before entering in a detailed discussion it should be noted
that a comparison of our previous calculations (Leugers et al.
1979) with the present results illustrates the amendments which
were achieved by improving the OMP sets and the systematics
for the level density parameter a. Major changes occured for
the odd isotopes 81 Kr and 83 Kr b~t also for 78 Kr, mainly because
the new experimental data allowed for a refined evaluation of
~
in this mass region, including odd-even effects. For a few important cross sections, especially for 79 se , we tried to estimate
the uncertainties of our calculations. Neglecting the uncertainties due to the OMP sets (as justified above) we traced the propagation of the uncertainties from the radiative decay width
ry
and from the level spacing D. The radiative decay width depends
on the level density parameter a, the nuclear temperature T
2
(through U ) , the spin distribu~ion (through o ) and on the
X
parity distribution P(TI). As D also depends on
a ny
Although a and U
-
X
(~,
U
x
,
a 2 , ß,
~,
one obtains
P(n)).
( 1 5)
are correlated for a particular isotope the
correlation becomes negligible when these parameters are taken
frorn systematics. Therefore, in our analysis we assumed these
pararneters to be independent of each other. The uncertainties
of a, U
-
in Fig.
X
and ß were estimated from the scatter of the points
12. The difference between the experimental and
theoretical spin distributions was assumed as the uncertainty
2
of the spin cut-off factor o .
- 20 Finally, we have neglected the uncertainty from P(n), because an extrapolation of the equal distribution for the two
parities from the discrete levels to the whole energy range
seemed reasonable. With this procedure uncertainties of 20
.
and 23 % are estimated for 78 Se and 79 Se, respect1vely.
Comparison of the present results with other calculations
exhibits reasonable agreement for the Se and Br isotopes but
with three exceptions: the 78 se value of Holmes et al. (1976)
79
81
and the
se and
Br values of Harris (1981) are discrepant
from the other data by almost a factor 2.
For the Kr isotopes the discrepancies are more severe, in
particular if one compares the entire sequence of cross sections
rather than a single isotope. There seems to be a general trend
to underestimate the cross sections of the even, neutron-poor
isotopes but also the results for 84 Kr are highly discrepant.
This shows clearly the virtue of the local parameter systematics
which provides a consistent set of parameters for each of the
investigated isotopes. This seems to be the more important close
to magic neutron numbers.
The good agreement between our calculation and the experimental data is illustrated in Fig. 14 for all investigated isot opes. The f ac t th a t th e re 1 evan t ra d 1oac
t'1ve nuc 1 e1' 79 s e an d 81 Kr
.
have always two stable neighbours makes it possible to deduce
their parameters from our systematics by interpolation. Therefore we are confident that our approach yielded reliable values
for these cross sections.
In addition to the cross sections we have also calculated
the isomeric ratio IR and the average gamma cascade multiplicity
79
m for
se. This case was considered only for completeness because the population of the isomeric state in 79 se by neutron
capture is not important for the s-process (it decays almost exclusively to the ground with a half life much shorter than the
neutron capture time scale). At 30 keV neutron energy we get IR
79
( se) = 0.52. In the calculation of the isomeric ratio we found
that a maximum cascade multiplicity mF4 was sufficient to account for 97 % of the cross section; the average multiplicity
- =
was m
2.7.
- 21 -
5.
ASTROPHYSICAL INTERPRETATION
5.1
s-Process modeland the 79 se-branching
We adopted the phenomenological s-process model of Clayton
et al.
(1961) which assumes a rather weak neutron flux and an
exponential distribution of neutron exposures T
p (T)
( 16)
56
f 1 , 2 are the fractions of the solar
Fe abundance N56 which
act as seed for the s-process and T01 , are mean fluences in
2
1
(mb- ). While the second term accounts for the bulk of s-process
abundances the first term in eq. (16) is required to reproduce
the enhanced s-process contributions in the region 56<A<90. In
ry
the following we accept the fluence distribution determined
recently by Käppeler et al.
(1982) who derived the parameters
fand TO by a bestfit of the calculated products oNs(A) to the
empirical values for s-only isotopes. These normalizing points
were determined from evaluated experimental cross sections which
are folded with the Maxwellian neutron energy distribution and
from the solar abundances N quoted by Cameron (1982), We note
0
at this point, that the adopted model and also the fluence distribution should be considered as an approximation. Modifications
to that simple picture could for instance be that the two terms
of the fluence distribution might be characterized by different
neutron densities and temperatures - and both these effects
would have significant impact on our branching analyses. We will
come back to this problern in the following sections.
In this model the characteristic product oNs can be calculated
as a function of mass nurober by the relation
ON
s
(A)
A
TT (1
=
+
i=56
( 1 7'
A
-II
i=56
(1
+
.
1
°i To2
)
-1
- 22 -
For convenience the factors (1 + -------)
l
sX (AZ) for isotope A of elernent Z.ai ox
-1
are abbreviated by
Frorn equation (17) it can be seen that aN
is a srnooth function
s
of A which is deterrnined by the product ai'o· For large cross
sections or a., >1 aN depends only weakly on Aas it is the
0 'V '
l
s
case in the Se, Br, Kr-region.
The specific situation for the 79 se branching is illustrated
in Fig. 15. The branching points 79 se and 80 Br are shaded and the
80
82
s-only isotopes
Kr and
Kr are rnarked by double boxes. The
involved isotopes are linked by the s-process rnass flow as it
is considered in our calculations.
79
That there is certainly a significant branching at
se is
8
82
.
f rorn th e 1sotop1c
'
. a b un d ances o f s-on 1 y °K r an d
Kr,
o b v1ous
80
because
Kr would be bypassed completely otherwise. For a
quantitative treatrnent one rnust consider the product aN
s
rather
than the abundances. A sirnilar although less pronounced observat 1on
·
· to b e expecte d f or t h e aNs-va 1 ues o f 78 se and 80 se as
1s
both these isotopes are also produced significantly by the s79
process. A third possibility to investigate the branching at
se
8
80
is provided by the cornparison of aNs for
se and °Kr. All these
cases will be considered below.
The branching at 79 se can be expressed in terrns of the
beta decay rate AßAn
=
nn vTa where t
=
ln2/t
and of the neutron capture rate
112
79
is the effective half live of
se at
112
s-process ternperatures Ts and nn is the corresponding neutron
density; vT
= I ~~T
is the average thermal velocity with ~
being the reduced neutron rnass. Then the branching ratio Bn
reads
Aß -( 79 se)
The beta decay rate Aß- is expected to be ternperature dependent
and can be deterrnined frorn the analysis of the branching. For
79
the neutron capture rate An one needs the cross section of
se
and the neutron density nn.
( 1 8)
-
23 -
80 Br occurs because of the two
The (minor) branching at
decay modes of this nucleus, whereas neutron capture can be
neglected due to the short half lives. In this case one obtains
( 1 9)
80
80
Aß- ( Br) + AEC(
Br)
The problern with this branching is that the ratio of the two
decay rates in 80 Br depends also on temperature. In section 5.3
the parameters required in eqs.
(18, 19) are discussed in detail.
With these definitions the products aN
for the isotopic pairs
(
80
82
Kr,
Kr),
(
78
Se,
can be evaluated
s80
Se) and
(
80
Kr,
80
Se).
The first pair is certainly the most promising case because both
isotopes are of pure s-process origin. The corresponding aNs values
can be expressed as
aNs(
80
Kr)
=
2
X
78
IoNs(
Bß-(
Se)
x=1
79
Se)
79
1-Bß- ( Se)
( 2 0)
and
B -(
79
ß
1-B - (
se)
79
ß
Se)
+
(2 1)
where
sm
is given by
= (
1
1-B -(
ß
79
+
se)
o(
79
1
Se)'ox
-1
)
( 22)
-
According to Käppeler et al.
24 -
(1982) different weight has to be
78
given to the two components of the fluence distribution (aN~( se)/
2 78
.
80
82
aNs( Se)= 0.52). Apart from th1s, the ratio aNs( Kr)/aNs( Kr)
is independent of any assumption on elemental abundances and is
determined completely by the quantities sx(AZ) and the branching
ratios for 79 se and 80 Br. The effective s-process branching ratio
for 79 se results from eqs.20 and 21 by inserting the empirical value
8
82
for the ratio aN ( °Kr)/aN ( Kr). As one deals with two isotopes
s
s
of pure s-process origin the associated uncertainty is caused
8
82
only by the cross sections of °Kr and
Kr.
Contrary to this ideal case, the determination of B -( 79 se)
8
via the aN -value of the isotope pair ( 78 se, 80 se) is complicated
s
because a correction must be made for the abundance contribution
from the r-process. For 78 se this correction can be taken from
the calculated aNs-curve of Käppeler et al. (1982) as 80 se is part
79
of the
se branching. The required r-process contribution is determined by interpolation of the respective values for 76 Ge, 78 se
82
86
and
se,
Kr. Another drawback comes from the fact that for 78 se
no experimental cross sections are available. Because 78 se and
80
se are the immediate neighbours of the branching point the ratio
80
78
aNs( se)/aNs( se) is influenced by fewer isotopes and the corres80
ponding expression for aNs( se) is simpler than eq. 21
2
I
x=1
B -( 79 se)
+
ß
1-B -( 79 Se)
( 2 3)
ß
The third possibility for defining B -( 79 se) is to compare
8
the empirical aNs-value for 80 se and 8 °Kr. However, this procedure requires the abundance ratio of Se and Kr and therefore
suffers from the large uncertainty of the krypton abundance. In
principle, one can use the aN curve to deduce the Kr-abundance
s82
such that aN ( Kr) is normalized to the curve as it is discussed
s
in section 5 .3. Butthis leaves still a considerable uncertainty because the abundance ratio of Kr and Se cannot be verified
by this method as long as an experimental cross section for the
76
corresponding normalization point
se is lacking. For complete-
- 25 -
ness, we also give the expression for this pair of nuclei:
8
oN ( °Kr)
s
80
oN ( se)
s
2
[
I
1-Bß-(
:::::
79
Se)]
-l
Bß-(
79
X 79
X 79
Se)i';tri(
Se)i'; (
Br)
Bß-(
80
Br)i';
X
(
80
X 78
Kr)oN (
Se)
8
x=1
2
X 79
X 80
i';m(
Se)t; (
Se)+Bß-(
\
L
79
Se)(
X
(
79
Br)
[1-Bß-(
80
Br)]L;
X
(
80
Se)
ON
x=1
X
s
(
78
( 2 4)
Se)
All quantities which are required to evaluate the effective
79
branching ratio Bß-( se) under s-process conditions will be
discussed in section 5.5.
The cross sections determined in this work can also be used to
improve the respective s- and r-process abundance contributions.
This decomposition can easily be done by the approximate
relations
oN (A)
8
: : : c(A)
Ns(A)
and
N (A)
r
=
N - N
0
s
( 2 5)
which are valid under the assumption that abundance contributions
from other processes,
(e.g. from the p-process) are negligible
(see also Käppeler et al.
5.2
1982).
Decay parameters of 79 se and 80 Br
The beta decay rate of both isotopes depends on temperature,
at least in the range of interest around kT
=
30 keV. Fig. 16
79
illustrates that this is a very strong effect for
se. The first
excited state at 96 keV is thermally polulated to
~1
% (Walter and
Beer 1982) at s-process temperature and undergoes allowed beta
79
transitions to
Br with a half life of ~ 20 d while the ground
4
state decay is first forbidden with a half life of < 6 x 10 yr.
As thermal equilibrium is achieved on a much faster time scale
than the decay, the population of the excited state is constant
in time and given by
P. =
1
(2J.+1)
1
exp (-E./kT) I
1
Z
( 2 6)
- 26 -
where Z is the partition function, J. the spin and E. the energy
l
l
of the excited state. The total beta decay rate \ß- is given by
the surn of all partial rates
\ =
p
(27)
0
As can be seen frorn Fig. 16, there are several possibilities
for allowed beta transitions frorn excited states in 79 se and
even a back-decay frorn the 207 keV state in 79 Br cannot be excluded.
These transitions, however, have to be weighted with the respective population probabilities and this, finally, reduces the
nurnber of effective links to the decay of the first excited
79
state in
se to the ground state of 79 Br. In Table 12 all the
pararneters are surnrnarized which we considered in this respect.
Unknown log ft-values were taken frorn Conrad
(1976) and are estirnates
based on available values for sirnilar transitions in neighboring
nuclei. Because the high ternperature leads to alrnost cornplete
ionization in the rnass region around A = 80 the phase space
for the ernitted electrons is rnodified cornpared to the terrestrial
situation. The resulting effects
(bound state beta decay, capture
of continuurn electrons, harnpered electron capture frorn bound
states etc.) have been taken into account in deterrnining the
s-process decay rate
12 lists
\~
l
(Conrad 1976). The last colurnn of Table
the decay rate of each level, leading to an overall
= 4.3 yr at kT = 30 keV. This value is slightly
2
longer than the 3.3 yr derived by Conrad because in th~ rneantirne
the J~ assignrnent for the 130 keV state in 79 se has been settled
half life of t1;
(Walter and Beer 1982 and references therein). The back decay frorn
the 207 keV state in 79 Br turned out to be not significant under
s-process conditions. It can be all the rnore neglected as Se is
6 tirnes moreabundant than Br
(Anders and Ebihara 1982).
79
The ternperature dependence of the half life of
se is
9
plotted in Fig. 17 for the range between 0 and 10 K. One finds
a very steep slope between
and 3 x 10 8 K just where the s-process
ternperature is supposed. The dashed lines indicate the range of
uncertainty which results frorn the 10 % uncertainty of the log
ft-value for the decay frorn the 96 keV state. This state is an
isomer With 3.9 rn half life against garnrna-decay to the ground
- 27 -
state. This time rnay be long enough that it eventually perrnits
to rneasure the beta decay branch frorn this state directly.
At present, a first atternpt for such an experirnent is being prepared. If it succeeds, it would provide a rnajor irnprovernent for
deterrnining the s-process ternperature. The thin solid line in
Fig.
17 represents the sornewhat higher estirnate of Newrnan (1973)
and Cosner and Truran (1981) who neglected the effect of ionization.
The decay of the second radioactive isotope in the 79 se80
branching,
Br, also depends on ternperature. In that case it
is not the half life which is affected but the branching ratio
\ 8 -/AEC' which Conrad (1976) predicts to change frorn the terrestrial value of 11 to 28 at kT = 30 keV for the reasons rnentioned
above. For sirnplicity, all calculations in this work will use a
80
constant value B -( Br) = 0.97.
