This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Bacher, A.D.

Berg, G.P.A.

Cupps, V.R.

Low, D.A.

Miller, D.W.

Olmer, C.

Opper, A.K.

Park, B.K.

Sawafta, R.

Stephenson, E.J.

Wissink, S.W.

English

IUScholarWorks

t Permanent address: Department of Physics, Bangalore University,Bangalore 560 001, 
India. 
1. N. Austern, Nucl. Phys. A292, 190 (1977). 
2. W.D.M. Rae, Ph.D. Thesis, Oxford University, 1976 (unpublished). 
3. K. Platchkov, J.B. Bellicard, J.M. Cavedon, B. Frois, D. Goutte, M. Huet, P. Leconte, 
Phan Xuan H6, P.K.A. de Witt Huberts, Phys. Rev. C25, 2318 (1982). 
4. P.C. Li, W.W. Daehnick, and R.D. Rosa, Nucl. Phys. A442, 253 (1985). 
5. A.E.L. Dieperink and I. Sick, Phys. Lett. 109B, 1 (1982). 
A TEST OF COPLANARITY AND FAR-SIDE DOMINANCE IN 
INTERMEDIATE ENERGY (d,p) AND (p,d) REACTIONS 
E.J. Stephenson, A.D. Bacher, G.P.A. Berg, V.R. Cupps, D.A. Low, D. W. Miller 
C. Olmer, A.K. Opper, B.K. Park, R. Sawafta, and S.W. Wissink 
I Indiana University Cyclotron Facility, Bloomington, Indiana 4 74 08 
In a recently published report'-2 on the '1%n(d,p)'17~n reaction, it was found that 
the current model of transfer reactions is particularly poor for well-matched 
j, = 4, - transitions. This model, based on the distorted wave formalism, treats the 
deuteron scattering wavefunction adiabatically3 (to include the effects of S-wave breakup), 
includes non-locality  correction^,^ and contains both the deuteron S- and D-states through 
a finite range calculation. The dynamics of (d,p) reactions produced by 80 MeV deuterons 
makes the reactions coplanar (the neutron orbital angular momentum lies preferentially in 
the plan defined by the asymptotic deuteron and proton momenta) and far-side dominated, 
at least insofar as the model calculations are reliable. These dynamics make sufficiently 
large differences among the various spin-dependent reaction amplitudes that only two are 
significant away from OO. This leads to redundancy relations among the spin observables 
that may be used as a test of the coplanar and far-side dominant features of the distorted 
wave model.5 
In the case of the j" = ;+ transition in "GSn(d,p)'17~n, only the deuteron vector (Ay) 
and tensor (Ayy) analyzing powers were available, so only the relationship 
Ayy = -2 - 3Ay could be tested. Although significant deviations were observed beyond 
the small ones present in the model calculations, it was noted that much of the model dif- 
ference from this calculation arose from the deuteron D-state. This raised the possibility 
that the remaining differences could be due to similar contributions from deuteron chan- 
nel tensor optical potentials or stripping from D-wave breakup states, neither of which 
is included in the model calculation. These same model calculations also showed that 
the relationship 3 p  + 1 = -2A,, connecting the deuteron tensor analyzing power with 
the outgoing proton polarization was relatively free of these complications. To make a 
useful precision measurement, it is best to measure the analyzing power in the time- 
reversed (p,d) reaction in place of the polarization. For this, a case must be found where a 
. . 
jn = ln - transition connects the ground states of two stable nuclei, such as 6 6 ~ n  and 
6 7 ~ n .  
Angular distribution measurements have been made for the cross section and vec- 
tor and tensor analyzing powers for the 66Zn(d,p)67~n reaction with 88.0 MeV polar- 
ized deuterons, and for the cross section and analyzing power (here quoted as p) for the 
6 7 ~ n ( p , d ) 6 6 ~ n  reaction with 91.6 MeV polarized protons. This ground state transition has 
Jn = $,en = 3, one unit of angular momentum smaller than the Sn case. 
Figure 1 shows the measured cross section angular distribution, along with calculations 
that include or omit the deuteron D-state. From the difference between these calculations, 
we may estimate where tensor potential and breakup effects might appear. The slope 
of the model calculation differs from the measurements, a fact that may reflect the use 
of optical potential parameters from the 11G~n(d,p)"7~n calculations of Ref. 1. Clearly 
Figure 1. Measurements of the cross sec- 
tion for the ground state transition in 
6"n(d,p)67~n. The model calculation 
with the solid (dashed) line includes 
(omits) the effects of the deuteron 
D-state. 
before any final conclusions are drawn, more appropriate potentials must be obtained. 
Like the ll%n(d,p) l17sn case, a comparison may be made with data for the rela- 
