This work was supported by the National Science Foundation Grants NSF PHY 78-22774 A03, NSF PHY 81-14339, and by Indiana Universit

Collins, J.C.

Daehnick, W.W.

Foster, C.C.

Friesel, D.L.

Hall, J.R.

Jacobs, W.W.

Jones, W.P.

Kaitchuck, M.D.

Schwandt, P.

Stephenson, E.J.

English

IUScholarWorks

LIGHT-ION SCATTERING 
MEASUREMENTS OF X2 AND OTHER RESULTS IN THE ANALYSIS OF d + 5 8 ~ i  ELASTIC SCATTERING 
E.J. Stephenson, J.C. Collins, C.C. Foster, D.L. Friesel, J.R. Hall, W.W. Jacobs, 
W.P. Jones, M.D. Kaitchuck, and P. Schwandt 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
W.W. Daehnick 
University of Pittsburgh, Pittsburgh, Pennsylvania 15260 
During 1981, measurements have been completed Gaussians was chosen to match the deuteron 
of the tensor analyzing powers Ayy and X2 = (2Axx wavelength, and their width was chosen to ruinimize 
+ A ~ ~ ) / ~ T  in the elastic scattering of 80 MeV oscillations in their sum. Only the strengths were 
deuterons from 58~i. All of the elastic scattering varied to improve agreement between the calculation 
measurements, including the cross section and and the data. The resulting calculation is a 
vector analyzing power Ay, are shown in Fig. 1. 
The new measurements of Ayy are large near 21°, 
compromise that favors good reproduction of the 
cross section and vector analyzing power (the solid 
showing an effect of interference that is also curve in Fig. 1). The cross section minima and 
prominent in Ay. The measurements of X2 were made large angle slope are well-reproduced, as is the 
on a special scattering table set at 54.7' to the patteru of the oscillations in Ay. The large Ayy 
horizontal plane (described in Ref. 1). To first values near 21' are reproduced, but the calculation 
order, X2 does not depend on spin-orbit  force^,^ overestimates the oscillatory pattern at larger 
and is expected to be a sensitive test of the angles. No tensor potentials were included in this 
presence of tensor potentials between the deuteron fit, and the structures in Xg, which depend to 
and the nucleus.3 The measurements of X2 show first order on those terms, are not reproduced. 
little structure, and are about half the size of The "arbitrary" potential is depicted in Fig. 
measurements at 56 M ~ v . ~  At large angles they are 2 by the cross-hatched bands corresponding to 
much smaller than the predictions of Ref. 3. one-standard-deviation errors in the potential. 
While most of the general features of the data The width of the bands was computed from the 
shown in Fig. 1 can be reproduced with global diagonal elements of the error matrix of the fit. 
optical potential calculations, significant (Although correlation coefficients were not large, 
improvements can be made if the potential they may alter the error band in a complete 
parameters are adjusted. It was found that the use calculation.) The solid curve is a "best-fit" 
of a squared Woods-Saxon form for the radial potential using traditional radial shapes. There 
dependence of the real central potential was are significant differences. The real central 
significantly better than a Woods-Saxon form. This potential is more shallow in the surface and deeper 
led to the use of an "arbitrary" shape composed of in the interior. The imaginary aud spin-orbit 
a series of Gaussian functions added to the 
traditional potential. The spacing of the 
parts seem well-reproduced by the traditional 
shapes. The data determine the real parts of the 
potential to a much higher precision than the 
imaginary parts. This is an artifact of rainbow 
scattering, in which the real parts of the 
potential play a dominant role. 
Most analyses4 of the effects of tensor 
potentials in deuteron elastic scattering have 
found that the TR potential is predominantly 
imaginary. Adding such a potential to our 
calculation (with half the strength) serves to 
reproduce some of the diffractive structure of the 
Figure 1. Measurements of 
the cross section (ratio to 
Rutherford), vector (A ) , 
and tensor (Ayy and x2Y 
analyzing powers for 80 MeV 