8
5.3
The solar krypton abundance
The observation that
82
Kr can be forrned only by the
s-process and that the total s-process flow passes through this
isotope, provides a possibility to deterrnine the solar krypton
82
abundance by cornparison of aN ( Kr) with the respective value
s
of the aN(A)-curve. The total krypton abundance foLlows then frorn
the well known isotopic ratios. A possible p-process con82
tribution to the
Kr abundance can be neglected in th ~.s context:
78
if one accepts the
Kr abundance as an upper lirnit then a possible
82
p-process cornponent of
Kr is ~ 3 %. This problern will be addressed
in rnore detail below because it is of sorne concern to
the analysis of the 79 se branching.
Adopting the aN
curve of Käppeler et al. (1982) with
aN s (A=82) = 557 rnb (Si = 10 6 ) and an estirnated uncertainty of
~ 25 % (as obtained frorn Table 3 in this reference) one finds
8
-
directly
aN (A=82)
= .- as (82Kr) =
6
6.6+1. 7 (Si::::10 )
( 2 8)
and
0
0
NKr = N (82Kr)
I 0.116 =57+ 15
(29)
- 28 -
The uncertainty of this krypton abundance comes mainly from the
fact that for A<85 the oN -curve is composed of two neutron fluence
s
82
components. The softer one contributes ~ 30 % to oN 8 ( Kr) but
cannot be accurately defined at present because of lacking ex.
.
70G e, 768 e 1n
.
perlmental
cross sections f or t h e s-on 1 y 1sotopes
the neighborhood of 82 Kr.
This krypton abundance is in fair agreement with the values
estimated in recent abundance compilations by interpolation between
.
.
.
83
81
85
84
1sotopes of ne1ghbor1ng elements ( Kr between
Br and
Rb,
Kr
80
88
between
se and
sr). In this way, Cameron (1981) abtairred
N~r = 41.3 while Anders and Ebihara (1982) report a value of 45.3.
83
The latter authors assumed the 11 % difference between the
Kr
84
and the
Kr interpolation as an estimate for the uncertainty of
the Kr abundance. However, interpolation requires a smooth abundance variationwith mass nurnber which only holds for the r-process
contribution. Both isotopes, 83 Kr and H4 Kr, do have sizeable
abundance components from the s-process
vely, Käppeler et al.
(33 and 38 %, respecti-
1982) and therefore a simple interpolation
is not correct. In fact, as most of the abundances used for the
interpolation are dominated by r-process contributions, this
procedure determines rather the r-process component of the krypton
abundance. A quite different krypton abundance N~r
=
25 is given
by Palme, Suess and Zeh (1981) which is derived from the composition of solar rare gas components in gas rich meteorites (Marti,
Wilkening and Suess 1972).
5.4
r-Process abundances in the Se, Br, Kr region
With the branching analysis, the related capture cross sec-
tians and the oN-curve of Käppeler et al.
(1982) it is possible
to decompose the observed isotopic abundances into their s- and
r-components. The p-process contributions are small (as is obvious for 8 °Kr) and will be neglected in our discussion here.
Selenium: For 77 , 78 se the decomposition is Straightforward
yielding fractional r-process contributions of 67 and 47 %.
The s-process contribution to 80 se follows from the branching
80
ratios at 79 se and
Br and is found to be 76 % of its observed
abundance.
- 29 -
Bromine: Both these isotopes lie within the branching and
their decomposition depends therefore on the branching ratio.
Other complications are the contributions from their radioactive
.
79
81
1sobars
Se and
Kr. Nevertheless, the r-process component
dominates the bromine abundance.
Krypton:
83 , 84 Kr showalso a strong r-process contribution.
In Table 13 all the numerical values relevant for the Separation of s- and r-process contributions are summarized including
75
As for comparison. For our calculated cross sections a 40 % uncertainty was assumed except for those of 78 , 79 se which are estimated
in Table. 11. For the 77 se cross section a somewhat larger uncer
tainty of 50 % was admitted. The aN -values from Käppeler et al.
s
(1982) were estimated to be accurate to 25 % and for the solar
abundances the uncertainties quoted by Anders and Ebihara (1982)
were used. The resulting r-process abundances are plotted in
Fig.
18.
While the odd mass isotopes show fairly constant values
for N , a strange pattern is found for the even isotopes. Obr
80
84
.
viously,
Se and
Kr are h1gher by a factor two compared to
the trend of their even neighbors. This feature seems to be
significant as is illustrated by the estimate of N ( 80 se) based
r
on a capture cross section of only 20 mb instead of the 47 mb
84
from our calculation. Also the
Kr-value is difficult to move
downwards. A reduction of the Kr-abundance would not help because
83
then the
Kr value would go down, too. In addition, the
discrepancy of the present oN-values for 8 °Kr and 80 se would be
increased. In view of the unsatisfactory situation with many of
the involved cross sections, better experimental data have to be
awaited for a thorough discussion of these problems.
- 30
5.5
-
The s-process temperature
With the numerical data presented above the branching ratio
79
Bß- at
Se can be determined:
(i)
BüKr, B2 Kr:
From the experimental cross sections and the
the accurately known isotopic abundances one finds
R
ONs(BüKr)
(B 2 ) = ü.59 + 0.04
s
Kr
= aN
(30)
The quoted uncertainty of 7 % is somewhat smaller than one
would expect from the cross sections listed in Table 3.
But for R only the cross section ratio is needed which
means that part of the systematic uncertainties
(e.g. due
to the gold standard cross section and most of the multiple
scattering and self shielding correction) cancel out. The
uncertainty in the isotopic
ratio was neglected. Inserting
R into eqs. 20, 21 yields the branching ratio Bß- = 0.50.
It is interesting to note that the uncertainty of Bß- is dominated by that from the cross section ratio of BOKr and
2
B Kr. All other cross sections do not affect Bß- significantly. If, for instance, the calculated value of 47 mb for the
cross section of Büse is reduced by its likely uncertainty
of 3ü %, Bß- is changed only by 3 %. The effect of the additional branching at BüBr is even smaller. If the electron
capture branch is completely neglected at this point, Bßis not changed by more than 1 %. The systematic urcertainty
introduced by the model in splitting oN into two components
is also not severe. From the work of Käppeler et al.
(19B2)
one may assume an uncertainty of 35 % for the quoted
ratio 33/67 for the two fluence components at A
=
7B.
Changing this ratio to 21/9ü results in Bß = ü.52. Therefore,
the branching ratio at 79 se as deduced from the oN-values
of BüKr and B2 Kr is
Bß- = 0.50 + ü.ü5
( 31 )
with a conservatively estimated uncertainty of 1ü %.
· th'1s d e t erm1nat1on
·
·
(1.1.) 7 Bse, Büse.· The two camp 1'1ca t'1ons 1n
of
Bß- (correction for r-process contributions and poor
cross section information) do not allow for a meaningful
analysis. If one starts from aN ( 7 Bse) = 693 mb (Käppeler
s
- 31
78
et al. 1982) one gets N ( se) = 7.7 and N
s
r
The r-process abundance can be interpolated:
Nr(
80
se)
=
1/2 (Nr(
78
se) + N°(
82
se))
=
= 6. 9.
7.2
(32)
which leads to
= 23.7.
( 3 3)
With these s-process abundances and the calculated cross
80
78
sections one finds that aN ( se)>oN ( se). A solution of
s
s
this dilernma would require a drastic reduction of the cross
80
section ratio o( se)/o( 78 se). Therefore, an accurate measurement of this ratio needs tobe carried out. However, even
then the r-process subtraction might be too uncertain to
derive Bß- sufficiently reliable, so that, in turn, Bßcould be used to fix N (SOS ) .
r
(iii)
8
°Kr 1
e
80 se: Evaluation of equation (24) shows that this combi-
nation is also not suited for a determination of Bß-. An
additional uncertainty due to the elemental abundance ratio
krypton/selenium is added to the problems discussed under
80
(ii) for
se. Similar to the case above, comparison of
. ld an accura t e va l ue f or
ON( SOKr) and oN( 80 se) may no-t y1e
Bß-, but in turn, Bß- may be used to estimate the ratio
0
.
80
80
N0 /N'
The compar1son of
Kr and
Se tenas to underKr
Se.
estimate Bß-, probably because the calculated cross section
80
of 80 se is too high; but it seems that Variation (f o( se)
alone does not solve the problem.
In summary, we adopt
( 34)
Bß = 0.50 + 0.05
as the present best value for the branching ratio at
In order to derive the effective ß-decay rate of
79
se.
79
Se under
s-process conditions from this result, we have to evaluate the
neutron capture rate A
n
=
nn ovT and that means we havc to find
the neutron density nn. It has been attempted repeatedly to
32 -
determine this parameter from other s-process branchings. In
principle there are at least two such branchings which do not
185
85
depend on temperature for T<5x10 8 K ( Kr,
w) and some others
·
t
l
wh ere th e tempera t ure e ff ec t lS no very arge ( 151 S m, 17 OT m,
204
Tl). Up to now, the problern has always been that there was
not enough accurate information on cross sections and/or decay
schemes to allow for an accurate analysis. We do not want to
digress deeply in a comparison of the existing work on the sprocess neutron density, which we have listed partly in Table
14. However, some comments might be in order to explain our
adopted value for nn. Although the result of Käppeler et al.
85
(1982) from analysis of the
Kr branching was reduced by a
86
factor 2 (due to a new
Kr cross section and the new isomeric
85
ratio in
Kr) this value appears too high compared to the
other data in Table 14.
Käppeler et al.
(1982) note that their
analysis could not solve for a severe overproduction either
86
87
86
87
of
Kr and
Rb or of
Se and
Sr dependent on how they normalize their analysis. Therefore their value (based on the
oN-product of s-only 86 sr) should not be taken as final and
one should keep in mind that it could also be 6x10 7 cm- 3 if
85
86
the
Kr normalization would have been used; the
Kr-branching
was therefore not considered in our estimate of the neutron
density. The numbers quoted from the 151 sm branching are taken
from a recent study of Beer et al.
(1983). This work comprises
a careful investigation of the temperature dependence of all
involved beta decay rates. The 170 Tm result is taken from Beer
et al. (1981). The problern with this branching and that at
185
w is that in both cases the neutron capture probability is
very low. For that reason it is very difficult to perform a reliable analysis.
In addition, all three branchings contain
only one s-only isotope and must therefore be normalized to the
oN-curve which is most crucial when the neutron capture part
of the branching is weak.
In
we are left with two sets of values for the
8
7
-3
neutron density which group around 5x10 and 5x10 cm . Recent
precise cross section measurements for 148 , 150 sm (Winters et al.
su~mary,
1983) indicate, however, that the oN-curve in the mass region
A>140 has tobe raised by ~ 25 % which implies that the neutron
33 .
d ensities derived from the branch1ngs
at 170 Tm, 185 W and 204 Tl
have to be increased significantly. For this reason we favour
the larger values of the neutron density and adopt nn = 3+2x108 cm- 3
as a reasonable estimate.
The effective beta decay rate of 79 se can now be calculated
A.
n
B
1-B
---- =
-1
0.5 + 0.4 yr
_
=1.4+-0.6
yr {3 6)
5 6
and with this result only a lower limit of ~ 3 x 108K for the
Th is leads to an associated half life of t
112
mean s-process temperature can be read from Fig. 17.
The main uncertainties of this estimate are of different
nature:
(i)
The nuclear physics aspects comprise the unknown beta decay
79
rate from the isomeric state in
se and the poorly known
capture cross sections which are needed to improve the value
for the neutron density. Any further improvement of the
situation can be achieved only with better nuclear physics
data.
(ii) The assumption that s-process nucleosynthesis can be described by the simple model used and especially by assuming
that the two fluence terms are characterized by the same
neutron density and temperature. In order to investigate
this quantitatively, more reliable analyses in the mass
region A>100 are needed to define the conditions for the
second irradiation term of equation (17).
8
Although we find a lower limit of 3 x 10 K for the mean
s-process temperature, our result is not conclusive with respect to the question whether the 22 Ne (a,n) or the 13 c(a,n)reaction was the neutron source of the s-process. These neutron
sources are believed to operate at significantly different temperatures (kT>25 keV and kT>10-15 keV, respectively). We feel
that the present uncertainties need to be reduced considerably
for a detailed discussion (possible differences in T and n
the two fluence components, pulsed scenarios).
n
for
-
6.
34 -
CONCLUSIONS
For the first time the neutron capture cross sections of
the stable krypton isotopes 78,80,82,83,84 and of elemental
krypton were measured between 3 and 250 keV neutron energy.
The experimental uncertainties of the Maxwellian average cross
sections for kT
=
30 keV are typically 5 - 12 %.
The measurements were supplemented by detailed cross section
calculations using the Hauser-Feshbach model. These calculations were carried out with consistent sets of model parameters
which were evaluated using as much experimental information as
possible.
Together with the decay parameters of 79 se and 80 Br these data
were used for a study of the s-process flow through the mass
79
region 78<A<84 with special emphasis on the branching at
se.
82
Normalization of the oN-value of
Kr to the aN-curve of
Käppeler et al.
0
(1982) yields a krypton abundance of N
(Kr)=57~15
which is in fair agreement with recent abundance compilations
(Cameron 1981, Anders and Ebihara 1982). The new cross sections
allowed also for a decomposition of the observed abundances into
their s- and r-process contributions.
The s-process branching at 79 se is characterized by a very
steep temperature dependence and can therefore be used to
estimate the actual s-process temperature. It was found that in spite of the new cross sections - a reliable interpretation
is not possible unless more quantitative information is avail79
able for the beta decay branch of the isomeric state in
se.
Nevertheless, the present estimate tends to confirm the
8
commonly assumed s-process temperature of ~ 3 x 10 K.
- 35 -
Table
Isotopic composition of the samples
Sample
Enrichment (%)
in
----------------------------------------------------------"Kr-78"
8.8
34.8
34.8
"Kr-80"
4•1
93.8
2. 1
"Kr-82"
0.2
20.2
"Kr-83"
9.5
11 . 8
75.6
3.8
0.2
16.0
71.4
1 2. 6
"Kr-84"
100.0
"Kr-nat"
Table 2
0.3
0.35
2.25
11.6
11 . 5
57.0
17. 3
Parameters of the neutron source and the
accelerator
Neutron producing reaction
7 Li(p,n) 7 Be
reaction threshold energy
1.881 MeV
neutron spectrum
4 < En < 250 keV, continuous
proton energy
2.025 MeV
accelerator repetition rate
1 MHZ
typical beam current
7
~A
pulse width
<
1 ns
long term machine stability .