tionship Ayy = -2 - 3Ay. So as to compare similar things, the plots in Fig. 2 show Ay 
N 
and pseudo-Ay (Ay) composed from tensor analyzing power data through the relationship 
N 
Ay = (-2+Ayy)/3. These measurements bear a close resemblance to the " ' ~ n ( d , ~ )  l17sn 
measurements, thus illustrating that the problems with the model calculations transcend 
any one transition, and are likely to be general features of intermediate-energy (d,p) re- 
N 
actions. The difference, shown in the bottom panel of Fig. 2 as Ay - Ay, is clearly larger 
than the model value, but a part of it, especially _at large scattering angles, is due to effects 
of the deuteron D-state. The difference, Ay - Ay is always positive since it corresponds 
to the presence of a measurable cross section for spin up (md = 1 relative to the Madison 
convention y-axis) deuterons. 
The new information available with the 6%n(d,p) 67 zn measurements consists in a 
comparison between the outgoing polarization and the tensor analyzing power. This is 
66 
~ n ( d , p ) ~ ~ ~ n  88 MeV 
t I I I I I 1 1 I I 
Figure 2. Measurements of the vector an- 
alyzing power (A,), and the tensor ana- 
lyzing power (Ayy) replotted to simulate 
the vector N analyzing power through the 
formula Ay = -(2 + Ayy))/3. In the bot- 
tom panel is shown the difference Ay - 
iy. The model calculation with the solid 
(dashed) line includes (omits) the effects 
of the deuteron D-state. 
' ' ~ n ( d , ~ ) ~ ~ ~ n  88 MeV 
F i ~ u r e  3. Measurements of the outgo- 
ing proton polarization (p), and the tensor 
analyzing power (Ayy) replotted to simu- 
late the polarization through the formula 
p" = -(1 + 2Ayy)/3. The bottom panel 
shows the difference p - p". The model 
calculation with the solid (dashed) line in- 
cludes (omits) the effects of the deuteron 
D-state. 
shown in Fig. 3 in a fashion similar to Fig. 2. The top panel shows the polarization and its 
equivalent p" = - (1 + 2A,,)/3, along with the model calculations. Again, the difference is 
larger than the model value, as shown by the bottom panel of Fig. 3. In this case, however, 
the inclusion of deuteron D-state effects makes little difference in p - p". The N measured 
values are also closer to the model calculations than was the case for Ay - A,, suggesting 
the tensor potential and breakup effects may still have a role to play in accounting for 
these differences. 
A separate contribution to this reporte explores the possibility of large near-side am- 
plitudes which are absent in the distorted wave model. Such amplitudes could account for 
both the deviation in the difference functions and the oscillation pattern clearly present in 
all three polariztion observables. As plotted in Figs. 2 and 3, all interference patterns have 
a similar appearance, suggesting a common origin. An analysis similar to that in Ref. 6 
also reveals large near-side amplitudes. 
For this case, the transfer l ,  is one unit smaller than for 116~n(d,p)117~n. Here, 
N 
the difference functions show interference effects where the Ay - Ay measurements for 
" ' ~ n ( d , ~ )  l17sn show none.' This transition is less well momentum matched at the nuclear 
surface, hence the model near- and far-side amplitudes are more nearly equal. In this case, 
it appears that the "missing" amplitude has a far-side piece that creates an interference 
pattern with the model near-side component in the p - p" angular distribution. The spin- 
orbit potentials change the location of the resonance singularities in the semi-classical 
description of Ref. 6, and the measurements of p - p" for this case are the first indication 
that spin-orbit shifts are measureable for the same "missing" matrix element. These shifts 
appear in Fig. 3 as a difference in the period of the interference pattern between p or p" 
and their combination, p - p. 
In an effort to improve the model calculation, measurements were recently completed 
of proton elastic scattering from " ~ n .  These are shown in Fig. 4, along with a "best-fit" 
optical model calculation. The optical potential parameters are given in Table I, and follow 
the conventions of SNOOPYS. To obtain a correct model calculation for (d,p), we also 
need a folding model adiabatic potential for the deuteron wave function. Work on this is 
in progress. 
Table I: Optical Potential Parameters for p + " ~ n  Elastic Scattering at 91.6 MeV. 
V r a 
Coulomb 1.25 
Real Central 27.78 1.251 0.694 
Volume Imaginary 7.04 1.473 0.604 
Real Spin-Orbit 4.941 1.065 0.692 
Imaginary Spin-Orbit - 1.099 1.002 0.546 
