Paris, C . H .
Endt, P.M.
1954
ANGULAR
PhysicaXX
585-591
DISTRIBUTIONS
OF FOUR NEUTRON
F R O M T H E l°B(d, n ) l ' C R E A C T I O N
GROUPS
b y C. H. P A R I S and P. M. E N D T
Physisch Laboratorium der Rijksuniversiteit, Utrecht, Nederland
Synopsis
M e a s u r e m e n t s are d e s c r i b e d of t h e a n g u l a r d i s t r i b u t i o n s of the four m o s t e n e r g e t i c
n e u t r o n groups f r o m t h e l°B(d, n ) l I c r e a c t i o n at a d e u t e r o n e n e r g y of 0.6 MeV.
N e u t r o n s w e r e d e t e c t e d b y t h e i r recoil p r o t o n s in n u c l e a r emulsions. T h e a n g u l a r
d i s t r i b u t i o n s h a v e been a n a l y z e d in t e r m s of a s t r i p p i n g c o n t r i b u t i o n and an, ass u m e d l y isotropic, c o n t r i b u t i o n f r o m c o m p o u n d n u c l e u s f o r m a t i o n . F r o m B u t l e r
a n a l y s i s l# = 1 is f o u n d for t h e s t r i p p i n g c o n t r i b u t i o n of t h e n e u t r o n g r o u p l e a d i n g
to t h e l I c g r o u n d state, a n d lp = 0 for t h e g r o u p leading to t h e second e x c i t e d state.
This is in a g r e e m e n t w i t h p r e v i o u s results o b t a i n e d f r o m t h e m i r r o r r e a c t i o n
l°B(d, p ) l l B a n d w i t h p r e d i c t i o n s f r o m t h e n u c l e a r shell model. S t r i p p i n g c o n t r i b u t i o n s of t h e o t h e r t w o n e u t r o n g r o u p s are v e r y small.
§ 1. Introduction. In a previous paper 1) angular distribution and yield
measurements have been described of four proton groups from the l°B(d, p) liB
reaction. It seemed interesting to supplement these measurements with an
investigation of the l°B(d, n ) l l C reaction. This latter reaction leads to llC,
which is the mirror nucleus of 1lB. For this reason we m a y expect that angular distributions and yields of corresponding neutron and proton groups are
very nearly identical.
The nucleus tiC has excited states at 1.85, 4.23 and 4.77 MeV 2)3). All
these levels and the 11C ground state should be reached from the l°B(d, n)llC
reaction at E d =-0.6 MeV, as the ground-state Q-value amounts to 6.472
MeV 2). Angular distribution measurements of all neutrons from the
'°B(d, n)llC reaction detected b y an energy insensitive "long" counter at
E d = 0.71, 1.06 and 1.43 MeV have been reported b y Burke e.a. 4).
In § 2 a description will be given of the experimental procedure used for
detection of neutrons b y means of the nuclear emulsion method. The results
of the measurements are presented in § 3 and discussed in § 4.
§ 2. Experimental procedure. Neutrons were detected and their energy was
measured b y means of their recoil protons in nuclear emulsions placed at
15° intervals around the target. The aluminum plate holder was very much
- - 585 - -
586
C. H. P A R I S A N D P. M. E N D T
the same as the one used for (d, p) angular distribution measurements 5)
with the following alterations:
a) the surface of the emulsion was put parallel to the direction of the
incoming neutrons ;
b) to reduce the background of neutrons resulting from bombardment of
the slit system defining the deuteron beam, the slit to target distance was
enlarged from 25 mm to 195 ram;
c) the average distance of target to emulsions was enlarged from 60 mm
to 100 m m t o reduce the uncertainty in the position of the target spot due
to its finite extension and its possible eccentricity.
To prevent charged particles from reaching the emulsion an aluminum
shield of 1 mm thickness was mounted between target and emulsions.
Of the proton recoil tracks found in the exposed and processed nuclear
emulsions the following quantities were actually measured:
a) the projection of the track on the surface of the emulsion;
b) the "dip" of the track as measured b y its component perpendicular
to the surface of the emulsion;
c) the angle between the direction of the incident neutron and the direction
of the projection defined under a).
From elementary geometrical considerations (taking into account the
shrink of the emulsion b y development) the actual range of the proton recoil
can be found and the angle ~ between neutron and proton direction. The
proton energy Ep can be found from the range-energy relation and finally
the neutron energy from the expression:
E,, = Ep/cos 2 0.
These computations were much simplified b y the use of suitable nomograms,
in whicli the "corrected range" (the range of protons from head-on collisions)
was used as an intermediate quantity. Only proton tracks were accepted of
which the dip angle was smaller than 7.5 ° (in the unprocessed emulsion), and
in which the azimuth angle, defined under c), was smaller than 15°.
For larger dip and azimuth angles the error in E,,, due to the errors in the
measurements of the proton track parameters, rises rapidly.