< 10- 3
Table 3
Maxwellian average cross sections of the measured
Kr-isotopes as a function of kT (Reference Au
cross section is ENDF/B-IV)
<av>/vT(mb)
kT
=
20 keV
25
30
35
40
45
50
78Kr
386+47
370+45
359+44
-
338+41
326+40
-
315+38
-
306+37
80Kr
317+16
-
288+15
265+13
248+13
234+12
223+11
213+11
82Kr
1 03+ 7
94+ 7
87+ 6
82+ 6
78+ 6
-
-
-
-
-
-
75+5
-
83Kr
334+20
287+17
250+15
-
228+14
209+12
194+11
84Kr
49.5+5.7
42.2+4.8
37.3+4.3
33.7+3.9
31.1+3.6
29.1+3.3
natKr
81+ 5
-
70+ 4
-
63+ 4
-
-
58+3.5
54+ 3
51+ 3
72+ 5
-
182+11
27.5+3.1
48+ 3
w
"'
I
37-
Table 4
Sources and magnitudes of the experimental
uncertainties
(%).
Uncertainty originating
Rel. contribution to the
from
uncertainty in <ov>/vT
Au standard
3
gamma-ray self-absorption in the sample
1
neutron scattering and selfabsorption in the sample
2
pile-up correction
1
lower threshold correction
0.5
sample mass determination
1-2
time dependent background
subtraction
1-2
weighting function
0.5-1
effective neutron binding energy
2-3
isotopic impurities
2-10
statistics
2-3
Total
5 -
12
Table
Comparison of s- and p-wave strength functions and scattering radii as
5
calculated with our OMP sets to the respective values taken from
systematics or from experiment (Mughabghah and Garher 1973)
Mughahghah and Garher (1973)
Systematics
Target
Isotope
s0
X
10
4
s1
x 10
This work
Exp.
4
R{fm)
S
0
10
X
4
s0
X
10
4
s1
x 10
4
R(fm)
----------------------------------------------------------------------------------------------76Se
1. 6
2.2
6.8
78Se
1.5
2.6
6.8
79Se
1.4
2.8
6.8
80Se
1 . 35
3.0
7.0
1.7 + .7
1.2 + .3
1.6 + .6
1.5
2.2
7. 1
1.4
2.5
7.1
1 . 35
2.65
7.0
1.3
2.85
7.0
w
(J)
79Br
1.4
2.8
6.8
1.2 + .18
81Br
1.3
3.2
6.8
1.2 -+ .18
78Kr
1. 5
2.6
79Kr
1. 4
80Kr
+)
1.3
2.9
6.9
1.2
3.4
6.85
6.8
1.4
2.5
7.05
2.8
6.8
1 . 35
2.6
7.0
1 . 35
3.0
7.0
1.3
2.85
7.0
81Kr
1.3
3.2
7.0
1.3
3. 1
6.95
82Kr
1. 2
3.4
7.0
1 . 25
3.3
6.9
83Kr
1.15
3.6
7.0
1.2
3.55
6.9
84Kr
1•1
3.8
7.0
1.2
3.8
6.85
+)
values deduced from an elemental sample
-
+)
I
Table
Evaluation of the level density parameter ~ from experimental data
6
(average capture cross sections or neutron resonance schemes}
RES
Exp *)
rt =0 #
Da
aa
DRES §
NRES
a
n,y
y
OBS
OBS
_____________ i~L ____________ i~§YL __________ i§YL ______ i~§Y=~L ____ i§YL _____________ i~§Y=~L _____ _
Target
Isotope
0
74Se
500+250
6
13.6.::_~:j
76Se
760+300
13
14.2.::_~:~
77Se
136+30
23
13.0.::_~:~
78Se
1700+500
13
13.7.::_~:~
80Se
3500+2000
10
1 3.
-
1.::_~: ~
w
\!)
79Br
57+23
78Kr
357+44
230++50+
225+90
80Kr
257+15
290+30
460+90
-
13.9.::_~:~
13.6.::_~:j
1300+400
12.8.::_~:~
82
Kr
-
84+6
-
230++50+
83Kr
251+16
215+50
84Kr
36.5+4.5
215++50+
*This work, # Maguire et al.
+ Assumed value
(1978),
§
95+25
11. 5.::_~: ~
4000+1600
11.6.::_~:~
Mughabghab and Garber (1973),
6
13.0.::_~:~
Table
7
40 -
Adopted level schernes of
79
se up to
the excitation energy Ecut for calculating the
isorneric ratio IR*
Level
Nurnber
Energy
(MeV)
Spin
Parity
Branching ratio
(Level nurnber, probability in %)
--------------------------------------------------------------------79Se
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0.0
0.096
0.130
0.365
0.499
0.528
0.572
0.620
0.729
0.790
0.819
0.897
0.974
0.982
1 . 00
1.06
1 • 0 71
1.079
3.5
0.5
4.5
2.5
1.5
0.5
2.5
2.5
2.5
4.5
3.5
5.5
1.5
1.5
5.5
3.5
6.5
1.5
+
( +)
(+)
(-)
+
+
+
+
+
+
+
+
(Isomerie state)
(1,100)
(1,100)
(2,100)
(2,100)
(2,100)
(1 ,34) (3 ,~) (4,33)
(1 ,100)
(1 ,50) (3,30) (4 ,20)
(1 ,20) (3,80)
( 1, 10) ( 3, 90)
(2,80) ( 4 , 15) ( 5 , 5)
(1,100)
(1,Tö) (3,90)
( 1, 20) (3,30) (_1,,50)
( 12-;1"00)
(4;100)
--------------------------------------------------------------------*
The Jn values between brackets and underlined garnrna decay
probabilities have been assigned as described in the text.
-41-
Table 8
Comparison between calculated and eKperimental results for the average radiative width*
Target Isotope
76Se
78se
79Se
80se
79Br
81Br
78Kr
79Kr
80Kr
81Kr
82Kr
83Kr
84Kr
~
=0
~
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
230 .:!:. 50 ( 1 /2+, 5)
254
230 -+ 55 ( 1 /2+, 4)
243
124(4+)
132 (3+)
230 -+ 100 (1/2+ ,2)
236
Experimental
Calculated
Experimental
Calculated
360 .:!:. 40 ( 1-, 2)
362
278 .:!:. 50 ( 1 , 1)
272
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
242 ( 1 /2+)
315.:!:_50(2 - ,3)
314
275.:!:_45(2 , 1)
247
-)
230 ( 1 /2-)
217 (3/2-)
223 ( 1/2
210 (3/2
334 (2-)
303 (3-)
236 ( 1/2
200 (3/2-
287 (0+)
368 ( 1 +)
320 (2+) 266 (3+)
278 (0+)
272 ( 1 +)
247(2+) 218 (3+)
231 ( 1/2
220 (3/2
266 (0+)
262 ( 1 +)
249 ( 1/2
234 ( 3/2
233(4
199(5-)
253 (2+)
266 (0-)
290 .:!:. 30+ (?, 1)
260 ( 1/2 )
296 ( 1
226 (3+)
242 ( 1 /2+)
105 (4 +)
259 (2-)
187 ( 1 /2-)
241 (3-) 208(4-) 185(5-)
184(3/2-)
179 (5+)
285 (3-)
215 (4
242 ( 1 /2-)
239 (3/2-)
215 + ~0 (?, 2)
211 (4 )
266 ( 1 /2+)
-)
194 <5
* The respective Jn values and the nurober of resonances taken for averaging are given
in parenthesis. Experimental values are from Table 4.2 or from Mughabghab and Garber (1973) ·
§ Average experimental values for ry cannot be quoted in this context due to
fluctuations;
the calculated values represent only the contributionfrom statistical capture.
159(6-
Table 9
Target
Isotope
The final parameter set used for the cross section calculations
uX
E
a
(MeV- 1 )
(MeV)
76
78Se
79Se
80Se
Se
13.9*
13.7
12.9
13.0*
7.3
6.8
6.3
5.8
.581
1.079
2.090
1. 21 0
79
81Br
Br
13.0
12.4*
7.1
6.0
.400
. 100
78
79Kr
80Kr
81Kr
82Kr
83Kr
84Kr
.Kr
13.9
13.0*
13.6
1.2.8*
12.8
11.5
11.3*
7.4
7.0
7.0
6.5
5.9
5.2
4.5
.907
1.600
.300
1. 885
1. 099
3.300
2.160
*
§
cut
MeV
0
2
LVL
ß
5.5
4.9 §
2.6,6.3
2.7
2.2
4.0
§
6.1,12.2
10.0
590
5.5 ,16.0
7.0
6.3
§
4.3, 9.0
E1
MeV
r1
MeV
mb
E2
MeV
01
r2
MeV
02
mb
.32
.25
.21
. 17
14.85
14.8
14.35
15.8
3.45
3.45
3.3
3.65
75
78
80
74
17.6
17.5
17.6
17.15
4.85
4.8
4.85
4.7
103
106
107
111
.25
. 17
14.2
14.7
3.3
3.4
82
81
17.6
17.4
4.85
4.75
107
.32
.29
.25
. 21
. 17
. 13
. 10
14.8
14.7
14.7
15.2
15.7
15.6
15.6
3.4
3.4
3.4
3.5
3.6
3.6
3.6
78
79
80
78
77
78
79
17.5
17.5
17.4
17.2
1 7. 1
17.0
17.0
4.8
4.8
4.8
4.7
4.7
4.7
4.6
106
108
110
112
114
116
118
Value adopted from systcmatics of Fig.12
Value adopted as being mostplausible according to Fig.13.
111
"""
rv
Table
10
Calculated neutron capture cross sections between 1 and 1000 keV
Neutron
Energy
(keV)
76Se
1
5
10
15
20
1100
390
273
220
188
643
254
173
136
25
30
35
40
60
78Se
79Se
80Se
79Br
CaEture Cross Section (rnb)
81Br
78Kr 79Kr 80Kr
81Kr
82Kr
83Kr
84Kr
-----------------------------------------------------------------------------------------------
80
100
150
200
400
600
800
1000
11 3
2800
760
470
350
290
362
149
95
72
59
5510
1770
1180
960
830
2850
950
650
510
430
2710
878
618
514
450
6640
2150
1440
1170
1025
1696
607
435
356
307
5900
1930
1300
1050
910
766
301
200
155
128
2570
880
560
414
332
335
135
84
62
51
165
149
164
127
103
98
88
80
74
61
250
218
196
180
139
51
45.5
41.5
38.4
31.5
740
672
620
576
461
375
333
301
275
211
406
372
345
323
265
927
855
800
755
630
272
245
225
209
167
810
738
679
6 31
459
110
98
88
81
65
278
241
213
192
140
43
38
35
32
27
92
85
75
69
61
54
50
43
39.5
35.5
117
103
66
50
28
27.8
25.2
21.4
19.4
17. 4
392
347
283
249
92
176
154
124
108
61
232
212
1 86
174
160
550
500
410
290
121
146
133
116
108
98
360
300
223
185
113
58
54
47.5
44
41
11 3
97
74
63
46
23
21
18
16. 7
15.2
41
28.6
26.5
36.6
16.4
14.5
20
17
12
17.6
8.0
6.6
56
42
32
39
27
22.5
94
81
80
71
47
36
103
56
55.6
50.2
43
35.3
21.5
42
39.5
37.8
1 5. 1
15. 8
8.6
*""
w
- 44 -
Maxwellian average capture cross sections
for kT = 30 keV: comparison of present theoretical
Table 11
and experimental values with previous results
Target
Isotope
<a>30 keV
Holmes
et al.
(1976)
Leugers
et al.
(1979)
This work
Prince
Harris
(1979)
( 1 981)
Exp.
Calc.
----------------------------------------------------------------------76Se
149
83
138
78Se
49
80
79Se
260
274
514
80Se
41
41
34
47
79Br
520
661
749
657
81Br
460
360
596
322
78Kr
203
284
253
1130
368
857
359 + 44
79Kr
80Kr
148
228
156
242
265
81Kr
1030
800
994
682
82Kr
122
95
77
79
100
83Kr
571
345
295
259
237
84Kr
25
30
29
13
40
126
89.5
185
90+18
218+50
Additional experimental cross sections <o> 30 keV (mb):
80
79
81
se
35 + 5
Br 800 + 150
Br 360 + 70
compilation by Benz i et al.
( 19 7~:)
+ 13
87 -+ 6
350 -+ 16
37.3 + 4 .3
-
Table
45 -
Parameters for the decay of 79 se under s-process
12
conditions
Level
Isotope
J
79Se
1T
+)
lg ft
,Energy(keV)
7/2+
1/2
5/2
,
0
'
96
5.4 (0.5)
6.0x10
I
130
5.4 (0.6)
2.1
I
365
5.4(0.6)
2.7x10
-
9/2+
§)
Tß-(yr)
-
1 0. 17
6.5x1o
4
\~
§)
(yr -1 )
l
l
1 • 4x 1 0
-2
-2
P.
-5
\.(yr-1)
l
-5
1 . 3x 1 0
15.3
1 . 5x 1 0
0.75
9.5x10
26.5
9.7x10
-1
-3
-5
*
t1/2=4.3 yr
79Br
9/2+
,
207
5.4(1.1)
9.4
2.1x10
-2
5.3x10
-5
*
4
t1/2=1.3x1o yr
+
estimates from Conrad (1976)
§ stellar rates from Conrad
(1976)
including effects
due to almost complete ionization (bound state
beta decay, modification of electron capture etc.)
- 46 -
Table 13
Decomposition of isotopic abundances into s- and
r-process contributions (p-process neglected)
Isotope
76Se
+
Nr/ 0
oN s
N
845
1.72+0.44
N
s
6.79+0.75
5.1+1.4
75
9.20+0.86
9.2+0.9
100
0
783
5.25+2.1
5.59+0.36
Se
767
1.81+0.92
4.72+0.30
2.9+1.0
62
78Se
693
7.70+1.9
14. 6 +0.93
6.9+2.1
47
79Se
332
80Se
289
23.7+3.2
76
5.70+0.36
5.7+0.4
100
*77
(%)
decayed to 79Br
6.14+2.46
30.9+1.98
82Se
79Br
341
2.04+0.52
5.98+1.14
3.9+1.3
66
81Br
281
2.22+0.72
5.82+1.10
4.5+1.7
77
80Kr
329
1.28+0.33
1.28+0.14 #
81Kr
325
82Kr
555
6.61+1.72
6.61+0.73 #
83Kr
540
2.15+0.56
6.56+1.04
84Kr
450
0
decayed to 81Kr
12.3 + 3. 2
#
32.5 +5.1#
=
+
Calculated from oN(78 e)
8
(Käppeler et al.,1982)
§
Anders and Ebihara (1982)
*
o taken from Woosley et al.
