This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Byrd, R.C.

Carey, T.A.

Gaarde, C.A.

Goodman, C.D.

Horen, D.J.

Huang, W.

Kiang, G.C.

Marchlenski, D.

Rapaport, J.

Rybarcyk, L.J.

Sailor, B.

Sugarbaker, E.R.

Taddeucci, T.N.

Wagner, J.

Wang, Y.

English

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with our expectations from previous experience. The preliminary results with these cuts 
suggest that the GT to Fermi interaction strength ratios for l g ~ ( p , n )  and 3 9 ~ ( p , n )  are 
consistent with the ratios obtained from '4C(p,n)14N, using the 0+ -, I+ and O+ + O+ 
transitions as the references. 
1. J. Rapaport, C. Gaarde, J. Larsen, C. Goulding, C. D. Goodman. C. Foster, D. J. 
Horen, T. Masterson, E. Sugarbaker, and T. N. Taddeucci, Nucl. Phys. A431, 301 
(1984). 
WEAK INTERACTION MATRIX ELEMENTS AND (p,n) CROSS SECTIONS 
Y. Wang, C. Goodman, W. Huang and G.C. Kiang 
Indiana University Cyclotron Facility, Bloomington, Indiana 47408 
T.N. Taddeucci, R.C. Byrd, T.A. Carey, B. Sailor and L.J. Rybarcyk 
Los Alamos National Laboratory, Los Alamos, New Mexico 87545 
C.A. Gaarde 
Niels Bohr Institute, DK-2100 Copenhagen, Denmark 
D. J. Horen 
Oak Ridge National Laboratory, Oak Ridge, Tennessee 97891 
J. Rapaport 
Ohio University, Athens, Ohio 4 5701 
E.R. Sugarbaker, D. Marchlenski and J. Wagner 
Ohio State Uniuersit y, Columbus, Ohio 4 9210 
A proportionality between zero-degree (p,n) cross sections and GT (Gamow-Teller) 
and F (Fermi) beta decay matrix elements was demonstrated about a decade ago and 
has since been exploited as a quantitative measure of GT strength functions in order 
to better understand nuclear structure and to calibrate neutrino detectors. The (p,n) 
reaction can be used as a quantitative probe because the specific cross sections,' eGT 
and eF, show very little dependence on the structure details of the nucleus under study 
(eGT=oGT (p, n) /B(GT); eF=oF (p, n) /B(F)) corrected for phase space and momentum 
transfer). The general trend of the mass dependence of the specific cross sections is under- 
stood in terms of an inceasing distortion with higher mass. However, in detail fluctuations 
of as much as &SO% have been observed betweeen adjacent masses. These fluctuations are 
not understood. 
Only with the use of an empirically discovered relationship between the GT and F 
strengths in the reaction has it been possible to infer GT transition probabilities with 
greater precision than implied by the fluctuations. This relationship may be described as 
R~ = cGT/aF and R = Ep/Eo where Ep is the proton beam energy and E, is a constant, 
~ 5 5  MeV. This relationship allows one to normalize GT transition peaks in a spectrum to 
the easily observed IAS peak. This empirical relationship does not have firm theoretical 
underpinnings. 
The purpose of experiment 320 is to measure (p,n) cross sections for transitions with 
known beta decay strengths over a wide mass range, especially for odd-mass nuclei, in 
order to try to gain a better understanding of the fluctuations in the specific cross sections 
and the relationship between the GT and F strengths in the (p,n) reaction. 
The experiment determines the specific cross sections, CGT and CF, and the ratio 
R ~ = & ~ ~ / & ~ .  The ratio eGT/t?~ is determined more precisely since it is independent 
of target thickness and current integration. The empirical values of R for 7 ~ i ,  13j1*c, 
2 6 ~ g ,  3 7 ~ 1  and 4 2 ~ a ( p , n )  in 605 Ep 5200 MeV can be well represented by the relation1 
R = Ep/ E, where E0=55f 0.4 MeV. However, some unexpected fluctuations of the ratio R 
are observed. In order to have a better understanding the physics behind these fluctuations, 
more data of R for medium and heavy weight nuclei are needed. Unfortunately, very few 
cases exist of known GT matrix elements in transitions that are accessible to (p,n), and 
the cross sections for these transitions are small. 
The data shown here were taken with the stripper loop, which provides pulse separa- 
tions greater than 2 ps without much loss of average beam current. The incident proton 
energy Ep was 160 MeV and the flight path was 120 m. The background from wraparound 
is strongly suppressed compared to operation without the stripper loop with a pulse sep- 
aration of 120 ns. 
An energy spectrum for ' ~ i ( ~ , n )  is shown in Fig. 1, the two peaks correspond to 
the ground-state (gs) of 7 ~ e  and the first excited state where the excitation energy, E,, 
is 0.43 MeV. The energy resolution is about 300 keV in the combined spectrum for ten 
detectors. 
Kinetic Energy of Neutron (MeV) 