The target consisted of a 80 #g/cm 2 t°B layer on a 6 ~ aluminum backing.
It was prepared b y electromagnetic separation b y Dr R. H. V. M. D a w t o n
at the Atomic Energy Research Establishment, Harwell, England. The lib
content was too low (2.5 -4- 1.5%) to interfere with the present measurements
as was found from separate ~B enriched target bombardments. The same
was found for ~aC b y bombarding an enriched 13C target. The contaminants
~2C a n d ~60, usually present on every target,.do not interfere because the
Q-values of their (d, n) reactions are very low.
The 1°B target was bombarded b y a 1 #A current of 600 keV deuterons
during 20 hours. The effective deuteron energy obtained b y subtracting half
the deuteron energy loss in the target amounted to 576 keV.
ANGULAR DISTRIBUTIONS OF FOUR NEUTRON GROUPS
587
§ 3. Experimental results. In Fig. 1 the energy spectrum of neutrons Jeaving
the target in the forward direction (~ = 0 °) is shown, in which the "corrected
range" (see § 2) is used as a measure of neutron energy. A certain amount of
background was present at ranges below 100 #, and has been subtracted in
Fig. 1. It is caused b y D(d, n) 3He neutrons from the slit system defining the
deuteron beam, as could be certified b y bombardments of a blank aluminum
target. This background is most serious in emulsions placed in the forward
direction (~9 = 0 ° - - 4 5 ° ) , although these emulsions have the greatest
distances to the slit system, because then the neutrons from the target and
from the slit system reach the emulsion from almost the sam4 direction,
which makes their recoil protons indistinguishable.
• 6O
1%cd.nl"C ~d: 0.S76 M,,V. O"
u
o
(0)Ex=0
( 1 ) Ex= 1.85
( 2 ) Ex--{*.23
( 3 ) Ex=/,,77
0
MaV. 0=6/*7 MeV.
MeV,
MeV.
MeV.
~ ,-o
(ID)
(I)
J
(0)
20
%.
1oo
260
--
300-
"
~6o
Ronge in ~.
500
Fig. 1. E n e r g y s p e c t r u m of n e u t r o n s e m i t t e d at ~ = 0 ° f r o m a I°B t a r g e t b o m b a r d e d
b y 0.58 MeV d e u t e r o n s . T h e n u m b e r of c o u n t e d t r a c k s is p l o t t e d as a f u n c t i o n of
"'the c o r r e c t e d r a n g e " of recoil p r o t o n s i.e. t h e r a n g e of p r o t o n s w i t h t h e full n e u t r o n
energy. T h e n e u t r o n g r o u p m a r k e d (D), results f r o m t h e D(d, n) 3He reaction, t h e
g r o u p s m a r k e d (0), (1), (2) and (3) f r o m the l°B(d, n ) l l C r e a c t i o n . The t o t a l n u m b e r
of t r a c k s c o u n t e d for Fig. 1 a m o u n t e d to 416.
In emulsions placed at 0 = 60 ° and larger angles t h e recoil protons
directed radially away from the target, and originating from D(d, n)3He
neutrons from the slit system, have such a low energy, that they can not be
mixed up with the four l°B(d, n) llC groups which were counted.
Four different neutron groups can be seen in Fig. 1. The group at a range
of about 100 # is due to D(d, n)3He neutrons from the target. The four other
neutron groups marked (0), (1), (2) and (3) originate in the l°B(d, n)llC
reaction. They correspond to transitions to the llC ground-state and to the
588
C. H. PARIS AND P. M. ENDT
three lowest excited states. Background has already been subtracted.
Differential cross sections of the three most energetic l°B(d, n)11C groups
are given in Figs. 2, 3 and 4. For the conversion of counted number of tracks
into differential cross sections one has to take into account the escape probability of proton tracks from the emulsion 6) and the neutron proton elastic
scattering cross section 7). The statistics of the neutron group leading to the
11C third excited state were too poor to allow the drawing of conclusions
regarding its angular distribution. For this low-intensity and low-energy
group the background correction was especially serious.
]
~ " 1
10B(d0n)11C
Ex= 0 MeV.
'
:l...~..t~._....
\
"
0°
30 °
60 °
\,
\,
90 °
120 °
150 °
[
180 °
Fig. 2. Differential cross section of the ground-state n e u t r o n group from the reaction
l°B(d, n ) l l c at E a = 0.58 MeV plotted in the laboratory system. The cross section
(full drawn curve) is analyzed as a sum of a stripping c o n t r i b u t i o n for lp = 1
(dotdash curve) and an isotropic compound nucleus c o n t r i b u t i o n (dashed curve).