67 Zn ( p,p) 6 7 ~ n  91.6 MeV 
lo4 
Figure 4. Cross section and analyzing 
power measurements for p + 6 7 ~ n  elastic 
scattering at  91.6 MeV. The calculations 
represent a "best-fit" optical model. 
The discrepancies between model and measurement values of the difference functions, 
Ay - Xy and p - g, indicate a significant shortfall of the distorted wave model. Additional 
evidence from the interference pattern suggests that at least the feature of far-side dom- 
inance is incorrect. However, the near-side amplitude may also be coplanar, and in the 
semi-classical limit of Ref. 6 it is. Work is continuing to understand the characteristics of 
the additional near-side strength and what physical processes produce it. Until such time 
as a more complete picture of transfer reactions emerges, the extraction of spectroscopic 
information based on model calculations is subject to substantial error. 
1. V.R. Cupps, J.D. Brown, C.C. Foster, W.P. Jones, D.W. Miller, H. Nann, P. Schwandt, 
E.J. Stephenson, and J.A. Tostevin, Nucl. Phys. A469, 445 (1987). 
2. E.J. Stephenson, V.R. Cupps, J.A. Tostevin, R.C. Johnson, J.D. Brown, C.C. Foster, 
W.P. Jones, D.W. Miller, H. Nann, and P. Schwandt, Nucl. Phys. A469, 467 (1987). 
3. G.L. Wales and R.C. Johnson, Nucl. Phys. A274,168 (1976). 
4. F.G. Perey and B. Buck, Nucl. Phys. 32, 353 (1962). 
5. E.J. Stephenson, R.C. Johnson, J.A. Tostevin, V.R. Cupps, J.D. Brown, C.C. Foster, 
J.A. Gering, W.P. Jones, D.A. Low, D. W. Miller, H. Nann, C. Olmer, A.K. Opper, 
P. Schwandt, J.W. Seubert, and S.W. Wissink, Phys. Lett. B 171, 358 (1986). 
6. E.J. Stephenson, R.C. Johnson, and J.A. Tostevin, contribution to this report. 
NATURE OF THE MISSING NEAR-SIDE AMPLITUDE IN CALCULATIONS 
OF INTERMEDIATE ENERGY (d,p) AND (p,d) REACTIONS 
E.J. Stephenson 
Indiana University Cyclotron Facaeilit y, Bloomington, Indiana 4 7405 
R.C. Johnson and J.A. Tostevin 
University of Surrey, Guildford, Surrey G U2 5XH, United Kingdom 
Model calculations of the cross section and analyzing powers for (d,p) and (p,d) trans- 
fer reactions at energies near 100 MeV often bear little resemblance to the measured 
angular distributions. To provide a basis for a detailed investigation, cross section and 
analyzing power angular distributions have been made for two time-reverse pairs of re- 
actions, 116Sn(d,p) '17sn with 117~n(p,d) l16sn (Refs. 1 and 2) and 6 6 ~ n ( d , p ) 6 7 ~ n  and 
6 7 ~ n ( p , d ) 6 6 ~ n  (presented elsewhere in this report). These studies find the greatest prob- 
lems for j, = l ,  - $ transitions, where the presence of a marked interference pattern 
in the analyzing power angular distributions indicates nearly equal contributions to the 
reaction amplitude from the far and near sides of the nucleus.* In distorted wave Born 
approximation calculations there is almost no near-side contribution, and the model an- 
gular distributions show almost no interference pattern. We have continued to investigate 
this issue using semi-classical reaction analysis techniques with the intention of extracting 
a phenomenological extimate of the size and character of the missing near-side amplitude. 
The data for this investigation come from the l ,  = 4, j, = $ transition in " ' ~ n ( d , ~ )  '17sn. 
A semi-classical analysis of the reaction amplitudes may be pursued in this case for 
two reasons. First, the typical deuteron and proton partial waves that contribute to 
the stripping or pick-up amplitude are large enough that semi-classical approximations 
are a useful representation of the reaction. Second, the dynamics of angular momentum 
matching at the nuclear surface have sufficiently strong effects that only a few of the 
possible amplitudes contribute significantly to the reaction. This leads in the case of the 
model calculations to redundancy relations among the polarization observables which are 
not matched by experiment.4 
In Fig. la ,  this dynamic selectivity picks out one projection (A,) of the transferred 
neutron's orbital angular momentum. In a model calculation (without spin-orbit distor- 
t ions for simplicity), this is the maximal projection normal to the asymptotic reaction 
plane with the sense of rotation commensurate with far-side scattering. Since this is a 


A Test of Coplanarity and Far-Side Dominance in Intermediate Energy (d,p) and (p,d) Reactions

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A Test of Coplanarity and Far-Side Dominance in Intermediate Energy (d,p) and (p,d) Reactions

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