#
this work
0
4.4+2.1
67
20.2+5.7
61
2
1
oN (78 8 e) + oN (78 8 e)
(1978)
=
(276 + 416) mb
Table 14
Estimates for the neutron density during the s-process
Brauehing
temperature
point
dependent
(in units of
10 7. cm -3 )
Ref
Bß-
Problems
nn
85Kr
no
0.5
(30 - 200)
(1)
.
86
87
overprocudt1on of
Kr and
Rb,
therefore n
151Sm
yes
'V
20 - 100
0.01
(2)
154
n
possibly too high
Gd cross section needs confir-
mation, temperature effects
170Tm
yes
'V
0.9
185w
no
'V
0.95
1 -
4
20 - 60
(3)
B - very large
8
uncertainty
( 4)
same as for 170 Tm, but no tempera-
+
systematic
ture dependence
204Tl
References:
no
1 - 8
0.8
(1) Käppeler et al.
(1982),
(4) Käppeler (1983)
,
( 5)
(2) Beer et al.
(5)
(1983),
lead abundance uncertain
(3) Beer et al.
Macklin and Winters {1976)
(1981),
*'--l"
n- monitor
~~
~~
~//
~
6~~~
poroffin
~
~
ffi
//
7.
/
/ //> . / /
/
/
////
~/
////.//
///
/,// /
/
/
~
*"'
CO
Fig.
1
Schematic experimental set-up
NEUTRON
MONITOR
C6 06 -SCINTILLATORS
(6Li -GLASS)
Gate
Generator
0
~
-o
STOP
Gate
Generator
~
1..0
biti0-10
bit 111-11.
bit 10-10
bit 10-10
Digital
Coincidence 1----------------r
16
X
102!.
X
2 eh_
NOVA- Computer
Fig. 2
Block diagram of the electronics and the data acquisition
system
1021. eh_
- 50 -
'&'-peak
2
empty
2
-
lO
0
..--
~
V)
1-
00
150
300
450
600
750
--9oo
300
450
600
750
900
750
c
::>
u
300
4.5
z
0
150
3.0
1.5
00
4.5
Au
3.0
1.5
00
150
TIME-OF-FLIGHT (0.87ns/channel)
Fig. 3
Summed TOF-spectra (without corrections)
- 51 -
~
z
:J
81
--·--.-
150
3
300
450
(Au -empty)
2
TIME-OF-FLIGHT (0.87ns/channel)
Fig.
4
TOF-spectra after subtraction of the
spcctrum for thc cmpty canning
900
~_____j_J
- 52 -
~-peak
Au
3
2
1
--.
Lf)
0
~
-
00
X
150
300
450
600
750
900
150
300
450
600
750
900
U)
I-
z
~
0
so Kr
3
(_)
2
1
0
0
TIME-OF-FLIGHT (0.87ns/channel)
Fig. 5
Final TOF spectra corrected for neutron scattering
2400-.-------------------------,
2000
Kr-not
1600
E
1200
0
..0
E
0
Ul
w
800
400
-400
3
10
100
NEUTRON ENERGY (keV)
Fig. 6
Capture cross section for natural krypton
4000
3200
Kr-84
U1
.t:.
-
x20
0
-800
-1
3
10
100
NEUTRON ENERGY (keV)
Fig. 7
Capture cross section for 84 Kr
1250r---
1000
aoKr{n,y) 81Kr
l
750
1t
:a
E
l
Osoo
f
-
11
111) \
1
1
11
:1
I
,
I\ 1~
11 I
1
:1~ 1 t~l ~
I
I li :.
I lli
'I' r
II
III
1
.t j II
il
250
t
11
I#
I
1111! II
1111
I trI
Vt 11~ ~
!
1~ ,tv.~ I~
I II I I\
t I 11
I
~ ~ .,.-~'. :.,.,.,. _~ '·"··-*·. ~
I.
U1
U1
-'/~ ..
I
.,
..
..•
llllltl"''i'""''"''''"•!tr!
•
,
1\]11
I
3
I' I 111!
llllTITT 1 '
I
10
100
NEUTRON
Fig. 8
Capture cross section for
8
°Kr
ENERGY {keV)
300
" Kr-78"
x10
cI....
_g
U1
E
-
"'
0
100
NEUTRON ENERGY (keV)
Fig. 9
Capture cross section for the mixture enriched in 78,80Kr
II
Kr-82
IJ
1600
cL..
.8
I
E
llllniii!AIAIU
Ul
-....]
/II
0
-800
-12
3
100
10
NEUTRON ENERGY (keV}
Fig.
10
Capture cross section for the rnixture enriched in
82
Kr
"Kr-83"
c
_g'-
U1
CO
E
0
NEUTRON
Fig.
11
ENERGY (keV)
Capture cross section for the rnixture enriched in 83Kr
-
59 -
o• Kr(even,odd)
o
Se (even , odd )
A Br(odd)
111
o~-.-.~~--~~~~~~_J
40
45
50
NEUTRON NUMBER
F ig. 12
Level density parameter -a, matehing energy UX
and deformation parameter ß as a function
of neutron nurober in the investigated compound
nuclei. While
~
shows a significant odd-even
effect this trend does not reproduce for Ux and ß.
60 -
79Se
sose
U)
--_j
w
w
_j
10
lL
0
0:::
w
Cl)
'() 12
2:
8
2
::)
z
w
>
~
_j
10 12
4
2
81Kr
82Kr
::)
2
::)
u
10
10
4
-
3
~ 2
/
/
...\
1
0
o
0.5
1.5
2
4
8
10
2
12
4
EXCITATION ENERGY (MeV)
F ig.
13
Comparison between the calculated cumulative
nurober of levels (solid line) and
known discrete
levels forsome compound nuclei. The energy E
CU
t
where the level continuum was supposed to
start is marked by an arrow. In
the respective
inserts the theoretical spin distribution
(dashed line) and the spin distribution of
discrete levels below E
is given.
cut
-
61
-
-
. .0
E
>w1000~--~~~~--~--~--~----.---.
'
~
0
(V)
II
~
~
1./)
z
0
t;
w
1./)
~ 100
er::
0
u
w
er::
::>
b::
()
z
0
0:::
r::>
w
z
0
w
10
~
er::
w
111
Se( even, odd)
...
z
0
<(
~
Kr (even,odd)
[J
~
:J
w
oe
43
Br ( odd)
As(odd)
45
47
49
NEUTRON NUMBER
<(
::E
F
ig. 14
Experimental and calculated Maxwellian averaged
capture cross sections for kT=30 keV versus
neutron nurnber in the compound nuclei.
The experimental points are plotted with error bars.
75
For
As the calculated value of Benzi et al. (1973)
was adopted.
-
62 -
r------------------
Kr
Br
Se
Fig.
15
The s-process flow throuqh the mass reqion 78<~<84.
Branching points are shaded and s-only isotopes
are marked by double boxes.
500
E (keV)
100
159; 10.1
3;2-~--
Fig.
16
0
79
Level schemes of
se and 79 Br with the possible links
in a hot environment. The by far most important decay
of the 96 keV isomer in 79se is indicated by the white
arrow. The numbers correlated with the links designate
Q- and log ft-values of the transitions.
-
63 -
10 3
I
-;: 10 2
w
LL
_j
LL
_j
<(
10
I
w
>
.......
u
w
LL
LL
1
w
10-1-+---r----.---.--..----.---.-----r--r--.,--0
5
ID
TEMPERATURE (10 8 K) _....,.,
Fig.
17
79
Effective half life of
se as a function of ternperature.
The solid black line represents the result of this work.
The dashed lines indicate the range of uncertainty
which results frorn the 10 % uncertainty of the log ftvalue for the decay frorn the 96 keV state. For cornparison the results of Newrnan (1973) and Cosner and Truran
(1981) are shown (thin solid line) who neglected ,the.
effect of ionisation.
- 64 -
100
I
I
oe
IJ
-
I
Br
x
Ge
Q
As
(47mb)\'
•••/
0
z
'-
··.;;::_120mb)
.
(!)
tf)
-
-
-
111
r
I
Kr (even, odd)
Se (even,odd l
1111
Ä
30 -
I
I
*
.·
: · · · · · i./
10 -
~
.••
••
\•
•
.}
..
.··
\ .·
3 -
....... _
I
75
I
--
I
I
I
I
I
I
80
MASS NUMBER
Fig.
18
-
-
-
"
I
T
•
CD
z
~
••
The r-process abundances in the rnass region
78<A<84 as deduced frorn aN systernatics.
- 65 REFERENCES
Almeida, J. 1982, KfK-Report 3347, Kernforschungszentrum Karlsruhe
Almeida, J., and Käppeler, F. 1983, Ap. J., 265, 417
Anders, E., and Ebihara, M. 1982, Geochim. Cosmochim. Acta,
!§_, 2363
Beer, H., Käppeler, F., Wisshak, K., and Ward, R.A. 1981, Ap. J.
Suppl . .!§_, 295
Beer, H., and Käppeler, F.1982, "Neutron-Capture Gamma-Ray
Spectroscopy and Related Topics 1981", The Institute of Physics,
Bristol and London, Conference Series nurober 62, p. 558
Beer, H., Käppeler, F., Takahaski, K., and Yokoi, K. 1983,
submitted to Ap. J.
Benzi, V., D'Orazi, R., and Reffo, G. 1973, Nuovo Cimento, 13B, 226
Cameron, A.G.W. 1981, in "Essays in Nuclear Astrophysics",
ed. C.A. Barnes, D.D. Clayton, and D.N. Schramm, Cambridge
University Press, Carnbridge, p. 23
Clayton, D.D., Fowler, W.A., Hull, and Zimmermann, B.A. 1961,
Ann. Phys.
~'
331
Clayton, D.D. 1968, in "Principles of Stellar Evolution
and Nucleosynthesis", McGraw-Hill, New York, p.552
Conradi J.H. 1976, Ph.D. thesis, University of Heidelberg
Cosner, K., and Truran, J.W. 1981, Astrophys. Space
Fuller, G.H., and Cohen,
v.w.
Sei,~'
85
1969, Nuclear Data Tables, A5, 433
Fröhner, F.H. 1968, Report GA-8380, Gulf General Atomic
Garber, D. 1975, ENDF/B-IV, Report BNL-17541
(ENDF-201) Brookhaven
National Labaratory
Gilbert, A., and Cameron, A.G.W 1965, Can.J.Phys. j]_, 1446
Harris, M.J. 1981, Space Sei. Rev., 77, 357
Hensley, F. 1980, KfK-Report 2918, Kernforschungszentrum Karlsruhe
Holmes, J.A., Woosley, S.E., Fowler, W.A., and Zimmerman, B.A. 1976,
Atomic Data and Nuclear Data Tables,
~,
305
- 66 -
Käppeler, F., Beer, H., Wisshak, K., Clayton, D.D., Macklin, R.L.,
and Ward, R.A. 1982, Ap.J., 257, 821
Käppeler, F. 1983, unpublished
Lederer, C.A., and Shirley, V.S. 1978, "Table of Isotopes",
John Wiley & Sons, New York
Leugers, B. 1979, KfK-Report 2895, Kernforschungszentrum Karlsruhe
Leugers, B., Käppeler, F. Reffo, G., and Fabbri, F. 1979,
"Nuclear Reaction Mechanisms", CLUED, Milano, p. 309
Macklin, R.L., and Gibbons, J.H. 1967, Phys.Rev., 159, 1007
Macklin, R.L., Halperin, J., and Winters, R.R., 1975, Phys. Rev.
C11, 1270
Macklin, R.L., and Winters, R.R. 1976, Ap.J. 208, 812
Macklin, R.L. 1982 (private communication)
Maguire, H.T. Jr., Fisher, H.M., and Block, R.C. 1978, "Neutron
Physics and Nuclear Data for Reactors and other Applied Purposes",
OECD/NEA, Paris, p. 472
Marti, K., Wilkening, L., and Suess, H.E. 1982, Ap. J., 173, 445
Mughabghab, S.F., and Garber, D.I. 1973, "Neutron Cross Section,
Resonance Parameters", BNL-Report 325
3rd ed., Vol. 1, Brookhaven
National Laboratory
Mughabghab, S.F., Divadeenam, M., and Holden, N.B. 1981,
"Neut~on
Cross Sections", Vol. 1, Academic Press, New York
Newman, M.
(1973), M.S. thesis, Rice University, Heuston
Palme, H., Suess, H.E., and Zeh, H.D. 1981, in "Landolt-Börnstein",
New Series VI/2, chaps. 3,4
Perey, F.G., and Buck, B. 1962, Nucl.Phys. 32, 353
Prince, A. 1979, BNL-Report NCS-51028, Brookhaven National
Laboratory, Upton, New York
Rau, F. 1963, Nukleonik,
~,
191
Reffo, G. 1980a, IAEA Report SMR-43, p.205 Int. Atomic Energy
Agency, Vienna and CNEN-Report RT/FI (78)11, Comitato per l'Energia
Nucleare, Bologna
- 67 -
Reffo, G. 1980b, in "Theory and Applications of Moment Methods
in Many Fermion Systems", B.J. Dalton et al. Eds. Plenum Press,
New York
Reffo, G., and Fabbri, F. 1981, unpublished
Reffo, G., Fabbri, F., Wisshak, K., and Käppeler, F. 1982,
Nucl. Sei. Eng., 80, 630
Stelson, P.H., and Grodzins, L. 1965, Nucl. Data A,
l,
21
Walter, G., and Beer, H. 1982, KfK-Report 3327, Kernforschungszentrum Karlsruhe
Walter, G., et al., 1983, tobe published
Ward, R.A., Newman, M.J., and Clayton, D.D. 1976, Ap.J.Suppl.
~'
Wilmore, D. and Hodgson, P.E. 1964, Nucl.Phys., 55, 673
Winters, R.R., Käppeler, F., Wisshak, K., Reffo, G. and Mengoni A.
1983, private communication
Wisshak, K., Walter, G., and Käppeler, F. 1983, KfK-Report 3542,
Kernforschungszentrum Karlsruhe and Nucl. Instr. Meth.
(submitted)
Woosley, S.E., Fowler, W.A., Holmes, J.A., and Zimmerman, B.A.
1978, Atomic Data and Nuclear Data Tables, 22, 371.
