Physica X X l I
1062-1068
Amsterdam Nuclear
Reactions Conference
Endt, P. M.
1956
CAPTURE REACTIONS
b y P. M. E N D T * )
Physisch Laboratorium, Rijksuniversiteit, Utrecht, Nederland
Synopsis
Capture reactions will be considered here from the viewpoint of the nuclear spectroscopist. Especially important to him are the capture of neutrons, protons, and alpha
particles, which may proceed through narrow resonances, offering a well defined
initial state for the subsequent deexcitation process. Each of these particles mentioned
above has its own advantages and disadvantages, largely depending on particle
energy and on the mass number region in which one is going to work.
The y-radiation produced at a resonance may be investigated through measurements
of the y-ray spectrum and its angular distribution, and through coincidence and angular correlation measurements. The theory is well established, and has been fully
supported by experiment in a large number of cases. Complications in the interpretation may arise from interference between different resonances (if these are broad),
and from mixing of different channel spins, of different orbital momenta of the incoming particle, and of different y-ray multipolarities.
Very fruitful have proved (p, y) reactions on light elements. They offer an almost
ideal opportunity for spin and parity determinations of resonance levels and lower
levels. From y-ray intensities it may be possible to test isobaric spin selection rules for
E 1 radiation, or, inversely, to determine isobaric, spins.
A n y nuclear r e a c t i o n m a y be s t u d i e d for two reasons. T h e first reason ot
interest m a y be t h e r e a c t i o n process itself, b u t once enough is k n o w n a b o u t
the process, t h e r e a c t i o n m a y also be applied as a tool to s t u d y the final
nucleus. T h e c a p t u r e process h a s clearly passed to the second stage. T h e
t h e o r y has b e e n d e v e l o p e d to such a p o i n t t h a t t h e c a p t u r e r e a c t i o n h a s
b e c o m e a v e r y useful i n s t r u m e n t in nuclear s p e c t r o s c o p y . W e shall first go
into the question which particles, particle energies a n d m a s s n u m b e r regions
are m o s t a d v a n t a g e o u s in this respect.
0 n l y c a p t u r e of protons, n e u t r o n s a n d a l p h a particles h a s to be considered. C a p t u r e of d e u t e r o n s or t r i t o n s leads to a highly excited c o m p o u n d
s t a t e d e c a y i n g t h r o u g h emission of particles a n d n o t of g a m m a rays.
M a n y y - r a y s p e c t r a h a v e been i n v e s t i g a t e d f r o m (n, y) r e a c t i o n s m a k i n g
use of t h e r m a l pile neutrons. T h e best resolution h a s been o b t a i n e d w i t h a
m a g n e t i c p a i r s p e c t r o m e t e r (Ev > 3 M e V ) 1 ) a n d
a magnetic Compton
*) Paper read at the Amsterdam Nuclear Reactions Conference on July 4th, 1956.
I
1062
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CAPTURE REACTIONS
1063
spectrometer (Ev > 0.3 MeV)2). The low-energy spectrum has also been
investigated with scintillation spectrometers. The best results v~ere obtained for the lighter elements because at high Z the y-ray spectra get very
complicated. The (n, y) reaction has the disadvantage that the compound
state m a y have the spin values J i - 1/2 or J i + 1/2 or a mixture of these
two and thus is not uniquely determined (unless Jt = 0). This obviously
presents difficulties in the interpretation of the observed y-ray spectra.
Apparently it would be better to work with higher energy neutron beams
b u t so far intensity reasons have prevented the investigation of y-ray
spectra at single neutron resonances. Another disadvantage of the neutron
work is the fact that slow neutrons are captured in s-states, which prevents
spin determinations of lower states from y-ray angular distribution measurements.
Let us now consider (p, y) and (~, y) reactions. Resonances are observed
in an energy region which is limited on the low-energy side b y the condition
that the particle has to penetrate the Coulomb barrier, while on the highenergy side one should not go above the threshold for neutron emission. The
condition that resonances be resolved experimentally imposes another highenergy limit, strongly depending on A. These conditions confine the observation of (p, y) and (~, y) resonances to light nuclei up to A ~-~ 40. As
radiation widths are (with a few exceptions) of the order of at most a few
eV yields are generally small, which has prompted the use of scintillation spectrometers rather than that of magnetic spectrometers for y-ray
detection.
The y-radiation produced at a specific resonance m a y be investigated
through measurements of the y-ray spectrum and the angular distribution
of its components, and through coincidence and angular correlation measurements. To exploit fully the possibilities of the method it is of advantage to
investigate several resonances. Transitions to a specific lower level, which
are absent at one resonance, m a y be of great intensity at another resonance.
Valuable information on spins, parity and isobaric spins of the resonances
m a y be obtained b y exploring not only the radiation channel, but also the
channels corresponding to emission of particles. For instance the (p, y)
work is greatly strengthened b y an investigation of the (p, p), (p, p'y) and/or
(p, ~) reactions at the same resonances.
