This work was supported by the National Science Foundation Grant NSF PHY 78-22774 A02 & A03 and by Indiana Universit

Collins, J.C.

Daehnick, W.W.

Foster, C.C.

Friesel, D.L.

Goldberg, D.A.

Hall, J.R.

Jacobs, W.W.

Jones, W.P.

Kailas, S.

Kaitchuck, M.D.

Schwandt, P.

Stephenson, E.J.

English

IUScholarWorks

LIGHT-ION SCATTERING 
FEATURES OF THE ANALYZING POWERS 
IN DEUTERON ELASTIC SCATTERING NEAR 80 MeV 
E.J. Stephenson, J.C. Collins, C.C. Foster, D.L. Friesel, J.R. Hall, 
W.W. Jacobs, W.P. Jones, S. Kailas, M.D. Kaitchuck, and P. Schwandt 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
W.W. Daehnick 
University of Pittsburgh, Pittsburgh, Pennsylvania 15260 
D.A. Goldberg 
University of Maryland, College Park, Maryland 20742 
the differential cross section and vector analyzing I d+"Ni I 
10 I 
power for 80 MeV deuterons elastically scattered from 
5 8 ~ i  back in angle to 112'. To this we also added new 
measurements of the tensor analyzing power Ayy. The 
results of these measurements are shown in Figure 1. 
This experiment was motivated by earlier 
experiments1) where the more forward angles were 
measured. In those experiments it was apparent that as 
the angle increased, the diffraction pattern in the 
vector analyzing power became less pronounced and the 
analyzing power itself was rising toward unity. This 
effect was coupled with the observation of an 
enhancement in the cross section near 40" followed by a 
smooth exponential decline at larger angles. These 
latter effects have been recognized for some time as 
signatures of rainbow scattering, and have been 
observed predominantly with 3 ~ e  and 4 ~ e  projectiles.2) 
When the effects of the spin-orbit potential are 
considered within the context of the rainbow-scattering 
picture, it becomes apparent that large analyzing 
powers are expected.3) Each projection of the deuteron 
spin along an axis perpendicular to the scattering 
plane may be considered independently.4) Then, in the 
presence of a spin-orbit potential, the spin-up 
deuterons see the strongest attractive force in the 
surface region of the nucleus, and tend to follow 
trajectories where they bend towards the nucleus, 
During the past year we extended measurements of 
MeV 
I I I 1 I 
K Q  I 
Figure 1. Measurements of the cross-section ratio to 
Rutherford, and the vector (Ay) and tensor (Ayy) 
anal zing powers for 80 MeV deuteron elastic scattering 
on ~lNi. The calculations are from an optical-model 
program with potential shapes given by the global 
analysis of Daehnick. 5 ,  
and tend to follow trajectories where they bend towards 
the nucleus and emerge at large angles on the opposite 
side. The dominance of back-angle scattering by 
spin-up deuterons gives values of Ay and Ayy near 
unity. The extension of the measurements on 5 8 ~ i  was 
undertaken to explore the signatures of rainbow 
scattering and to observe saturation of the vector and 
tensor analyzing powers. In the past, extensions of 
the measurements well beyond the rainbow peak have 
model description for the deuteron optical potential 
in terms of nucleon-nucleus optical potentials is 
useful as a general guide, but does not produce 
detailed agreement with model prescription for the 
deuteron optical potential the measurements. Such a 
calculation is shown by the dashed curves in Figure 2. 
The nucleon-nucleus potentials were taken from the 
analysis of Becchetti and ~reenlees.~) New Ayy 
measurements at forward angles have been added to this 
proven useful in determining the radial shapes of the figure for completeness. Generally, the 
phenomenological optical-potential components, even in phenomenological optical potential requires more 
to the nuclear half-density radius.2) The longer-term absorption, a less diffuse spin-orbit term, and 
aims of the experiment are to provide a complete set of substantially weaker tensor terms. As seen in Figure 
analyzing power measurements for deuteron elastic 2, such a potential overestimates the large-angle cross 
scattering at intermediate energies, and to use that 
set to investigate the spin-orbit and tensor components 
of the deuteron-nucleus interaction. 
The extended measurements in Figure 1 show clearly 
the smooth exponential decline in the cross section 
associated with rainbow scattering. Both the Ay and 