deuterons elastically 
scattered from 58~i. The 
optical model calculations 
employ the "arbitrary" 
potential displayed in Fig. 
2. 
measurements of X2 (see Fig. 3). Contrary to 
experience at lower energies, such a potential has 
a profound effect on other analyzing powers. The 
vector analyzing power has no values larger than 
0.8 and the Ayy tensor analyzing power is 
noticeably reduced in magnitude. These differences 
occur primarily in the region beyond the rainbow 
angle, in a range of momentum transfer not seen in 
lower energy measurements. 
It has been previously reported that microscopic 
80 MeV 
units: MeV, fm 
Figure 2. Comparison between the "best-fit" potential using traditional radial shapes (solid line), and the error 
band associated with an "arbitrary" potential. Beyond 6.5 fm, the real central potentials are multiplied by 10 to 
make the differences visible. 
calculations of deuteron elastic scattering that 
include coupling to break-up states7 provide a 
surprisingly precise reproduction of the measurements.1 
d + 5 8 ~ i  80 MeV The calculations for ~2 are shown in ~ig. 4 .  They are 
in general agreement with the measurements and tend to 
C support the microscopic calculation. Figure 4 also I contains predictions for &, which may be measured if 
the quantization axis of the polarized deuteron beam is 
placed in the scattering plane at 45' to the beam 
momentum. Unlike X2, large differences are seen 
between the predictions of the microscopic model and 
Measurements of 4, that followed the solid curve would 
constitute evidence that the optical model is incapable 
Figure 3. Measurements of X2 and an optical model of successfully reproducing deuteron elastic scattering 
calculation including a TR potential of half the 
strength of the one reported in Ref. 4. data. 
d t ' * ~ i  80 MeV 
0.4 
1) C.C. Foster, J.C. Collins, D.L. Friesel, 
J.R. Hall, W.W. Jacobs, W.P. Jones, M.D. 
Kaitchuck, P. Schwandt, E.J. Stephenson, 
and W.W. Daehnick, IUCF Scientific and 
Technical Report 1980, p. 71. 
2) D.J. Hooton and R.C. Johnson, Nucl. Phys. 
A175, 583 (1971); R.C. Johnson, Nucl. Phys. 
-
A293, 92 (1977). 
-
3) E.J. Stephenson, C.C. Foster, P. Schwandt, 
and D.A. Goldberg, Nucl. Phys. A359, 316 
(1981). 
4) K. Hatanaka, M. Nakamura, K. Imai, T. Noro, 
H. Shimizu, H. Sakamoto, J. Shirai, T. 
Matsusue. and K. Nisimura. Polarization 
Phenomena in Nuclear Physics - 1980 
(AIP ~onf.Pr- 69) p. 478. 
5) W.W. Daehnick, J.D. Childs, and Z. Vrcelj, 
Phys. Rev. C 2, 2253 (1980). 
6) I. Brissaud and M.K. Brussel, J. Phys. G. 
3, 481 (1977). 
- 
7) G.H. Rawitscher and S.N. Mukherjee, Nucl. 
Phys. E, 90 (1980). 
Figure 4. Measurements of X2 and calculations of 
X2 and &, using a microscopic model of Ref. 7 
(solid curve) and an optical model with and without 
(dashed and dotted) the real TR potential of Ref. 
3. 
MEASURENENT OF THE RELATIVE SIGN OF NEUTRON (%) AND PROTON (Mp) TRANSITION MATRIX ELEMENTS FOR THE 2+2 STATE 
IN ~i BY INELASTIC ALPHA-PARTICLE SCATTERING. 
A. Saha, K.K. Seth and D. Barlow 
Northwestern University, Evanston, Illinois 60201 
H. Nann and W.W. Jacobs 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
One of the most exciting recent developments in excitations. In inelastic scattering, the cross 
the study of nuclear structure has been the section for the transition to an excited state can be 
appreciation of the isovector characteristics of described in terms of separate matrix elements for 
nuclear excitation. A number of different experimental proton and neutron excitations, P$ and h, 
techniques have been developed to examine the separate respectively, or in terms of isoscalar and isovector 
roles played by neutrons and protons in the nuclear matrix elements, Mo=M,+Mp and MI=%-$. The cross 


Measurements of X_2 and Other Results in the Analysis of  d + 58-Ni Elastic Scattering

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Measurements of X_2 and Other Results in the Analysis of d + 58-Ni Elastic Scattering

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