To illustrate the usefulness of angular distribution measurements for spin
determinations we take the 26Mg(p, y)lYA1 reaction. The 3/2- resonance at
Ep = 0.339 MeV is deexcited through E1 radiation to lower levels in 2~A1
with spins 1/2 +, 3/2 + and 5/2+. The y-ray angular distribution is of the form
1 + A cos2~ with A = -- 0.60 for J1 = 1/2, A = + 0.75 for J s = 3/2,
and A = -- 0.14 for J f = 5/2. These A-values differ so much that no very
good statistics are needed to decide on the spin of the final level.
Complications in the interpretation of the experimental material m a y
1064
P.M.
ENDT
arise from a number of causes, as from interference between partly overlapping resonances, and from mixing of different channel spins, of different
orbital momenta of the incoming particle, and of different y-ray multipolarities. Narrow, non-interfering, resonances are found at low bombarding
energies, and at not too low Z, say above neon. Mixing of channel spins m a y
be obviated either b y working with alpha particles, or, in (p, y) reactions,
b y bombarding zero spin initial nuclei. There are other cases where only one
channel spin can contribute. E.g. a 2- resonance level in the reaction
29Si + p (with J (Si ~9) = 1/2 +) can only be produced through a channel
spin with J = 1. In cases where channel spin mixing has to be considered
the channel spin ratio m a y often be determined b y measuring the angular
distribution of a y-ray transition proceeding from the resonance level to a
lower level with known spin. Once the channel spin ratio is known angular
distribution measurements of other y-rays deexciting the same resonance
can be used for the determination of unknown spins. Almost the same
considerations hold for mixing of orbital momenta of the incoming particle.
It is absent for zero spin initial nuclei, and often negligible in many other
cases. E.g. in the 29Si + p example given above one could have mixing
of p- and ]-capture, but barrier penetration at low bombarding energies
might bring down the ]-contribution to one percent or less of the p-capture
intensity.
We now still have to consider the mixing of y-ray multipolarities. Highly
excited nuclear levels chiefly decay through the emission of dipole radiation,
either E1 (unmixed), or M1 with possibly a small E2 admixture. This fact
m a y be used to determine the parity difference of initial and final state from
angular distribution measurements. If the measured angular distribution
does not agree with the theoretical prediction for pure dipole radiation initial
and final state have the same parity. However, in practice there are all
too many cases where experiment shows no deviation from the pure dipole
prediction, excluding conclusions concerning the parity difference. The best
w a y to determine parities is to observe the polarisation of the emitted
y-radiation, which has been done b y searching for photo-protons in irradiated
deuterium loaded nuclear emulsions. The method requires long exposures
and tedious track counting.
One could hope to obtain information on E1 or M l character from the
radiation width. If in (p, y) reactions the resonance width F is small compared to the target thickness, the radiation yield of the resonance is proportional to (2J + 1) FpF~/F, where J is the resonance spin, Fp the proton
width, and Fv the radiation width. If J is known from angular distribution
measurements and Fp >~/'r, the radiation yield determines F~. The uncertaintly in theoretical estimates of /'p m a y be a factor of I0 or 20.
A survey of measured radiation widths has been made b y W i l k i n s o n 8)
for A < 20. He gives I'v/E~ for some 100 cases, where the El or M1
CAPTURE REACTIONS
1065
character is known with fair certainty. The two groups have a cor~siderable
width and overlap largely. His only safe conclusion is that if Fr (eV)/E~
(MeV) > 0.02 the transition can be classified as E1 (but only ~-~ 40% of the
observed E1 transitions fulfil this condition). One can thus say that as yet
there is no unique criterion to distinguish between E1 and M1 transitions
from the radiation width. It would be useful to make an analogous survey
of the large amount of material available for nuclei with A > 20. Such a
Ep. 339 key
El:,./.54 keY
Ep. 661 key
8~898
15 13.&0 1~ 18
=_l
20 13 18 49
1/2
I1 17 22
41
Ep. ?23 keY
8 95
#2-
12 26 36 28
I13 3
*
(5.6) 3.00
3/2
t?) ~
°'
V2
16
8
i
i!
(2)
tl)
0.8/,2
:
3,ot~ s,~
(01
i 276p
I
! I
', V2
I t t
5''2¢
Fig. 1. Gamma-rays from the reaction a6Mg (p, y) ~VA1.
survey might also give more information on the isobaric spin selection rule
for E1 radiation (A T = i 1 when Tz = 0), which, at the moment, is still
very scanty.
1066
P.M. ENDT
As illustrations of the remarks made above some examples will be given
of experimental work on (p, ~) reactions of the last two years.
The 94Mg(p, ~) 2SA1 reaction has been studied in much detail at some ten
resonances b y L i t h e r l a n d , P a u l , B a r t h o l o m e w , and G o v e 4 ) . They
have collected evidence, notably from measurements of ~,-ray intensities
and angular distributions, for E2 transitions competing favourably with
M1 transitions of higher energy. The interpretation of these anomalies in
terms of collective states in ~'SA1will be discussed more fully b y the authors
themselves.