A,,,, analyzing powers become smooth and saturate near 
unity, the largest value of Ay being 0.97 2 0.01 and of 
A,,,,, 0.98 f 0.02. This is the largest vector analyzing 
power ever observed for deuteron scattering. 
The curves in Figure 1 are optical-model 
calculations using the global prescription of 
~aehnick. 5 ,  The potential shapes were determined from 
fits to forward-angle measurements of the cross section 
and vector analyzing power. They reproduce the 
measurements quite well in that region. At large 
angles, the calculated vector analyzing power is too 
small, and the tensor analyzing power too large. 
Attempts to correct this deficiency have met with only 
limited success so far, and investigation of the 
problem will continue. 
section by a factor of two and shows diffraction 
patterns in the analyzing powers that are much too 
small. 
Starting from this point, Rawitscher and 
~ukherjee~) have included channel-coupling to deuteron 
breakup states. In this calculation, the 
neutron-proton continuum is divided into several energy 
bins, each of which is treated as a separate state. 
Relative neutron-proton angular momenta of 0 and 2 are 
included. Their calculation for deuteron elastic 
scattering is shown by the solid lines in Figure 2. 
The effects of channel-coupling are large. The 
cross section is reduced a factor of two, and the 
analyzing powers become more diffractive and more 
positive. The agreement with the cross section is 
comparable at forward angles with the agreement 
provided by the optical model. In the region of the 
exponential decline, the reproduction by the 
channel-coupling calculation is better. The 
calculation also does well with Ayy, successfully 
reproducing the positive-going excursions between 10" 
It has been known for some time that the folding- and 40°, and the magnitude at angles less than 90". 
beam = 80 MeV 
Figure 2. The measurements are the same as in Figure 1. The dashed curves are optical model calculations using a 
folding-model deuteron potential. The solid curves use the same potential but include coupling to deuteron 
breakup states. 
The general shape of the vector analyzing power is interaction) is coupled in explicitly. The high 
given, but the differences between the calculation and quality of the agreement also suggests that this is a 
the measurement are substantial at forward angles. nearly complete microscopic description. 
This microscopic treatment of the deuteron-nucleus 1) C.C. Foster et al., IUCF Scientific and Technical 
Report, 1979, p. 53. 
interaction is considerably more successful at this 
2) D.A. Goldberg, S.M. Smith, and G.F. Burdzik, Phys. 
energy than at lower bombarding energies. 7, Rev. C g ,  1362 (1974). 
This also represents the first successful 3) E.J. Stephenson, C.C. Foster, P. Schwandt, and D.A. 
Goldberg, to be published in Nucl. Phys. 
comparison between such a calculation and a tensor 
4) R.C. Johnson and E.J. Stephenson, to be published. 
analyzing power. This result suggests that the 
5) W.W. Daehnick, J.D. Childs, and Z. Vrcelj, Phys. 
derivation of a deuteron-nucleus potential through the Rev. C g ,  2253 (1980). 
folding model is sound, provided that the breakup 6) F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182, 
1190 (1969). 
channel (the new feature not already included in the 
7) G.H. Rawitscher and S.N. Mukherjee, Nucl. Phys. 
nucleon-nucleus A342, 90 (1980). 
+ 
MEASUREMENTS OF THE TENSOR ANALYZING POWER, X2, FOR 58~i(d,d)58~i AT 80 MeV. 
C.C. Foster, J.C. Collins, D.L. Friesel, J.R. Hall, W.W. Jacobs, W.P. Jones, 
M.D. Kaitchuck, P. Schwandt, and E.J. Stephenson 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
W.W. Daehnick 
University of Pittsburgh, Pittsburgh, Pennsylvania 15260 
As part of a detailed study of elastic deuteron progress. Angular distributions of cross sections, 
scattering from 5 8 ~ i  at Ed = 80 MeV, measurements of a(8), vector analyzing powers, Ay(0), and the tensor 
the tensor analyzing power X2 a 2Axx + Ayy are in analyzing powers, Ayy(0), have been measured in 


Features of the Analyzing Powers in Deuteron Elastic Scattering Near 80 MeV

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Features of the Analyzing Powers in Deuteron Elastic Scattering Near 80 MeV

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