Figure 1. Neutron energy spectrum from '~i(p,n)  at 0". The two peaks correspond the 
transitions from the 312- ground-state of 7 ~ i  to the 312- ground-state of 7 ~ e  and 112- 
lat excited state (E,=0.42 MeV) in ' ~ e .  
The medium and heavy weight nuclei we studied in this experiment are 61V, l131n, 
'18Sn and 141pr. The previously measured and published data2 on 51~(p ,n )  were taken un- 
der poor conditions with a resolution of nearly 1 MeV. The IAS transition (Ez=6.61 MeV) . 
was not resolved from nearby strong GT transitions (E,=5.96, 5.83 and 5.56 MeV). In the 
present study with an energy resolution 300 keV, the IAS transition is well resolved from 
these nearby GT transitions. The transition from the 712- gs of "V to the 712- gs of 
61Cr is a well isolated, weak GT transition and an excellent case for comparing the GT to 
F cross sections. The energy spectrum of 61V(p,n) is shown in Fig. 2. 
The GT transition from the 9/2+ gs in li31n to the 7/2+ isomeric state in l13Sn at 
78 keV is more than 1 MeV away from the competing GT transition. The 1/2+ gs and the 
third excited 5/2+ state (E,=0.41 MeV) in l13Sn will not be excited to the zero-degree 
spectrum. The energy spectrum of 113~n(p,n) is shown in Fig. 3. 
The transition from the 0+ gs of ll8Sn to the 1+ gs of l18Sb (GT) is also resolved 
from the from nearby competing states. The transition from the 5/2+ gs of the I4lpr to 
the 3/2+ gs of 141Nd (GT) is about 1 MeV away from nearby GT transitions, therefore 
it can been resolved. However, this transition is weak and our spectrum contains only 77 
counts in that peak. The uncertainty resulting from the statistics, background subtraction 
and peak fitting for the GT transition is 23%. 
Kinetic Energy of Neutron (MeV) 
Figure 2. Neutron energy spectrum from " ~ ( ~ , n )  at OO. The peak at 158.5 MeV is the 
712- ground-state in ' l ~ r .  The peak at 151.9 MeV is the IAS transition. 
132 137 142 147 152 157 16.2 
Kinetic Energy of Neutron (MeV) 
Figure (9. Neutron energy spectrum from 1131n(p,n) at OO. The peak at 158 MeV is the 
7/2+ isomeric state in '13sn at 78 keV. The 1/2+ ground-state is not excited in the zero- 
degree spectrum. The peak at 146.4 MeV is the IAS transition; and it is above a giant 
GT transition. 
The empirical values R have been tabulated in Table I. In this Table, the B(GT) is 
the GT transition strength obtained from beta decay, and BpSn(GT) is the GT strength 
for (p,n) and it differs from B(GT) by a factor, (2Ji + I ) ~ , ~ , / ( ~ J ~  + l)(p,n), where Ji is 
spin of the parent state in beta decay or (p,n). In all cases, the Fermi transition strength 
was assumed to be B(F) = N-2. The aGT/aF is the ratio of the Gamow-Teller and 
Fermi transition cross sections, and the k(F) /k(GT) is the ratio of kinematic corrections, 
where k(F) and k(GT) goes to unity in the limit of zero momentum transfer. The values 
R are listed with corresponding uncertainties, which include statistics, their background 
subtraction and peak fitting. 
The observed R values are slightly higher than the value 2.91d~0.02 obtained using the 
relation E,/E,, (E, = 55 k0.4 MeV). Additional data to be taken at Ep=120 MeV should 
help to establish whether the apparent departures from the trend established from lighter 
even mass nuclei are real and whether they can be parameterized in terms of different 
values of E,. 
Table 1 Empirical Values of R 
Nuclei logft B(GT) Bp,n (GT) B(F) ~ G T  /OF k(F)/k(GT) R 
5 1 ~  5.3906k 0.0016~) 0.016Zk0.002 0.016Zk0.002 5 0.043Zk0.003 0.937 3.55k0.36 
l131n 4.65rfr 0 .12~) 0.087k0.042 0.070rfr 0.034 15 0.082rfr 0.009 0.887 3.95rfr1.56 
s n  4.524k 0.013~) 0.1 16k0.005 0.348k0.015 18 0.214k0.023 0.910 3.18k0.23 
l4'pr 5.25k O.Old) 0.022f 0.001 0.015rfr0.001 23 0.0096rfr0.0023 0.878 3.60Zk0.54 
a) Ref. 3, b) Ref. 4, c) Ref. 5 and d) Ref. 6. The B(GT) were calculated using Eq. 1.2 in Ref. 1 
7 
and coupling constant values are those recommended by Wilkinson . 
1. T.N. Taddeucci et al., Nucl. Phys. A496, 125 (1987). 
2. J. Rapaport et al., Nucl. Phys. A427, 332 (1984). 
3. R.L. Auble, Nucl. Data Sheets 23, 163 (1978). 
4. J. Lyttkens et al., Nucl. Data Sheets 33, 1 (1981). 
5. T. Tamura et al., Nucl. Data Sheets 51, 329 (1987). 
6. L.K. Peker, Nucl. Data Sheets 45, 1 (1985). 
7. D.H. Wilkinson, Nucl. Phys. A377, 474 (1982); P. Bopp et al., Phys. Rev. Lett. 56, 
919 (1986). 


Weak Interaction Matrix Elements and (p,n) Cross Sections

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Weak Interaction Matrix Elements and (p,n) Cross Sections

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