33
-
Appendix I
Capture cross section of natural krypton as a function
of neutron energy
--------------------------o(mb)
Lw (mb)
---------------------------
E(keV)
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
68 -
268.9
421.0
-62.3
1845.4
383.0
-236.4
555.9
14.8
-22.9
266.2
476.1
137.4
101.6
212.2
75.9
74.9
257.1
94.0
202.4
213.4
201.5
206.4
36.4
95.2
334.4
15 7. 8
149.5
218.3
241.7
12.4
228.0
293.3
105.1
182.4
134.1
231.9
114.1
139.2
98.5
45.2
94.7
78.3
95.0
276.8
385.1
299.8
153.8
483.5
441.5
392.7
353.8
321.6
295.4
274.0
255.7
240.0
226.4
214.5
204.2
195 .1
187.0
179.5
172.9
166.9
161.6
156.5
151.6
147.2
143.2
139.5
135.9
132.4
129.0
125.8
122.9
120.1
117.3
114.5
112.0
109.6
107.1
104.7
102.3
100.1
98.1
96.2
94.0
92.0
90.1
88.1
86.4
84.6
82.9
81.2
--------------------------o(mb)
!J.o(mb)
---------------------------
E(keV)
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
~.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11.3
11.4
11.5
11.6
11. 7
11.8
191.9
227.9
103.0
7.6
133.2
156.9
106.1
133.4
96.5
254.8
258.8
265.8
302.3
259.5
200.5
177.0
125.3
149.2
141.0
108.5
48.6
60.2
4.3
103.3
110.7
149.1
151.3
178.4
133.8
91.2
98.6
116.5
114.9
61.1
100.0
121. 1
135.8
135.9
135.6
142.1
172.9
254.5
276.1
323.3
227.9
192.9
150.4
79.5
78.0
76.5
74.8
73.4
71.9
70.5
69.1
67.7
66.4
65.3
64.1
62.9
61.7
60.6
59.4
58.3
57.1
56.0
55.0
54.1
53.0
52.1
51.2
50.3
49.4
48.5
47.8
47.0
46.1
45.5
44.8
44.0
43.2
42.6
42.0
41.3
40.7
40.1
39.5
39.0
38.4
37.8
37.3
36.7
36.2
35.6
- 69 -
--------------------------L'lo(mb)
o(mb)
---------------------------
E(keV)
11.9
12.0
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14. 1
14.2
14.3
14.4
14.5
14.6
14. 7
14.8
14.9
15.0
15. 1
15.2
15.3
15.4
15.5
15.6
15. 7
15. 8
15.9
16.0
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
127.8
107.7
101.6
119.7
108.3
97.6
98.5
95.9
136.6
128.1
77.7
52.7
68.3
94.8
71.1
77.1
99.2
139.6
129.5
139.4
132.3
88.3
68.8
79.2
102.7
123.8
126.4
137.2
128.2
115.9
146.3
134.1
129.2
88.2
74.1
76.2
70.7
74.5
108.8
65.4
56.8
58.4
104.5
120.4
69.8
47.3
84.5
100.2
125.9
173.8
148.5
35.1
34.7
34.3
33.8
33.3
33.0
32.6
32.1
31.8
31.4
30.9
30.6
30.3
29.9
29.6
29.3
29.0
28.6
28.3
28.0
27.7
27.4
27.2
26.9
26.7
26.5
26.2
25.9
25.8
25.5
25.2
25.1
24.8
24.6
24.4
24.2
24.1
23.9
23.6
23.5
23.3
23.2
23.0
22.8
22.6
22.5
22.4
22.2
22.1
22.0
21.9
--------------------------o(mb)
L'lo(mb)
---------------------------
E(keV)
17.0
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19.0
19.1
19.2
19.3
19.5
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22.0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
134.7
106.2
108.8
137.4
119.1
113.6
89.7
82.8
101.2
91.7
111. 1
91.2
103.7
109.7
75.5
88.8
72.6
84.8
57.8
72.5
83.9
97.3
70.1
63.1
91. 1
110.5
129.3
89.0
82.2
87.4
86.7
80.5
87.0
86.5
69.1
53.9
53.1
73.5
51.9
61.0
76.5
67.6
60.4
70.7
77.7
67.5
65.4
62.6
62.7
65.1
70.5
21.7
21.6
21.5
21.3
21. 1
21.0
20.9
20.8
20.7
20.6
20.5
20.4
20.3
20.2
20.1
20.0
19.9
19.8
19.8
19.7
19.6
19.5
19.4
19.3
19.3
19.2
19. 1
19.0
19.0
18.9
18.8
18.8
18.7
18.6
18.6
18.5
18.5
18.4
18.3
18.3
18.2
18.2
18.1
18.1
18.0
18.0
17.9
17.9
17.8
17.8
17.8
- 70 -
--------------------------o(rnb)
6o(rnb)
---------------------------
E(keV)
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30.4
30.6
30.9
31. 1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
89.5
83.3
78.6
72.4
78.6
75.5
87.8
90.3
76.0
101.8
109.9
91.8
98.0
83.0
76.5
83.9
94.5
74.4
79.9
90.7
92.6
100.6
98.6
83.2
62.0
58.4
50.0
55.8
55.8
47.1
53.8
58.5
66.4
61.3
63.9
63.1
60.9
61.4
60.2
58.1
56.1
62.3
68.1
69.9
66.7
69.9
64.4
60.3
61.0
66.3
61.4
17.7
17.7
17.6
17.6
17.5
17.5
17.5
17.4
17.4
17.4
17.3
17.3
17.2
17.2
17.2
17.1
17.1
17.1
17.0
17.0
16.9
16.9
16.9
16.8
16.8
16.7
16.7
16.6
16.6
16.6
16.5
16.4
16.4
16.3
16.3
16.2
16.1
16.1
16.0
15.9
15.9
15.8
15.7
15.6
15.5
15.4
15.3
15.2
15. 1
15.0
14.8
--------------------------o(mb)
6o(rnb)
---------------------------
E(keV)
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
37.3
37.6
37.9
38.2
38.5
38.9
39.2
39.5
39.9
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
47.7
48.1
48.6
49.0
49.5
50.0
50.4
50.9
57.6
63.3
66.9
71.0
86.3
94.9
87.6
71.0
63.0
56.6
51.3
55.3
51.8
49.4
45.7
41.6
45.2
47.1
44.4
47.5
46.1
45.3
48.1
45.7
43.7
48.2
5 'J. 9
54.7
51.6
48.9
47.5
41.6
49.2
62.2
67.4
67.2
62.8
57.6
50.2
43.4
42.9
44.0
39.9
38.7
43.2
51.5
52.2
53.0
55.3
53.1
52.0
14.7
14.6
14.4
14.3
14.1
14.0
13.8
13.7
13.5
13.3
13.1
12.9
12.7
12.5
12.3
12.0
11.8
11.6
11.3
11. 1
10.8
10.6
10.3
10.0
9.7
9.5
9.3
9.1
8.9
8.7
8.6
8.5
8.4
8.3
8.2
8.2
8.1
8.1
8.0
8.0
8.0
8.0
7.9
7. 9:
7.9'
7.9'
7.9'
7.9
7; 9.
7. 9'
7.9i
-
---------------------------
E(keV)
o(mb)
ßo(mb)
--------------------------51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75.1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
44.7
41.6
41.0
40.7
42.3
41.0
40.7
45.1
46.9
44.7
41.3
36.2
37.4
42.6
46.4
44.4
40.8
39.8
40.0
38.5
40.1
42.0
43.6
40.0
38.1
38.7
39.0
39.6
38.4
37.3
39.6
36.3
34.5
34.7
36.7
39.0
36.8
37.0
39.3
37.9
35.9
36.4
35.7
34.4
30.7
30.2
28.9
31.4
36.6
37.7
36.4
7.9
7.9
7.9
7.8
7.8
7.8
7.8
7.7
7.7
7.7
7.6
7.6
7.5
7.5
7.4
7.3
7.3
7.2
7.~
7.0
6.9
6.8
6.8
6.7
6.6
6.5
6.4
6.3
6.2
6.0
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.·9
4.8
4. 7
4. 7
4.6
4.5
4.4
4.3
4.3
4.2
4.1
71
-
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
114.6
116.3
118.0
119.7
121.4
123.2
125.1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
175.8
179.0
182.2
185.5
188.9
192.5
34.1
33.3
30.0
29.7
30.7
29.9
29.4
29.7
30.9
29.6
30.7
33.2
30.5
28.1
28.0
28.0
27.9
24.9
24.3
26.2
27.1
28.7
28.3
28.7
27.7
24.7
24.7
25.5
25.5
25.9
24.8
23.7
24.2
24.3
24.2
25.9
25.9
25.7
24.1
23.2
23.6
23.3
22.8
22.7
21.9
22.2
22.9
23.4
00
t.. '- •
~
I
20.9
21.5
4.1
4.0
4.0
3.9
3.9
3.8
3.8
3./
3.7
3.7
3.6
3.6
3.6
3.6
3.6
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.4
3.4
3.4
3.4
3.4
3.4
3.3
3.3
3.2
3.2
3.2
3.1
3.0
3.0
2.9
2.8
2.8
2.7
2.6
0
-
~.::>
2.4
,_,_,.
')
I
- 72 -
--------------------------D.cr(mb)
cr(mb)
---------------------------
--------------------------cr(mb)
D.cr(mb)
---------------------------
E(keV)
196.1
199.8
203.6
207.5
211.6
215.7
220.0
224.4
229.0
233.7
238.5
243.5
E(keV)
20.8
20.6
21.9
22.1
21.2
20.4
2.3
2.2
2.2
2.1
2.1
2.1
19.8
19.3
18.6
19.6
18.7
19.8
2.1
2.1
2.1
2.2
2.3
2.5
- 73 -
Appendix II
Capture cross section of Kr-78 as a function
of neutron energy
--------------------------o(mb)
t.o(mb)
---------------------------
E(keV)
10.0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11. 3
11.4
11.5
11. 6
11. 7
11.8
11. 9
12.0
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14.1
14.2
14.3
14.4
14.5
14.6
-222.8
172.1
1779.9
893.9
421.8
513.7
745.2
1075.2
2060.5
972.6
709.3
1705.2
353.2
-248.7
1116.0
486.7
906.5
99.9
481.6
423.3
-986.2
559.4
70.5
1145.6
542.4
1091. 1
1612.1
-367.2
325.0
372.1
492.7
300.8
1452.5
1574.5
418.2
487.6
-191.8
-84.0
-85.8
572.7
537.4
677.9
493.3
1216.6
1122.3
1005.2
891.7
101.0
92.7
91.8
90.8
89.6
88.4
87.4
86.4
85.5
84.5
83.6
82.7
81.7
80.8
79.~
79.0
78.1
77.1
76.2
75.3
74.6
74.0
73.1
72.2
71.5
70.8
69.9
69.2
68.6
67.7
67.0
66.3
65.7
65.0
64.3
63.7
63.0
62.3
61.7
61.0
60.3
59.9
59.2
58.6
58.2
57.5
56.8
--------------------------o(mb)
t.o(mb)
---------------------------
E(keV)
14.7
14.8
14.9
15.0
15 .1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16.0
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17.0
17. 1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19.0
19. 1
19.2
19.3
19.5
504.1
449.1
461.6
260.4
619.0
286.2
-2.4
807.7
776.5
341.8
328.6
130.7
308.4
501.2
1037.6
637.7
928.1
756.1
780.8
431.5
533.5
265.3
-46.2
437.9
587.2
494.4
665.2
429.9
474.9
675.5
419.5
290.1
230.2
283.0
173.5
-26.0
73.3
232.9
516.1
707.8
513.0
326.6
479.8
1032.5
904.5
747.2
618.1
56.4
55.8
55.1
54.7
54.0
53.4
53.0
52.5
52.1
51.5
50.8
50.4
50.0
49.6
48.9
48.3
47.9
47.5
47.1
46.7
46.2
45.8
45.4
45.0
44.6
44.2
43.6
43.0
42.6
42.2
41.8
41.4
41.0
40.6
40.3
39.9
39.5
39.1
38.7
38.3
37.9
37.6
37.2
36.8
36.4
36.1
35.7
- 74 -
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22.0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
696.5
544.5
360.8
311.5
533.6
613.8
496.1
396.0
221.6
141. 1
349.4
322.1
645.6
258.4
342.3
203.1
101.9
462.6
649.5
558.6
623.9
480.1
302.7
599.7
556.9
436.2
281.7
285.2
328.4
391.6
144.5
151.6
627.4
650.3
295.7
423.9
557.3
528.9
511.6
497.1
453.0
458.2
287.1
238.5
383.5
469.5
672.0
649.9
487.2
393.9
390.3
35.3
35.0
34.6
34.2
33.9
33.5
33.2
32.8
32.4
32.1
31.7
31.4
31.0
30.7
30.4
30.0
29.7
29.4
29.0
28.7
28.4
28.0
27.7
27.4
27.1
26.7
26.4
26.1
25.8
25.5
25.2
24.9
24.6
24.3
24.0
23.7
23.4
23.1
22.8
22.5
22.2
22.0
21.7
21.4
21.1
20.9
20.6
20.3
20.1
19.8
19.6
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30.4
30.6
30.9
31.1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
37.3
37.6
37.9
38.2
38.5
38.9
39.2
39.5
39.9
292.3
498.6
427.2
352.2
393.6
395.8
370.9
488.0
431.0
299.8
352.2
437.0
432.4
347.2
469.5
398.6
366.7
266.4
504.7
574.0
613.3
577.3
429.9
412.9
5 71. 7
612.2
549.3
415.9
471.3
365.1
310.7
335.2
313.0
359.5
325.4
340.6
431.9
345.3
197.2
255.4
255.1
229.0
33.5.6
291.4
175.1
150.4
210.7
190.4
271.6
410.9
423.1
19.3
19. 1
18.8
18.6
18.3
18.1
17.8
17.6
17.4
17. 1
16.9
16.7
16.5
16.2
16.0
15.8
15.6
15.4
15.2
15.0
14.8
14.6
14.4
14.2
14.0
13.8
13.6
13.5
13.3
13.1
12.9
12.8
12.6
12.4
12.3
12.1
11.9
11.8
11.6
11.5
11.3
11.2
11. 1
10.9
10.8
10.7
10.5
10.4
10.3
10.2
10.0
- 75 -
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
47.7
48.1
48.6
49.0
49.5
50.0
50.4
50.9
51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
299.3
307.1
287.3
222.3
343.8
468.9
343.3
359.8
389.5
364.7
380.5
384.3
283.1
380.7
305.1
232.3
299.4
382.1
377.0
353.4
446.4
503.1
292.1
278.8
331.5
349.7
235.2
370.3
299.6
317.8
372.1
404.4
344.2
308.4
234.6
288.3
364.4
333.3
355.8
344.4
356.2
285.3
299.6
400.1
332.1
363.2
274.7
238.0
264.7
296.7
293.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
9.9
9.9
9.8
9.8
9.7
9.7
9.6
9.5
9.5
9.4
9.3
9.2
9.1
9.1
9.0
8.9
8.8
8.7
8.6
