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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
ORNu-p-2117
Cont-660306-5'
CFSTI PRICES
MAY 10 1960
H.C. $ 1.00; MN 50
An Investigation of (p,n) Reaction Mechanism
via Isospin Analog Resonances
..
Turizm

RELEASED FOR ANNOUNCEMENT
H. J. Kim and R. L. Robinson
Oak Ridge National Laboratory
Oak Ridge, Tennessee
IN NUCLEAR SCIENCE ABSTRACTS
The isobaric analogues of low-lying bound states observed by (d,p)
reactions are observed as sharp resonances in proton elastic scattering
as well as in proton induced reactions such as (p,p') and (p,n). For
medium weight nuclei (A ~ 90) the analogue states are observed in the
region of excitation energy where the non-resonant background cross-
section is due mostly to compound nuclear reactions. Because these
analogue states are well separated and fall in the region of densely
populated compound nuclear states of normal isobaric spin, one can in-
vestigate certain aspects of the non-resonant, background reaction
mechanism by studying the effect of the presence of the analogue state
on the reaction mechanism.
Thus we have investigated the excitation
functions and the angular distributions of neutron groups produced by
the (p,n) reactions on sr and 59y in the energy region of well estab-
lished" 05/2 isolated resonances. These resonances are due to the iso-
baric analogues of the de la neutron states of 89sr and 9°y. The neutron
groups feeding the ground state of 88y, ground state of S9zr, and 590 kev
state of Zr were detected by time-of-flight methods in conjunction with
a pulsed proton beam accelerated by the ORNL 5.5 MeV Van de Graaff
Research sponsored by the U.S. Atomic Energy Commission under contract
with Union Carbide Corporation.
LEGAL NOTICE
This report was prepared as an account of Government sponsored work. Neither the United
Statos, por the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completoners, or usefulness of the information contained in two report, or that the use
of any information, apparatus, method, or process disclos d in the report may not Infringe
privaloly owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
uso of any information, apparatus, motbod, or process disclosed in eblo report.
As used in the above, "person acting on behalf of the Commission" includes any en-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such omployse or contractor of the Commission, or employee of such contractor prepares,
disseminator, or provides acceso to, any Information pursuant to his employment or contract
with the commosion, or hio employment with such contractor,
accelerator. Thin targets f & keV for 5 MeV protons) of normal iso-
topic abundance evaporated on thin Pt backing were used.
In the vicinity of an analogue state, the (p,n) reaction amplitude
to a specific final state is T(ilf) = T, + T, where T, is the non-
resonant, background amplitude and T, is the additional amplitude needed
to account for the presence of the analogue state. We assume T, to be
given correctly by Robson's theory and we shall use the same notation
as in Ref. 2. Since the analogue state is isobaric spin forbidden to
decay via (p,n) reactions, T, is entirely due to "mixing" of the compound
states with the analogue state.
The reaction amplitude is
T(1|f) = TB + FAV
EA-4-E
where I
-1.
A
E.-E-1(1/2)
buth's are elements of the collision matrix with J = Ī+ js = Îę + in and
appropriate parity. Its tps jego dn are the spins of the initial nucleus,
final nucleus, total particle spin & + s of incident proton and emitted
neutron, and Jh is the spin and parity of the analogue state. In this
investigation J is the result of adding a d5/2 proton to the initial
nucleus. Assuming is to be insensitive to small changes in the inci-
dent energy of order r, the differential cross-section near the analogue
state is
O(E;0) = op(0) + len(8) 94(0) + Int (0; 0)
(1
:
where $960) = orele de
where
C
prima
JAJI
CA(0) = cluma", e
02
and
= 2 Re
03nt (838) = 2 ** { "tn u'a" John
= 2 {ref} [,(0) + Rez] + 2 {1mp } IME
(2)
where
A = {Refc} + 1 {Impa] and c [ vA" JT* = Reg + 1 (mm:).
JEJA
The energy dependence of o(E;e) near E, is determined by the energy i.
pendence of 1FA1%, {Ref} and {Impa]. We note that I fal is symmetz* :*
about E, and {Refa} and {Imf} are as ymmetric about Ex Experimentai
(p,n) excitation functions are shown in Figs. 1, 2 and 4. The asymmetric
nature of the cross-section about the resonance energies can be seen in
these figures. If the random phase assumption concerning u A is made,
then Sot" JT* = 0 for y" + J," and
J.Te
o(E;€) = (g(@) + (1+y/® + 2 {Refa}} Ca(e)
(3)
A-4-E)2
= 0 (0) +
(E,-E)? + (1/22 - 1. olo)
One of the experimental excitation functions is compared to one
calculated using Eq. 3, and is shown in Fig. 3. The parameters A and I
were adjusted for a good visual fit to the experimental result and they
are also shown in the figure.
The calculated o(E;o) 's were averaged
over 8 keV energy internal in order to account for the 8 keV target
thickness.
Three resonances studied are superimposed in Fig. 4.
It is rather
striking to note that the shapes as well as the widths of the resonances
3
are very much the seme. From Eq. (3) it can be shown that the observed
width of the resonance is mainly determined by r if r < 141 and the
skewness to the high or the low energy side of E, is determined by the
sign of 1. Using the isobaric analogue resonance theory the ratio
141/17, where ra is elastic partial width, is about 100 and the sign
of A is determined to be negative for all three resonances. From Fig. 4
we can, therefore, infer that the spreading widths W = [- re are the
same for these 25/2 analogue states.
Jr*
Jan 2
If we take ƯA" ) uur = {U A I, which seems reasonable in view of
the preceeding resonance shape study, then we can proceed with the in-
quiry by studying the angular distributions of neutrons. At a given
incident energy the angular dependence of the neutron cross-section de-
caying to a specific final state is Ople) + KONA, where K is an angle
îndependent constant. Furthermore the analogue state is formed by coupling
a single jo = ja to the initial nuclear spin Ig. Therefore
where
Separating the kinematical factor of our from the dynamical one ano
becomes
+
Kico
Innj',v
x Thy, (JPA OPATIJA! M, (I 'n'IJA)Pr(e)
where t's contain all the dynamics of the reaction, R. are the coef-
ficients defined and tabulated by Satchler, and Prin are the Legendre
VS
polynomials.
In order to test the randomness assumption of t's, we have calcu.
lated one using Eq. (4) and the randomness assumption, i.e.,
tſipa, in, vindt*(3pa, 'n, "A] = It (3pa, in, um die By
bel where dj. is
the orbital angular momentum of the neutron. The calculated ole)'s are
compared with the experimental angular distributions in Figs. 5 and 6.
The on-resonance o(a) 's were obtained by simply adding suitably normalized
o(o)'s calculated by Eq. (4) to the off-resonance angular distribution
measured at the incident energies a few r's away from the resonance
energy. We have also ignored any contribution from the higher partial
wave than the lowest partial wave din.
If the randomness assumption is valid for U * , which is reasonable
JAT
in view of good fits shown in Figs. 5 and 6, it can be applied to all
relevant un (30. in) 's. Unäer this condition og(e)'s are symmetric
about 8 = 90° and become the cross-sections given by the Hauser-Feshbach
theory o(o), mWe have calculated on-resonance and off-rogonance
angular distributions using the Hauser-Feshbach theory and the additional
enhancement given by Eq. (4). The calculated o(s) are compared to the
experimental data in Figs. 5 and 6. . The magnitudes of the calcu-
lated o(0)'s are arbitrarily adjusted for good visual fits.
In conclusion we have demonstrated that the enhancement of the (p,n)
cross-section brought about by the presence of an isolated isobaric spin
analogue sta le can be used as a tool to investigate some aspects of the
reaction mechanism and to see if the randomness assumptions in the
statistical compound nucleus model are valid for (pen) reactions on
medium weight nuclei at incident proton energies of about 5 MeV.
-7-
References
1.
J. D. Fox, C. F. Moore, and D. Robson, Phys. Rev. Letters 12, 198
(1964); D. B. Ligłt body, G. E. Mitchell, and A. Sayres, Physics
Letters 15, 155 (1965); G. S. Mani and G. C. Dutt, Physics Letters
16, 50 (1965).
2. D. Robson, J. D. Pox, P. Richards, and C. F. Moore, Physics Letters
18, 86 (1965).
3. D. Robson, Phys. Rev. 137, 1535 (1965).
4. G. R. Satchler, Proc. Phys. Soc. (London) 56, 1801 (1953).
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r
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ORNL-DWG 66-1817