§ 4. Discussion and conclusions. To compute stripping angular distributions for the l°B(d, n)llC reaction leading to the itC states at E x = 0, 1.85,
4.23 and 4.77 MeV one m a y safely assume that the proton angular momentum transfers lp for this reaction are the same as the neutron angular
momentum transfers l, for the mirror reaction l°B(d, n)11B leading to the
'tB states at Ex = 0, 2.14, 4.46 and 5.03 MeV," i.e. respectively Ip = 1, 3, 0
and 2 1). Stripping angular distributions for these lp values were c o m p u t e d
ANGULAR
DISTRIBUTIONS OF FOUR NEUTRON
GROUPS
589
for the three most energetic neutron groups, using stripping theory in the
form given b y B h a t i a e.a. s). The l°B nuclear radius was taken equal
to 5.8 × 10 -la cm, the same value as was found to fit the I°B(d, p)llB angular
distributions 1).
The experimental differential cross sections given in Figs. 2, 3 and 4 were
now analyzed into a stripping contribution and a contribution for compound
nucleus formation which was assumed to be isotropic in the center of mass
system 9)1). It is seen that in this way a reasonable agreement can be
obtained between calculated and measured angular distributions. The
c.
10B(d.n)11G E
e)
: 1 . 8 5 MeV.
X
Ed =0.576 MeV.
R = 5.8x10-13om.
I =3.
P
1170
j-f"
/
i
0°
30 °
60°
90 °
i
120°
,
!
150°
.
180°
Fig. 3. D i f f e r e n t i a l cross section a t E a = 0.58 MeV of t h e l°B(d, p) l l c n e u t r o n g r o u p
l e a d i n g ito t h e I I c level at E x = 1.85 MeV. The s t r i p p i n g c o n t r i b u t i o n (dot-dash
curve) has been d r a w n for lp = 3.
agreement is worst for the neutron group leading to the I Ic first excited state
(Fig. 3), especially at the larger angles, but the discrepancy in this case might
well be explained by the relatively poor statistics.
In Table I are collected the total number of tracks counted for each
neutron group, the total cross section, and the contributions to the total cross
section from stripping and compound nucleus formation. Also the /p-value
used in the calculation of the stripping part has been indicated.
The stripping contributions show apparently a monotonic decrease with
590
C. H. PARIS AND P. M. ENDT
increasing /p-values, as is predicted by theory. Only group (3) shows an
exception to this rule. Its stripping contribution is smaller than can be
accounted for.
The angular distributions and relative intensities of the neutron groups
from the l°B(d, n)llC reaction agree very well with those of the proton groups
from the mirror reaction I°B(d, p)llB 1). Even the inverted intensity order of
groups (1) and (3) is found in both reactions. For a possible explanation of
this effect see reference 1. Also the absolute values of the total cross sections
600i
10B(d.n)110
x 576
Ed=0.
MeV.
E =4.23 MeV.
R= 5.8x10-13 crn.
,
I p =0.
500
400
~,1~I
30t2 I~,~XXI~
\
x
. . . . . . . . . . . . . . . . . . . . .
i
o" ' 3 ' 0 ° '
go.
i
90' ° ' - ' -120
-' °
150°
.
180°
Fig. 4. D i f f e r e n t i a l cross s e c t i o n a t E a = 0.58 M e V of t h e l°B(d, n) 11C n e u t r o n g r o u p
l e a d i n g t o t h e I IC level a t E x = 4.23 MeV. T h e s t r i p p i n g c o n t r i b u t i o n ( d o t - d a s h curve),
h a s b e e n d r a w n for lp = 0.
are nearly the same for the two reactions. Actually the sum of the total cross.
sections of the four groups at Ed = 0.58 MeV is 2.9 times larger for the (d, p)
as for the (d,n) reaction. This is outside the experimental error which is.
only 10% for the (d, p) total cross section but might be up to a factor of
two for the (d, n) reaction. However, a smaller cross section for the (d,n).
reaction might well be explained by Coulomb repulsion, which makes it more
difficult for the proton than for the neutron to enter the nucleus a f t e r
deuteron break-up outside the nucleus.
A N G U L A R D I S T R I B U T I O N S OF FOUR N E U T R O N GROUPS
591
TABLE I
Contributions of stripping and compound nucleus formation to the total cross section of the
a°B(d, n ) n C reaction at E d = 0.58 MeV leading to the four lowest nC states
Group
t'C excitation
energy (MeV)
Counted
number of
tracks
Total cross
section
(nab)
Stripping
cross section
(mb)
lp
Compound nucleus
cross section
(mb)
(0)
(1)
(2)
(3)
0
1.85
4.23
4.77
485
234
1406
463
2.0
0.8
2.2
0.7
0.7
0.2
I. 1
0.1
1
3
0
2
1.3
0.6
I. 1
0.6
Acknowledgements. This work is part of the research program of the
"Stichting voor Fundamenteel Onderzoek der Materie", which was made
possible by a subvention from the "Nederlandse Organisatie voor Zuiver
Wetenschappelijk Onderzoek".
The authors are indebted to Prof. J. M. W. M i 1 a t z for his interest in
this investigation. They wish to thank Miss A. M. H o o g e r d u ij n for
her untiring and capable assistance in counting plates.
Received 30-6-54.
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