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NATIONAL QUREAU OF STANDARDS -1963
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Paper to be subinitted for publication in the Proceedings of the International
Conference on Polarization Phenomena of Nucleons, Karlsruhe, Germany
September 6-10, 1965.
Conf.650928-7
.
OCT © 1965

Polarization Studies at the Oak Ridge Isochronous Cyclotron*
E. E. Gross, R. H. Bassei, L. N. Blumberg, *
A. van der Woude,' and A. Zucker
Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA
LIIA
IN ICHISCE ADSIZACIS
DI
Two polarization studies were undertaken with the Oak Ridge
Isochronous Cyclotron (ORIC) to test the optical model as a description
of elastic proton scattering and polarization near 40 MeV. Emphasis
was placed on demanding simultaneous fits to both the differential
cross section data and the polarization data over large angle regions.
In the first study, the polarized proton facility at ORIC was
used to measure the polarization of elastically scattered 40-MeV
protons from 12c, 40ca, 58ni, 90 Zr, and 208 Pb at 5° intervals from
10° to about 120° (lab). The differential cross section for the elastic
scattering of the unpolarized proton beam from the same targets was
also measured at every 2.5º , from 10° to 170° (lab). These data were
then fitted by an optical-model potential based on Woods-Saxon shape
parameters and including a complex spin-orbit interaction of the
Thomas type. The parameters which have been found to best represent
the data are shown in Table 1, together with the form of the potential
*Research sponsored by the U. S. Atomic Energy Commission under
contract with the Union Carbide Corporation.
*Present address: Harvard University, Cambridge, Massachusetts.
#Present address: University of Groningen, The Netherlands.
used and the x values for each fit. Also included are the parameters for
59co, 68 Zn, and 120 sn which are based on fitting cross section data only;
the ground state was not sufficiently resolved for these isotopes to justify
complete confidence in the polarization data.
The parameters in Table I reproduce the data satisfactorily for
all targets, except for 12C beyond 90º and for 40 ca beyond 130°. The
simultaneous fitting of cross section data and polarization data was found
to severely restrict the parameters, as evidenced by the low value of
x" for Co, Zn, and Sn with no polarization restriction. Although we are
continuing to gather more data and to obtain a more consistent set of
parameters, we can say that the general trend of v. with A suggests the
presence of an (N - Z)/A dependence of the real central well depth for
scattering at 40 MeV. In general, best fits are obtained by including
both volume and surface absorption. The present analysis also indicates
a spin-orbit well depth of 4 to 6 MeV and geometrical parameters
smaller than the real central well. In addition, the radius of the real
potential r. appears to be slightly smaller than the radius r' of the
imaginary potential.
In the second study we examined the energy dependence of optical-
model parameters for 40 ca. Polarization data were obtained over the
same angular interval as for the cross section data (10° to 170°). Results,
to date, include measurements at 35.8, 40.0, and 45.5 MeV. The
experimental polarization data and the best optical model fits obtained
so far are presented in Fig. 1. As before, these results represent
a simultaneous minimum in x for fitting cross section and polarization
data, with the added restriction of fixed geometrical parameters at all
سا
three energies. The fits are quite good out to about 130° for both cross
section and polarization, but beyond this angle the model used here apparently
breaks down for *° Ca. Fits can be obtained over the entire angular range
for cross section or polarization data alone, but we have been unsuccessful
so far in obtaining a good fit if both sets of data are treated simultaneously.
The parameters represented by the curves in Fig. 1 imply an energy
dependence of the real central well depth of -0.26 MeV per Me V increase
in proton energy. This is in good agreement with the findings of Perey'
at lower energies.
ORNL-DWG 65-8774
REFERENCES
1. L. N. Blumberg, E. E. Gross, A. van der Woude, and A. Zucker,
to be published in Nuclear Instruments and Methods.
2. F. G. Perey, Phys. Rev., 131, 745 (1963).
"
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''
Table I. Optical model parameters from least squares search of elastic cross section ind polarization data for 40-MeV proton.
:
580
120
42.0
590
6821
9027
1 2051
208 pb
V. (MeV)
40ca
41.2
1.23
42.7
44.6
49.2
47.2
49.0
54. 3
*o (F)
1. 20
1. 18
1.17
1.13
1.19
1.15
1.15
(F)
1.25
1.25
1.25
1.20
1.25
1.25
1.25
1. 25
0.68
0.77
0.72
0.75
0.80
0.56
0
5.0
1.20
0.69
4.0
4.1
7.5
6.6
5. 1
0.69
0
5.9
1.20
1.20
0.71
2.8
5.2
2.0
1.1
2.7
4.0
12.6
1.20
1.20
1.16
1.40
1. 34
1. 35
W. (MeV)
W (MeV)
ro' (F)
a' (F)
Vs (MeV)
W. (MeV)
s (F)
1.25
0.60
0.72
0.78
0.71
0.60
0.66
0.62
4.0
4.0
3.&
3.8
3.8
7.0
5.9
5.8
5.7
- 4.5
0
-0.07
0.2
0.4
-1.5
1. 20
1.06
1.15
1.15
1.06
1.05
1.05
1.11
1.13
0.56
0.62
0.60
0.84
0.67
0.69
0.75
0.50
4319
421
128
309
316
316
3300
659
213
187
238
543
151
680
V6Y = V - VIII - SW.- 4wb ametit
IV. * Walte de . i
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ORNL-DWG 65-8796

45.5 MeV
40.0 MeV
PIOC.M.!
35.8 MeV
0
20
40
60
120
140
160
180
80 100
C.M. (deg)
Figure I. Polarization for elastic proton scattering from *°Сa for 35. 8-,
40. 0-, and 45.5-MeV protons. Solid curves result from optical
model fits to both cross section and polarization data.
.
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VIET
END
DATE FILMED
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