897 (p, n) 89 Zr g.s.
00=0
-ENERGY SPREADY
RELATIVE σ (Θ)
28 kev
. -
180 por copsi.
Ep=4.806 1 0.020 MeV Ep=5.010 + 0.020 Mev
TATRICT
OL
33.2
33.5
34.1
34.4
33.8
f (Mc/sec)
"
A
Fig. 1
-
1.
--TY
..!.-
A
ORNL-OWG 66-1818

88sr1p, n) 88 yq.s.
0 = 0°
ENERGY SPREAD
RELATIVE ole)
28 kev
C
En = 5.052 = 0.020 Mev
34.0
34.2
34.4
34.8
35.0
36.2
34.6
f (Mc/sec)
Fig. 2
ORNL-DWG 66-2459
2.8

897 (p, n) 89Zr g.s.
2.4
(ER +1A1-E12
2.0 -
AVERAGE OVER 8 kev
SER-E12+
A=-- 80 keV
T= 20 keV
ER=5.016 MeV
RELATIVE O (@=0°)
4.912
5.08
4.968 5.024
Ep (MeV)
Fig. 3
ORNL-DWG 66-1822

0=0°
o 88 Sr (p, n) 887.g.s.
07 (5/2+) → 5/2+→ 413/2-)
• 8910, n) 892r g.s.
1/2-15/2+) → 379/2(3/2)
La 89 y 1p, ) 89Zr* (590 kev) -
1/2-15/2+) ► 2- → 12-65/2+)
-
RELATIVE σ (Θ)
Noooo 6000
CAA
ENERGY
Fig. 4
ORNL-DWG 66-1849

B9yle, ni 89zr
1.0
In=3
-
in=5/2,712
0 (0) H.F. + OR W (0)
do
I see
RELATIVE σ (Θ)
Lo (o).F.
0.2
W (0)=1-0.16 P (0)-0.004 Palo)
0
30
60
90
c.m. (deg)
120
150
180
Fig. 5
ORNL- DWG 66-1824
1.4

89yle, n) 897r* (590 keV)
1.2
LO (O) H.F. + OR W (0)
RELATIVE σ (Θ)
0.4
O (O) H.F.
0.2
W(0) = 1 +0.98 P2 (0) +0.4.5 PA (0)
O
30
120
150
480
60 90
Oc.m. (deg)
Fig. 6
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