Ep-5OOkeV
Ep.622 keV
Ep=675keV
Ep-760keV
79/~
?'7?/,
s.o~
.~
Ep-77BkeV
B.o,.3
~;
71°~
g$s
~5
z]
11
lS
12' 2S :11
SS
la,
27
~l I'-Ot"
m
3.7B
~6~ 3 - 5 0 8
~ 3.414
~J 3 . 2 9 2
c3~ 3.131
i
i
I
I
I
(½)
I I
-T,°T
~ 2.235
J
o~ 1.267
,=
i
•
is
:4
31p
Fig. 2. Gamma-rays from the reaction a0Si (p, 7) sip.
The interesting nucleus 26A1 with its long:lived T = 0, J --- 5 + ground
state and an isomeric T = 1, J -- 0 + first excited state at 230 keV has been
investigated with the ~SMg(p, ~)26A1 reaction. From angular distribution
CAPTURE REACTIONS
1067
measurements G r e e n , S i n g h and W i l l m o t t 5) could confirm the spin
assignments, which had been suggested from intensity considerations by
K l u y v e r , v a n d e r L e u n , and E n d t 6 ) and by K a v a n a g h , Mills,
and S h e r r 7). Some resonances seem,to decay almost only to T ---- 0 states,
while other resonances feed only T ----- 1 states, which suggests the operation
of the E1 isobaric spin selection rule. At M.I.T. B r o w n e s) has recently
succeeded in detecting an alpha-particle group from the 2sSi(d, ~)26A1
reaction corresponding to a transition to level (I), w.t~l~ transition is
forbidden by isobaric spin selection rules. The intensity is generally small
but at certain angles and deuteron energies it m a y become comparable to the
groundstate transition. Analogous results were obtained for the 160(d, ~)14N
reaction.
From angular distribution measurements 9) at four resonances in the
26Mg(p, ~)27A1 reaction spins have been determined of eight levels in 27A1
below 4.1 MeV (see Fig. 1).
The same breakdown of isobaric spin selection rules which was mentioned
above for the 160(d, ~)14N and 2sSi(d,,t)~6Al reactions, has now also been
observed lO) for the ~2S(d, ~)s0p reaction. Transitions to the ground state
and to the first excited state at 690 keV were observed with about equal
intensities, although (p, ~) angular distribution measurement~ Lll) are o n l y
consistent with an assignment of J = 1+ (and probably T = 0) to the
ground state and of J = 0 + (and probably T = 1) to the first excited state.
Magnetic analysis 12) of protons scattered inelastically from phosphorus
has yielded the excitation energies of six levels in 31p below 3.7 MeV (see
Fig. 2). Measurements at Chalk River 13), Liverpool, and Utrecht of angular
distributions of ~,-rays emitted in the 30Si(p, y)31p reaction have shown
that level (I) has certainly spin 3/2 while level (2) has very probably spin
5/2. Level (2) is deexcited through a E2 transition to the J = 1/2 ground
state rather than by a M1 transition to level (1). The same spin order has
been observed 14) for the three lowest states in ~'gSi, where also level (2)
is deexcited by an E2 cross-over transition rather than by a M1 cascade.
Again this suggests collective motion effects.
Short communications directly /ollowing this paper were read by Green,
p. I139, Gore, p. 1141 Paul, p. 114o and Akhiezer, p. 1176 o/this volume.
Received 13-7-56.
REFERENCES
l) K i n s e y , B a r t h o l o m e w , and W a l k e r , Phys. Rev. B3 (1951) 519, and Phys. Rev. B5 (1952)
1012.
2) G r o s h e v , A d y a s e v i c h and D e m i d o v , International Conference Geneva (1955), and A. M.
D e m i d o v , private communication to C. M. B r a a m s .
3) W i l k i n s o n , D. H., Phil. Mag. 1 (1956) 127.
1068
CAPTURE REACTIONS
4) L i t h e r l a n d , Paul, B a r t h o l o m e w and Gove, Phys. Rev. 102 (1956) 208.
5) Green, S i n g h and W i l l m o t t , Proe. phys. Soe. A 6 9 (1956) 335.
6) IKluyver, Van d e r L e u n and E n d t , Physica 20 (1954) 1287.
E n d t , K l u y v e r and v a n der Leun, Physiea 20 (1954) 1299.
7) K a v a n a g h , Mills and Sherr, Phys. ,Rev. 87 (1955) 248.
8) B r o w n e , C. P., Bull. Am. phys. Soc. I (1956) 212.
9) V a n d e r Leun, E n d t , K l u y v e r and V r e n k e n , unpublished.
I0) Lee, L. L. and Mooring, F. P., Bull. Am. phys. Soe. I (1956) 281.
II) B r o u d e , Green, S i n g h and W i l l m o t t , Phys. Rev. 101 (1956) I052, and Van d e r Leun,
V a n L o e I and Muller, unpublished.
12) P a r i s , C. H. and E n d t , P. M., unpublished.
13) P a u l , B a r t h o l o m e w , Gove and L i t h e r l a n d , Bull. Am. phys. Soc. I (1956) 39.
14) B r o m l e y , G o r e , L i t h e r l a n d , P a u l and A l m q v i s t , Bull. Am. phys. Soc. I (1956) 30.