8.5
8.5
8.4
8.3
8.2
8.1
8.0
8.0
7.9
7.8
7.7
7.6
7.6
7.5
7.4
7.3
7.3
7.2
7.1
7.0
7.0
6.9
6.8
6.8
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75.1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
11L;. 6
116.3
118.0
119.7
121.4
123.2
320.6
321.7
308.2
262.3
286.4
244.3
265.4
249.6
239.7
199.4
191.1
328.6
311.8
219.0
270.9
322.6
282.7
312.6
297.4
250.8
192.7
190.4
275.2
218.6
214.8
248.0
241.5
209.4
208.5
228.8
178.7
249.0
212.4
139.7
170.4
190.7
235.7
217.8
205.8
180.5
163.0
181. 1
216.7
216.5
189.5
153.2
199.4
212.7
250.4
211.2
177.3
6.7
6.7
6.6
6.5
6.5
6.4
6.3
6.3
6.2
6.2
6.1
6.1
6.0
5.9
5.9
5.8
5.8
5.7
5.7
5.6
5.6
5.5
5.5
5.4
5.3
5.3
5.2
5.2
5.1
5. 1
5.0
5.0
4.9
4.9
4.9
4.8
4.8
4. 7
4. 7
4.6
4.6
4.6
4.5
4.5
4.5
4.4
4.4
4.4
4.3
4.3
4.3
- 76 -
--------------------------o(mb)
t.o(mb)
---------------------------
E(keV)
125.1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
175.8
179.0
182.2
185.5
188.9
192.5
196. 1
199.8
203.6
207.5
211.6
215.7
220.0
224.4
229.0
233.7
238.5
243.5
E(keV)
189.4
208.9
163.0
165.2
177.2
173.0
131.6
136.8
143.5
200.1
269.0
287.8
298.5
291.8
207.6
243.0
249.3
281.5
167.0
155.0
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.4
4.4
4.5
4.5
4.5
4.6
4.7
4.7
4.8
--------------------------t.o(mb)
o(mb)
--------------------------176.0
172.5
223.4
197.4
190.6
209.5
157.8
176.2
166.3
132.1
192.6
235.0
214.9
195.7
201.3
155. 1
183.8
216. 1
272.4
4.9
4.9
5.0
5.1
5.2
5.2
5.3
5.3
5.4
5.4
5.4
5.3
5.3
5.2
5.0
4.8
4.6
4.3
4.0
- 77 -
Appendix III
Capture cross section of Kr-80 as a function
of neutron energy
--------------------------o(mb)
lw (mb)
---------------------------
E(keV)
4.0
4. 1
4.2
4.3
4.4
4.5
4.6
4. 7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8.3
8.4
8.5
8.6
858.1
1265.8
1190.1
798.9
346.0
156.9
-98.3
215.8
-673.8
-343.8
258.4
1188.3
1116.9
1299.0
114 7. 7
776.5
656.7
643.7
712.7
514.2
193.0
-191. 7
125.8
290.7
583.2
546.6
434.1
236.6
607.9
576.3
421.0
949.5
627.9
467.3
263.6
424.4
632.4
596.0
354.8
301.7
469.6
478.1
363.0
439.9
339.1
400.8
323.9
253.9
308.0
304.9
293.8
286.0
270.9
259.9
257.3
247.4
235.6
222.0
228.3
220.5
217.6
203.~
190.6
189.6
190.4
184.6
180.2
172.0
164.2
161.5
168.1
164.6
15 7. 8
151.8
148.1
143.6
139.2
136.1
133.4
129.0
137.4
135.5
129.6
126.5
123.3
117.4
114.7
113.2
109.8
108.4
104.6
103.6
100.6
95.6
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
8.7
8.8
8.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
12.0
12.1
12.2
12.3
12.4
12.5
12 .. 6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
45.5
132.5
225.0
391.6
497.7
533.4
580.7
472.1
427.0
356.4
349.6
526.0
370.8
596.7
679.8
521.3
438.2
304.9
271.2
259.7
239.9
166.0
166.4
178.8
223.1
303.2
288.4
154.8
270.6
213.2
274.1
335.2
441.5
530.0
381.4
274.8
248.6
354.7
429.6
486.4
610.9
550.7
481.9
398.0
291. 1
118.3
138.3
94.7
92.8
99.5
101. 7
99.6
98.2
95.2
91.7
89.1
86.6
83.8
82.1
81.0
80.3
78.6
76.2
73.2
72.2
71.6
69.3
66.3
66.4
65.3
63.8
61.8
61.6
60.5
58.4
58.8
65.5
68.7
68.0
68.8
67.2
64.1
62.0
61.0
60.1
61.4
60.4
59.5
58.4
58.4
57.1
53.9
52.6
52.5
- 78 -
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14. 1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
15.0
15. 1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16.0
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17.0
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
390.1
495.5
513.6
518.6
666.9
620.0
525.4
444.7
319.9
289.3
331.8
440.9
432.6
445.4
457.4
465.7
499.5
528.8
570.3
520.9
429.5
466.5
450.7
375.1
420.6
411.8
355.9
320.4
316.5
266.9
239.6
207.7
256.4
283.0
295.9
309.6
281.7
281.4
317.6
338.8
360.8
357.8
319.6
291.7
305.9
327.1
348.3
378.3
401.9
412.7
420.7
52.6
53.0
53.2
51.5
51.6
50.4
48.8
47.8
46.2
45.6
45.3
44.2
44.5
44.5
44.0
43.1
42.6
41.8
41.5
40.9
40.4
39.5
38.8
38.5
37.9
37.7
37.9
36.7
35.5
35.0
34.5
34.0
33.5
33.1
33.3
33.3
33.2
33.0
32.5
32.0
31.2
30.4
29.9
29.5
29.6
29.8
29.8
29.9
29.5
30.6
38.1
---------------------------
E(keV)
o(mb)
b.o(mb)
--------------------------18.6
18.7
18.8
18.9
19.0
19.1
19.2
19.3
19.5
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22.0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
426.9
390.6
339.6
335.5
356.4
203.0
220.8
269.9
294.7
273.0
278.7
266.2
317.5
339.3
344.4
386.4
431.6
461.2
503.1
478.7
467.9
363.7
431.6
381.5
372.1
403.6
323.0
324.8
343.1
310.9
315.0
358.8
327.1
360.6
366.1
373.6
382.4
378.2
363.3
376.1
360.2
281. 1
233.7
281.6
284.7
361.5
369.6
324.0
376.5
390.2
404.4
39.3
38.4
39.9
38.1
36.8
.36.8
36.0
34.9
34.9
33.9
34.5
35.8
35.2
34.5
33.7
34.2
34.5
34.4
33.8
32.6
31.7
32.4
30.9
30.5
30.0
28.7
28.7
28.1
28.3
28.2
28.1
27.3
26.7
26.6
26.4
26.2
26.0
25.1
24.4
24.0
23.4
21.7
21.4
21.0
21.1
21.0
20.6
20.4
19.9
19.9
19.4
- 79 -
--------------------------o(mb)
t.o(mb)
---------------------------
E(keV)
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30.4
30.6
30.9
31.1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
417.4
383.7
342.5
340.3
312.2
285.5
276.5
320.0
346.1
351.4
326.3
337.7
341.9
303.2
278.1
247.8
265.3
277.2
300.5
300.6
301.4
295.4
324.1
326.1
344.9
318.5
332.7
288.1
266.3
231.9
199.5
227.8
231.6
217. 1
227.2
238.1
275.3
303.8
328.3
313.4
308.7
296.6
279.1
286.6
254.3
238.8
232.6
234.7
225.8
234.2
232.6
19.4
19.6
19. 1
19.3
18.6
19.2
19. 1
19.6
19.5
18.8
18.6
18.8
18.7
18.1
18.2
17.4
16.8
16.8
16.1
15.8
15.8
15.2
15.0
15.0
14.4
14.3
14.4
14.1
13.7
13.6
13.5
13.3
13.2
13.1
13.2
13.3
14.4
14.8
14.7
14.7
14.5
14.4
13.8
13.8
13.1
12.1
11.7
11.6
11.3
11.3
11.4
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
37.3
37.6
37.9
38.2
38.5
38.9
39.2
39.5
39.9
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
4 7. 7
48.1
48.6
49.0
49.5
50.0
50.4
50.9
51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
230.3
244.9
264.2
271.5
281.5
295.4
296.5
296.6
289.2
285.3
270.3
269.1
271.2
276.0
265.5
258.9
246.5
242.0
249.2
244.6
228.3
227.3
185.0
188.8
183.6
158.7
1131.2
209.7
239.3
234.8
219.2
207.6
199.7
182.0
176.3
205.7
203.3
236.1
223.1
233.2
236.1
262.9
254.1
245.0
217.8
193.5
189.0
188.8
195.2
185.0
202.7
11.6
11.6
11.2
11.2
11.2
11.5
11.3
11. 1
10.4
10.3
9.9
9.7
9.6
9.7
9.7
9.3
9.2
9.1
9.0
8.9
8.7
9.0
8.8
8.6
8.6
8.5
8.8
9.0
9.0
8.8
8.5
8.3
8.1
7.9
8.4
8.5
8.5
8.8
8.9
8.8
8.6
8. 1
7.9
7.6
7. 1
6.9
7.0
7.2
I •
I
Lf
7.2
7.3
- 80 -
--------------------------o(mb)
b.o(mb)
---------------------------
--------------------------o(mb)
Lw (mb)
---------------------------
E(keV)
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75. 1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
114.6
116.3
118.0
119.7
121.4
123.2
125.1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
175.8
179.0
182.2
185.5
188.9
192.5
196. 1
199.8
203.6
207.5
211.6
215.7
220.0
224.4
229.0
233.7
238.5
243.5
E(keV)
196.5
191. 1
189.1
179.6
194.4
202.8
177.7
169.2
154.7
152.2
160.7
166.4
171.2
172.9
177.6
175.1
169.0
168.3
172.7
183.2
161.0
161.6
171. 1
158.5
153. 1
148.5
142.0
145.3
144.9
151.8
159.9
155.7
166.4
164.5
153. 1
146.9
150. 1
159.0
152.4
158.2
136.1
131.0
143.2
140.5
148.4
157.0
151.2
151.6
151.4
148.9
7.1
7.0
6.9
6.6
6.5
6.4
6.2
6.1
6.0
5.7
5.6
5.6
5.5
5.5
5.4
5.4
5.7
5.8
5.8
5.7
5.6
5.4
5.3
5.1
5.0
5.2
5.2
5.2
5.3
5.2
5.0
4.7
4.7
4.5
4.5
4.5
4.8
4.9
5.0
5.2
5.1
4.9
4. 7
4.5
4.2
4.3
4.4
4.5
4.5
4.3
146.2
139.2
136.1
139.6
145.8
139.5
146.2
132.8
140.8
149.5
140.9
139.4
140.7
137.4
137.7
143.2
151.2
152.9
146.2
130.0
111.6
95.7
88.9
86.3
111.7
107.1
107.2
86.1
113.9
115.7
119.4
119.8
102.2
113.0
116.9
106.8
120.2
117.6
115.4
119.2
104.2
89.0
92.0
104.1
99.5
105.5
97.9
95.7
96.2
4.2
4.0
3.8
3.8
3.8
3.7
3.7
3.8
3.9
4.0
~.. 0
4.0
3.9
3.8
3.9
4.0
4.4
4.7
4.9
5.3
5.5
5.9
7.3
8.7
10.9
11. 7
11.5
11.7
12.0
11.4
11.3
11.2
11.2
11.8
12.0
11.9
12.0
11.6
11.0
10.8
10.9
10.9
10.6
10.9
10.7
11.0
11.3
11.5
11.8
- 81 -
Appendix IV
Capture cross section of Kr-82 as a function
of neutron energy
--------------------------o(mb)
Llo(mb)
---------------------------
E(keV)
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4. 7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5. 7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
-608.7
-595.5
311.9
-150.0
-941.9
-139.4
-51.4
592.8
-63.6
127.9
456.7
200.2
233.4
185.5
288.3
328.7
-190.1
-382.4
-483.5
125.8
-105.6
740.8
-130.7
-183.9
-77.6
179.0
-238.9
195.6
-350.2
-824.6
-81.3
-145.8
-252.0
-374.0
-259.6
39.5
-216.1
67.3
729.8
426.7
162.5
6.2
285.8
235.2
83.1
426.4
265.6
743.7
641.0
583.7
539.0
502.2
472.3
447.6
426.0
406.9
389.8
374.4
360.3
347.4
335.5
323.9
313.3
303.4
294.2
285.2
276.3
268.1
260.5
253.5
246.5
239.7
232.9
226.7
221. 1
215.5
210.1
204.8
200.0
195.4
190.8
186.3
182.0
178.1
174.6
171.3
167.6
164.3
161. 1
157.9
155.2
152.5
149.9
147.3
--------------------------o(mb)
Llo(mb)
---------------------------
E(keV)
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11.3
11.4
11.5
11.6
11.7
11. 8
259.4
-132.3
159.8
126.3
10.1
83.1
168.6
265.2
249.3
109.1
103.6
287.1
325.2
169.4
164.2
186.1
120.5
145.0
-22.1
15.5
41.9
28.4
-44.6
57.4
68.6
100.0
198.0
295.0
511.4
374.2
354.6
194.0
-89.1
-102.2
-28.3
-35.8
84.8
183.7
176.1
65.9
-81.2
154.2
375.1
243.4
370.4
112.6
266.4
144.8
142.6
140.5
138.2
136.2
134.2
132.3
130.4
128.6
127.1
125.6
124.1
122.6
121.2
119.8
118.4
117.0
115.6
114.3
113.2
112.1
110.9
109.8
108.8
107.8
106.8
105.8
105.0
104.0
103.0
102.3
101.5
100.6
99.6
98.9
98.2
97.4
96.7
96.0
95.3
94.6
93.9
93.1
92.4
91.7
91.0
90.3
- 82 -
--------------------------o(mb)
lw (mb)
---------------------------
E(keV)
11.9
12.0
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
15.0
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16.0
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
100.2
91.8
183.6
146.9
166.7
216.3
96.7
57.5
-74.8
-49.4
86.1
141.8
204.6
132.0
295.0
263.5
174.6
325.2
2,98. 5
197.8
131.5
165.4
161.2
152.8
136.3
141.2
119.2
78.9
-4.4
97.9
173.3
182.5
149.3
181.0
233.0
219.9
217.7
223.2
172.8
183.6
115 .1
70.6
78.0
74.5
174.4
215.7
245.4
198.1
158.7
203.6
209.9
89.6
89.1
88.5
87.8
87.1
86.6
86.0
85.3
84.7
84.2
83.4
82.9
82.3
81.7
81.1
80.6
80.0
79.4
78.8
78.2
77.6
77.0
76.6
75.9
75.3
74.9
74.3
73.6
73.2
72.5
71.9
71.4
70.8
70.1
69.6
69.2
68.7
68.0
67.3
66.8
66.4
65.9
65.2
64.4
64.0
63.5
63.0
62.5
62.0
61.5
61.0
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
17.0
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19.0
19.1
19.2
19.3
19.5
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22.0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
248.6
234.1
191.6
97.1
53.8
97.8
160.4
182.2
187.2
207.2
244.1
225.0
223.8
213.8
186.1
169.9
129.5
170.3
198. 7
155.2
144.4
156.8
188.1
180.0
139.2
185.7
213.4
159.2
143.7
137.4
96.7
105.9
146.4
119.2
79.3
106.1
119.8
84.3
103.6
165.5
146.6
41.6
35.6
68.2
77.8
85.3
88.2
124.7
128.3
102.2
111.2
60.5
59.9
59.4
58.7
57.9
57.4
56.8
56.3
55.8
55.2
54.7
54.2
53.6
53.1
52.5
52.0
51.4
50.9
50.3
49.8
49.2
48.7
48.1
47.6
47.0
46.5
45.9
45.4
44.8
44.2
43.7
43.1
42.6
42.0
41.5
40.9
40.3
39.8
39.2
38.7
38.1
37.6
37.0
36.5
36.0
35.4
34.9
34.3
33.8
33.3
32.7
-
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30.4
30.6
30.9
31. 1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
117.4
86.5
44.7
74.3
97.9
97.3
130.6
147.6
158.5
96.0
87.2
119.2
125.8
89.9
118.1
118.1
114.8
128.2
152.3
166.0
132.2
147.6
145.7
125.0
98.9
73.7
39.3
47.6
57.5
66.2
75.5
83.7
66.0
55.3
48.1
42.9
48.2
57.0
96.3
112.1
122.7
87.4
92.4
108.5
104.5
95.9
71.4
81.0
96.1
90.6
83.6
32.2
31.7
31.2
30.7
30.2
29.7
29.1
28.7
28.2
27.7
27.2
26.7
26.2
25.8
25.3
24.8
24.4
23.9
23.5
23.1
22.6
22.2
21.8
21.4
21.0
20.6
20.2
19.8
19.4
19.0
18.7
18.3
18.0
17.6
17.3
17.0
16.6
16.3
16.0
15. 7
15.4
15.2
14.9
14.6
14.4
14.1
13.9
13.6
13.4
13.2
13.0
83 -
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
37.3
37.6
37.9
38.2
38.5
38.9
39.2
39.5
39.9
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
47.7
48.1
48.6
49.0
49.5
50.0
50.4
50.9
74.2
97.5
100.5
104.9
97.2
102.3
87.2
83.7
91.8
74.2
67.2
77.1
82.7
86.6
96.0
80.5
83.4
67.5
55.8
56.8
57.4
71.4
63.5
52.9
56.9
60.8
74.7
77.8
75.2
72.3
61.1
69.6
80.5
95.4
97.7
102.0
98.0
104.0
96.5
90.2
105.6
87.2
89.9
63.5
69.3
86.2
69.4
69.5
68.1
67.9
53.2
12.8
12.6
12.4
12.2
12.1
11.9
11.8
11.6
11.5
11.4
11.3
11.2
11.1
11.0
11.0
10.9
10.9
10.8
10.8
10.8
10.8
10.9
10.9
11.0
10.7
10.3
9.9
9.6
9.3
9.1
8.9
8.7
8.5
8.4
8.3
8.2
8.2
8.1
8.1
8.0
8.0
8.0
8.0
8.0
8.0
8.0
8.0
8.0
8.0
8.0
8.0
-
--------------------------!::.o(mb)
o(mb)
---------------------------
E(keV)
51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75.1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
64.3
63.0
63.9
60.3
54.4
48.9
44.1
60.4
66.1
67.8
63.2
47.4
53.1
57.9
55.2
57.8
61.2
65.9
62.6
46.2
47.0
51.8
62.1
65.9
63.8
53.5
57.4
58.4
61.6
54.3
51.8
48.6
53.3
66.1
62.0
55.4
56.8
63.5
61.8
53.1
50.1
58.4
48.6
49.6
59.6
48.3
44.3
46.3
56.5
53.3
49.8
8.0
8.0
8.0
8.0
8.0
8.0
8.0
7.9
7.9
7.9
7.8
7.8
7.7
7.7
7.6
7.5
7.5
7. 4
7.3
7.2
7.1
7.0
6.9
6.8
6.7
6.6
6.5
6.3
6.2
6.1
6.0
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.9
4.8
4. 7
4.7
4.6
4.5
4.5
4.5
4.4
84
-
--------------------------l::.o(mb)
o(mb)
---------------------------
E(keV)
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
114.6
116.3
118.0
119.7
121.4
123.2
125.1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
175.8
179.0
182.2
185.5
188.9
192.5
48.3
48.2
47.4
47.2
61.8
62.9
53.9
54.0
51.8
40.9
43.2
48.4
46.4
46.9
46.3
45.1
45.3
44.8
52.1
55.2
50.5
46.8
46.9
38.3
42.4
43.7
44.9
45.7
37.5
33.7
39.4
45.4
41.4
45.9
48.7
58.7
58.7
58.6
53.5
49.4
48.2
56.5
47.9
42.4
40.8
40.2
43.4
44.3
40.2
42.4
41.6
4.4
4.4
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.3
4.4
4.4
4.4
4.4
4.5
4.5
4.5
4.6
4.6
4.6
4.6
4.6
4.6
4.6
4.6
4.6
4.6
4.5
4.5
4.4
4.3
4.2
4.1
4.0
3.8
3.7
3.5
3.4
3.2
3.0
2.8
2.6
2.5
2.3
2.1
1.9
1.8
1.7
1.5
- 85 -
--------------------------Lw (mb)
o(mb)
---------------------------
E(keV)
196.1
199.8
203.6
207.5
211.6
215.7
220.0
224.4
229.0
233.7
238.5
243.5
E(keV)
42.4
46.4
43.9
44.1
50.7
50.5
1.4
1.3
1.3
1.2
1.2
1.2
--------------------------ßo(mb)
o(mb)
--------------------------45.7
39.5
38.7
43.5
42.1
47.8
1.2
1.2
1.3
1.5
1.7
2.1
- 86 -
Appendix V
Capture cross section of Kr-83 as a function
of neutron energy
--------------------------o(mb)
!J.o(mb)
---------------------------
E(keV)
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
961.2
927.9
1976.0
2355.1
3901.3
839.3
-576.3
1552. 2
1994.5
1850.1
2718.3
666.4
1680.2
36.5
1445.8
1595.3
1591.8
462.6
1325.1
786.7
1000.6
1498.1
1202.7
395.7
628.0
476.9
920.3
859.6
617.3
157.2
1603.3
1000.3
336.3
712.9
711. 1
408.3
912.7
1017.7
465.0
1079.8
1030.4
1051. 7
970.8
820.6
695.3
429.2
411.6
1123.2
1017.0
890.6
796.0
721.5
663.7
618.0
579.9
547.9
520.5
497.0
476.4
458.5
442.6
427.8
414.5
402.6
391.8
381.4
371.4
362.3
353.9
346.2
338.7
331.2
323.9
317.2
311.1
305.0
299.1
293.2
287.9
282.6
277.4
272.3
267.2
262.7
258.6
254.5
250.0
246.0
242.0
238.0
234.5
231.0
227.6
224.1
--------------------------o(mb)
!J.o(mb)
---------------------------
E(keV)
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11.3
11.4
11.5
11.6
11. 7
11.8
327.5
396.7
498.1
756.9
494.7
871.6
788.1
615.3
818.1
538.2
364.2
925.7
1023.6
1017.2
1076.4
1165.5
773.2
778.8
970.2
963.0
590.5
531. 1
701.1
686.3
818.5
650.1
632.6
549.6
560.7
409.9
417.7
388.1
344.3
583.2
523.0
176.5
729.3
643.5
587.4
548.3
407.4
474.4
782.8
702.4
550.3
623.2
781. 1
220.7
217.8
214.8
211.5
208.7
205.8
203.0
200.3
197.5
195.2
192.8
190.5
188.2
185.9
183.6
181.3
179.0
176.8
174.5
172.6
170.8
168.5
166.7
164.8
163.0
161. 1
159.3
157.8
156.0
154.2
152. 7
151.3
149.5
147.7
146.2
144.8
143.4
142.0
140.6
139.1
137.7
136.3
134.9
133.5
132.1
130.7
129.3
- 87 -
--------------------------o(mb)
/J.o(mb)
---------------------------
E(keV)
11.9
12.0
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14.1
14.2
14.3
14.4
14.5
14.6
14. 7
14.8
14.9
15.0
15. 1
15.2
15.3
15.4
15.5
15.6
15. 7
15.8
15.9
16.0
16. 1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
767.5
730.9
679.0
618.7
671. 1
701.5
496.8
591.3
679.2
552.4
617.1
700.0
799.2
598.7
395.0
515.2
398.2
189.6
3.61. 0
333.3
430.2
394.3
431.2
414.2
559.4
439.7
382.6
410.0
316.5
387.0
529.3
398.0
280.6
397.8
361.3
422.0
179.8
390.6
271.7
196.6
474.2
311.4
424.3
392.5
373.6
445.7
516.3
419.6
333.5
359.2
406.4
127.9
126.8
125.7
124.3
122.9
121.8
120.7
119.3
118.2
117.2
115.7
114.6
113.5
112.5
111.4
110.3
109.2
108.1
107.0
105.9
104.7
103.6
102.9
101. 8
100.6
99.9
98.8
97.7
96.9
95.8
94.6
93.9
92.8
91.6
90.9
90.1
89.3
88.2
87.1
86.3
85.5
84.8
83.6
82.5
81.7
81.0
80.2
79.4
78.7
77.9
77.2
----------~----------------
E(keV)
o(mb)
!J.o(mb)
--------------------------17.0
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19.0
19. 1
19.2
19.3
19.5
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22.0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
370.9
400.7
334.6
363.1
308.2
422.2
425.0
499.2
524.9
487.9
405.9
364.0
309.6
259.8
174.5
242.3
335.6
206.2
232.3
300.5
413.0
383.5
346.7
409.4
353.5
359.0
4n.9
383.0
347.8
386.9
354.5
367.5
322.7
371.8
341.3
330.1
339.6
355.0
3L+8. 4
368.5
363.8
236.9
251. 1
76.4
75.6
74.9
73.7
72.6
71.8
71.1
70.3
69.6
68.8
68.1
67.3
66.6
65.8
65.1
64.3
63.6
62.8
62.1
61.3
60.6
59.8
59.1
58.4
57.6
56.9
56.2
55.5
54.7
54.0
53.3
52.6
51.9
51.2
50.5
49.8
49.1
48.4
47.7
47.0
46.3
45.7
45.0
281.4
44.3
284.7
241.3
242.5
322.3
354.4
43.6
43.0
42.3
41.7
41.0
40.4
39.8
3~1.4
40~.5
- 88 -
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30.4
30.6
30.9
31.1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
449.2
389.9
329.5
378.6
313.7
320.9
342.7
284.7
378.1
344.3
355.0
331.8
361.9
321.6
350.5
347.6
352.3
305.3
267.8
308.2
324.6
322.9
303.6
282.0
273.7
252.6
251.3
201.1
223.4
273.8
263.1
245.0
251.2
287.9
264.6
286.8
277.7
245.8
244.1
237.0
277.8
269.4
238.3
276.7
231.5
250.8
277.9
256.0
265.9
263.6
234.5
39.1
38.5
37.9
37.3
36.7
36.1
35.5
34.9
34.3
33.7
33.1
32.6
32.0
31.5
30.9
30.4
29.9
29.3
28.8
28.3
27.8
27.3
26.8
26.3
25.9
25.4
24.9
24.5
24.0
23.6
23.2
22.8
22.3
21.9
21.5
21.2
20.8
20.4
20.0
19.7
19.3
19.0
18.7
18.3
18.0
17.7
17.4
17.1
16.9
16.6
16.3
--------------------------t.o(mb)
o(mb)
---------------------------
E(keV)
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
37.3
37.6
37.9
38.2
38.5
38.9
39.2
39.5
39.9
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
47.7
48.1
48.6
49.0
49.5
50.0
50.4
50.9
230.2
279.3
246.2
262.4
217.3
258.7
228.4
248.0
256.8
207.7
223.0
239.9
222.7
203.2
224.6
235.3
213.3
207.7
211.7
191.8
208.5
212.3
225.8
184.8
171. 1
179.7
189.2
202.8
194.5
194.1
199.5
187.4
184.0
188.1
179.2
155.1
179.2
173.0
174.6
178.1
195.0
189.2
201.2
205.9
173.2
166.2
175.0
194.3
191.5
163.0
188.7
16.1
15.8
15.6
15.4
15.2
15.0
14.8
14.6
14.4
14.2
14.1
13.9
13.8
13.6
13.5
13.4
13.3
13.2
13.2
13.1
13.1
13.0
13.0
13.0
13.0
12.9
12.9
12.8
12.7
12.7
12.6
12.5
12.4
12.3
12.3
12.2
12.1
12.0
11.9
11.8
11.7
11.6
11.6
11.5
11.4
11.3
11.2
11. 1
11.0
10.9
10.8
- 89 -
--------------------------o(mb)
L'lo(mb)
---------------------------
E(keV)
51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75.1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
177.3
152.8
167.5
147.8
163.8
183.4
184.3
178.1
170.5
170.9
183.2
184.7
179.6
187.6
176.7
150.9
144.8
160.0
136. 1
156.8
145.5
144.5
137.7
147.8
145.4
127.7
140.8
130.2
135.0
133.7
121.6
116.3
121.2
132.7
141.8
134.5
123.5
132.8
128.1
120.9
118.5
124.8
108.8
115.8
129.6
130.1
117.8
111.5
112.7
109.0
113.4
10.7
10.7
10.6
10.5
10.4
10.3
10.2
10.1
10.0
10.0
9.9
9.8
9.7
9.6
9.5
9.4
9.4
9.3
9.2
9.1
9.0
8.9
8.8
8.7
8.6
8.5
8.5
8.4
8.3
8.2
8.1
8.0
7.9
7.8
7.7
7.6
7.5
7.4
7.3
7.2
7.0
6.9
6.8
6.7
6.6
6.5
6.4
6.3
6.2
6.1
6.0
--------------------------o(mb)
L'lo(mb)
---------------------------
E(keV)
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
114.6
116.3
118.0
119.7
121.4
123.2
125. 1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
17 5. 8
179.0
182.2
185.5
188.9
192.5
114.3
120.2
113.9
105.7
101.3
110.8
117.3
107.9
117.2
97.9
93.9
103.6
96.8
91.1
90.5
82.3
96.9
98.8
108.4
103.0
98.0
101.1
90.4
90.3
91.0
92.3
93.1
86.7
83.5
85.3
84.7
89.6
89.6 .
83.0
86.4
80.6
88.4
80.5
78.0
77.8
79.1
74.4
78.6
68.3
77.3
71.7
67.3
67.1
63.9
68.7
68.7
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
4.9
4.8
4. 7
4.6
4.6
4.5
4.5
4.4
4.4
4.3
4.3
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.2
4.3
4.3
4.4
4.5
4.5
4.6
4. 7
4.8
4.9
5.1
5.2
5.4
5.5
5.7
5.9
6.1
6.3
6.4
6.6
- 90 -
---------------------------
---------------------------
--------------------------o(mb)
Llo(mb)
---------------------------
196.1
199.8
203.6
207.5
211.6
215.7
220.0
224.4
229.0
233.7
238.5
243.5
E(keV)
o(mb)
68.0
70.6
63.9
64.8
63.2
68.1
Llo(mb)
6.8
6.9
7.0
7.0
7.0
7.0
E(keV)
57.9
55.3
59.0
56.4
61.4
59.5
6.8
6.6
6.3
5.9
5.4
4.8
- 91 -
Appendix VI
Capture cross section of Kr-84 as a function
of neutron energy
--------------------------o(mb)
Ao(mb)
---------------------------
E(keV)
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4. 7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7.0
7.1
324.8
871.2
229.8
2330.1
583.2
-461.1
616.9
-412.8
388.7
-438.0
1261.2
804.6
326.3
602.7
129.4
194. 7
227.3
153.8
240.3
245.3
546.1
117.3
-351. 8
162.4
145.3
453.4
2.5
215.0
401.6
280.2
437.8
32.5
-13.6
377.7
240.6
111.8
6.1
73.3
73.6
-7.0
-270.3
199.9
104.9
375.2
286.9
229.8
86.0
1275.0
1115.5
949.7
825.7
728.7
654.3
596.5
549.3
510.6
478.5
451.7
429.2
410.3
394.3
379.9
367.6
357.1
347.9
339.5
331.6
324.7
318.6
313.2
307.9
302.9
297.9
293.5
289.4
285.4
281.4
277.5
273.9
270.2
266.6
262.9
259.2
255.8
252.6
249.4
245.8
242.4
239.0
235.5
232.4
229.2
225.9
222.6
--------------------------o(mb)
Ao(mb)
---------------------------
E(keV)
7.2
7.3
7. 4
7.5
7.6
7.7
7.8
7.9
8.0
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.0
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.0
10. 1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11.0
11. 1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
-135.2
66.9
-30.4
-78.0
245.5
74.7
167.2
213.6
51.8
340.8
266.5
412.3
482.8
378.7
96.7
60.5
5.0
2.3
140.5
-17.2
-104.0
51.2
-197.5
140.6
50.9
182.4
169.6
74.8
15.3
45.0
159.2
17.1
186.8
-70.6
38.2
104. 1
261.9
187.5
94.9
264.6
378.5
313.4
278.3
368.4
117.6
77.7
-11.3
219.2
216.2
213.2
209.7
206.6
203.5
200.4
197.2
194.0
191.2
188.5
185.7
182.8
180.0
177.1
174.2
171.3
168.4
165.5
163.1
160.6
15 7. 6
155.2
152.7
150.3
147.8
145.4
143.4
141.0
138.6
136.6
134.7
132.3
.130. 0
128.1
126.2
124.4
122.6
120.7
118.9
117. 1
115.4
113.6
111.9
110. 1
108.4
106.7
- 92 -
--------------------------o(mb)
Lw (mb)
---------------------------
E(keV)
11.9
12.0
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13.0
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14.0
14. 1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
15.0
15. 1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16.0
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
-3.9
6.5
-58.2
167.2
-73.0
14.6
-39.9
-87.1
-6.1
35.5
-49.2
-100.0
3.5
-19.6
-41.0
132.0
-37.7
113.4
2,06 .5
101.8
22.5
74.2
41.3
26.1
22.2
137.4
81.2
96.8
137.5
111.6
119.9
91.3
51.2
-50.6
85.1
35.7
-41.9
25.2
134.2
-12.3
-117.4
16.8
95.2
138.5
101.6
68.6
91.6
72.7
135.1
212.2
115.2
105.0
103.8
102.6
100.9
99.3
98.1
96.9
95.3
94.2
93.0
91.5
90.3
89.2
88.1
87.0
85.9
84.9
83.8
82.7
81.7
80.7
79.7
79.0
78.0
77.0
76.4
75.4
74.5
73.9
72.9
72.0
71.4
70.6
69.7
69.1
68.5
68.p
67.2
66.4
65.8
65.3
64.8
64.0
63.3
62.8
62.3
61.8
61.3
60.8
60.4
59.9
--------------------------/J.o(mb)
o(mb)
---------------------------
E(keV)
17.0
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18.0
18.1
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19.0
19.1
19.2
19.3
19.5
19.6
19.7
19.8
19.9
20.0
20.2
20.3
20.4
20.5
20.7
20.8
20.9
21.0
21.2
21.3
21.4
21.6
21.7
21.8
22 .. 0
22.1
22.2
22.4
22.5
22.7
22.8
23.0
4.0
-0.3
76.9
87.3
68.8
31.8
72.4
27.0
20.8
13.5
29.8
31.9
26.1
61. 1
21.9
9.8
7.5
32.7
51.4
75.7
47.7
33.5
-25.4
-40.4
-1.3
65.4
53.7
51.0
68.5
52.6
50.8
61.1
86.5
73.0
44.9
-5.9
-30.4
-16.3
6.0
-0.4
20.1
55.4
34.6
26.5
58.5
60.6
16.5
13.5
-11.5
-10.0
32.8
59.5
59.0
58.6
57.9
57.3
56.9
56.5
56.1
55.7
55.3
54.9
54.5
54.1
53.8
53.4
53.0
52.7
52.3
52.0
51.7
51.3
51.0
50.7
50.4
50.1
49.8
49.5
49.2
48.9
48.6
lf8. 3
48.1
47.8
47.5
47.3
47.0
46.8
46.5
46.3
46.1
45.8
45.6
45.4
45.2
45.0
44.8
44.5
44.3
44.2
44.0
-+3.8
- 93 -
--------------------------o(mb)
b.o(mb)
---------------------------
E(keV)
23.1
23.3
23.4
23.6
23.7
23.9
24.0
24.2
24.3
24.5
24.7
24.8
25.0
25.2
25.3
25.5
25.7
25.8
26.0
26.2
26.4
26.6
26.7
26.9
27.1
27.3
27.5
27.7
27.9
28.1
28.3
28.5
28.7
28.9
29.1
29.3
29.5
29.8
30.0
30.2
30. t..
30.6
30.9
31. 1
31.3
31.6
31.8
32.1
32.3
32.6
32.8
44.3
28.7
17.1
35.2
24.5
9.7
28.6
42.7
61.4
80.1
83.7
81.5
45.4
12.7
19.8
36.3
27.9
11.5
15.4
51.0
71.4
68.0
73.9
54.3
18.9
23.9
20.9
12.5
23.9
3.4
13.8
34.5
51.0
37.1
28.3
33.7
21.6
24.9
15.2
-2.9
17.4
42.7
36.3
15.4
34.3
28. !~
17.8
6.2
-2.6
-0.2
11.8
---------------------------
E(keV)
o(mb)
b.o.(mb)
---------------------------
43.6
43.4
43.2
43.1
42.9
42.7
42.6
42.4
42.2
42.1
41.9
41.8
41.6
41.5
41.3
41.2
41.1
40.9
40.8
40.6
40.5
40.4
40.2
40.1
40.0
39.9
39.7
39.6
39.5
39.3
39.2
39.0
38.9
38.8
38.6
38.5
38.3
38.2
38.0
37.9
37.7
37.5
37.3
37.2
37.0
33.1
33.3
33.6
33.8
34.1
34.4
34.7
34.9
35.2
35.5
35.8
36.1
36.4
36.7
37.0
37.3
37.6
37.9
38.2
38.5
3!3.9
39.2
39.5
39.9
40.2
40.6
40.9
41.3
41.6
42.0
42.4
42.7
43.1
43.5
43.9
44.3
44.7
45.1
45.5
45.9
46.4
46.8
47.2
47.7
48.1
36.8
"'-8.6
36.6
36.4
36.1
35.9
35.7
49.0
49.5
50.0
50.4
50.9
12.6
17.7
27.5
45.7
90.6
100.0
73.8
48.0
33.0
17.3
19.9
2.4
11.4
1.8
14.9
-1.9
5.4
-3.2
18.4
28.3
22.3
14.8
20.3
19.8
29.8
15.0
6.8
16.2
9.4
10.4
4.8
-1.2
11.9
34.7
57.9
67.2
57.9
36.1
32.5
12.0
13.1
3.7
17.5
3.9
11. 1
23.7
35.1
41.3
42.9
45.5
42.6
35.4
35.2
34.9
34.6
34.4
34.1
33.7
33.4
33.1
32.7
32.4
32.0
31.6
31.2
30.8
30.3
29.9
29.4
28.9
28.4
27.9
27.3
26.8
26.2
25.6
25.0
24.4
23.9
23.5
23.1
22.8
22.5
22.2
22.0
21. 7
21.5
21.4
21.2
21. 1
20.9
20.8
20.7
20.6
20.5
20.4
20.3
20.2
20.1
20.0
19.9
19.8
- 94 -
--------------------------o(mb)
Lw (mb)
---------------------------
E(keV)
51.4
51.9
52.4
52.9
53.5
54.0
54.5
55.1
55.6
56.2
56.7
57.3
57.9
58.5
59.1
59.7
60.3
61.0
61.6
62.3
62.9
63.6
64.3
65.0
65.7
66.4
67.1
67.9
68.6
69.4
70.2
70.9
71.8
72.6
73.4
74.2
75.1
76.0
76.9
77.8
78.7
79.6
80.6
81.6
82.6
83.6
84.6
85.6
86.7
87.8
88.9
18.5
27.5
26.0
14.5
14.3
15.8
23.4
23.7
16.7
17.6
8.4
5.7
10.2
11.2
23.3
26.4
14.7
14.4
13.1
20.2
22.5
24.9
38.6
19.5
20.9
20.7
25.5
26.3
20.1
30.0
29.5
24.8
15.6
11.3
19.0
24.8
23.7
27.7
28.9
21.6
26.7
25.3
19.7
20.8
16.8
16.4
10.7
14.9
24.7
25.0
24.0
19.7
19.6
19.4
19.3
19.2
19.0
18.9
18.7
18.5
18.4
18.2
18.0
17.8
17.5
17.3
17.1
16.9
16.6
16.4
16.2
15.9
15.7
15.4
15. 1
14.9
14.6
14.4
14.1
13.9
13.6
13.4
13.1
12.9
12.7
12.5
12.2
12.0
11.8
11.6
11.4
11.2
11.1
10.9
10.7
10.6
10.4
10.3
10.2
10.1
10.0
9.9
--------------------------o(mb)
ßo(mb)
---------------------------
E(keV)
90.0
91.2
92.3
93.5
94.7
96.0
97.3
98.5
99.9
101.2
102.6
104.0
105.4
106.9
108.3
109.9
111.4
113.0
114.6
116.3
118.0
119.7
121.4
123.2
125.1
127.0
128.9
130.9
132.9
135.0
137.1
139.2
141.5
143.7
146.0
148.4
150.9
153.4
155.9
158.6
161.3
164.0
166.9
169.8
172.8
175.8
179.0
182.2
185.5
188.9
192.5
17.3
13.6
12.7
16.8
14.8
17.2
17.4
13.6
16.0
20.4
20.5
27.4
20.3
15.4
12.5
11.6
11.7
13.4
11.5
11.3
14.1
14.6
12.9
18.1
16.9
11.0
]0.7
13.6
16.4
18.2
12.5
7.0
9.6
12.5
14.1
15.2
14.3
14.6
13.0
10.7
11.3
11.2
11.4
11. 1
13.5
12.5
13.9
15.2
11.9
10.8
13.7
9.8
9.7
9.6
9.5
9.5
9.4
9.4
9.3
9.3
9.3
9.3
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.2
9.1
9.1
9.1
9.0
8.9
8.8
8.7
8.6
8.5
8.3
8.1
7.9
7.7
7.5
7.3
7.0
6.7
6.5
6.2
5.9
5.6
5.3
5.1
4.8
4.5
4.3
4.1
- 95 -
E(keV)
196.1
199.8
203.6
207.5
211.6
215.7
o(mb)
10.9
9.4
10.8
11.4
11.2
10.9
ßo(mb)
3.9
3.7
3.6
3.5
3.4
3.3
E(keV)
220.0
224.4
229.0
233.7
238.5
243.5
o(mb)
10.9
12.7
11.8
11.8
11.3
8.7
ßo(mb)
3.4
3.4
3.6
3.9
4.3
4.9

Ni/Ti multilayer supermirrors for neutron optics - Reflective X

MasitahOthmanMFS2012ABS

Calibra`on*and*Modeling*of*Nuclear*and* Electron*Recoils*in

Review on Scintillators Review on Scintillators

PPT - SNOLAB 2005 Workshop

01/15 - MSU Chemistry

The atomic nucleus. Radioactivity. Nuclear radiations

Medical Cyclotrons Market - Size, Growth, Trends and Opportunity Analysis, 2018-2026

Wilkinson, W.E.; (1967)Branching processes in stochastic environment."

Fourier Series and FFT

Excimer Laser Devices Market - Industry Analysis, Size, Share, Growth, Trends and Forecast to 2025