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

Bacher, A.

Berman, B.

Bertozzi, W.

Buti, T.

Carr, J.

Emery, G.

Finn, M.

Foster, C.

Hersman, F.W.

Hyde, C.

Hynes, M.V.

Jones, W.

Kelly, J.

Kovash, M.A.

Love, W.G.

Miller, D.

Murdock, B.

Norum, B.

Petrovich, F.

Pugh, B.

Ulmer, P.

English

IUScholarWorks

PROTON ELASTIC AND INELASTIC SCATTERING AT INTERMEDIATE ENERGIES FROM ISOTOPGS OF OXYGEN 
AND 'Be AS PART OF A UNIFIED STUDY OF THESE NUCLEI 
W. Bertozzi, T. Buti, M. Finn, F.W. Hersman, C. Hyde, J. Kelly, LA. Kovash, B. Murdock, B. Pugh, and P. Ulmer 
Massachusetts Institute of Technology, Cambridge, 1.lassachusetts 02139 
A. Bacher, G. Emery, C. Foster, W. Jones, and D. Miller 
Indiana University Cyclotron Facility, Bloomington, Indiana 47405 
B. Norum 
University of Virginia, Charlottesville, Virginia 22901 
M.V. Hynes 
Los Alanos National Laboratory, Los Alamos, New Mexico 87545 
B. Beman 
Lawrence Livermore Laboratory, Liverinore, California 94550 
W.G. Love 
University of Georgia, Athens, Georgia 30601 
J. Carr and F. Petrovich 
Florida State University, Tallahassee, Florida 32306 
This report describes the status of an generalize our lineshape fitting procedures. 
experimental and theoretical program that combines In the IUCF annual report for 1978, we commented 
electron scattering at the MIT-Bates Linac and on a general lineshape which accurately describes the 
intermediate energy proton scattering at IUCF as part resolution function for the QDDM Spectrometer. This 
of a unified study of the oxygen isotopes and '~e. In shape is definitely not gaussian, and may be described 
the last year we have used 10 shifts of 180-MeV in the central region by an asymmetric hypergaussian 
polarized protons to measure the cross sections and and in the wings by exponential tails. Further details 
analyzing powers for states of 160 up to about 12.5-MeV may be found in Ref. 1. We have now generalized our 
excitation and of '~e up to 8-MeV excitation out to fitting procedures to include the option of convoluting 
momentum transfers of about 3.0 fm-l. We briefly this resolution function with an intrinsic lineshape. 
describe here the progress in the data analysis and in The intrinsic lineshape may be chosen as gaussian, 
the theoretical understanding of the effective Breit-Wigner, or Lorentzian. The Lorentzian lineshape 
interaction that has been achieved since our last includes the proper threshold behavior, an effect which 
report. can be observed in our data. This new fitting program 
The structure of '~e is interesting from many is called ALLFIT and also includes the kinematics for 
points of view. For example, the molecular model transfer reactions and an empirical lineshape that 
describes '~e as a system of two alphas weakly bonded describes electron scattering experiments. For 
by a shared neutron. As a highly deformed system, a electron scattering, the exponential tail on the large 
prominent rotational band is exhibited. However, energy loss side is replaced by an inverse polynomial 
because the binding is weak, the higher rotational radiative tail. The radiative corrections are applied. 
states quickly fly apart and appear as broad Many other options and features are available. 
resonances. In order to analyze the data for these An example of the quality of fit that can be 
states, and for the continuum, it was necessary to obtained is shown in Fig. 1, which displays a fitted 
Energy 
Fi ure 1. A fitted portion of a spectrum for 34" 
sctttering of 180-MeV spin-up protons from '~e between 
1.2 and 10.6 MeV inelasticity. Note the logarithmic 
verical scale. 
portion of a '~e(~,~') spectrum for Ep = 180 MeV. Note 
the threshold at 1.66 MeV. The strong, narrow peak at 
2.43 MeV is taken as the resolution function. The 
remaining peaks are described by Lorentzians whose 
widths are within the error bars of previous 
determinations of these widths.* It is important to 
realize that approximately 20% of the area of the 
dominant Lorentzian (6.76 MeV) is beyond the fitting 
region. Note that although the ability to convolute is 
not important for the broadest or narrowest states, it 
is important for the state nearest the threshold and 
for states whose intrinsic width is similar to the 
resolution width. This latter condition also occurs 
for several of the 160 states of interest. 
In our last report, we commented on the discovery 
of strong density dependence in the isoscalar 
spin-independent central component of the two-nucleon 
effective interaction near 150 b1ev.l~~ The cross 
section and analyzing power data exhibit striking 
signatures of this density dependence. These effects 
are well described by the local density approximation 
(LDA), in which the interaction is described by that 
appropriate to the scattering of a continuum nucleon by 
a nucleon in nuclear matter with the local density in 
the vicinity of the interacting nucleons. This 
effective interaction is constructed from the solutions 
of the scattering problem for nuclear matters4 given a 
two-nucleon potential for free nucleons. 
The selectivity of inelastic scattering to 
discrete nuclear states allows one to study the 
effective interaction from a greater variety of 
perspectives than are available in nucleon-nucleon 
experiments. Thus, it may be possible to use 
nucleon-nucleus scattering to distinguish between 
alternative potentials that provide essentially 
equivalent descriptions of the nucleon-nucleon data. 
Preliminary studies using the nuclear matter effective 
interactions generated by the Hamada-Johnston (HJ) and 
Paris potentials show that the data are sensitive to 
the differences between these potentials. The 
effective interactions we used in our LDA calculations 
were supplied by von Geramb . 
In Fig. 2 we compare the cross section and 
analyzing power predictions using the IIJ and Paris 
potentials with our 135 MeV proton scattering data for 
the first 1' state of 160. These calculations use 
distorted waves generated by the microscopic optical 
potentials calculated from the same interaction that 
induces the inelastic transition. The elastic 
scattering predictions are shown in Fig. 3. The 
details of these calculations may be found in Refs. 
1,3. 
Paris 
--- HJ 
Figure 3. Elastic scattering comparison similar to 
Fig. 2. Note the suppressed zero for the horizontal 
scale. 
Fi ure 2. Comparison of consistent LDA redictions for 
th: excitation of the first 1- state of P60 by 135 MeV 
protons using G-matrices based on the Paris and 
Hamada-Johnston (HJ) potentials. 
contributions to the real central optical potential are 
The elastic scattering predictions generated by both very large and of opposite sign, cancelling to 
the Paris potential are in much better agreement with produce a much smaller result. Thus, the local 
the data than are those of the HJ potential. For the approximation for exchange fails for the elastic 
elastic scattering, the most important difference scattering calculations using the HJ potential. In 
between these interactions is the exchange mixture. In the case of the Paris potential, on the other hand, the 
the case of the HJ potential, the direct and exchange direct and exchange contributions have the same sign, 
improving the accuracy of the local exchange interaction. The HJ potential correctly predicts the 
approximation. strong negative analyzing powers that result from the 
For the inelastic scattering predictions, the most enhanced repulsion of the central interaction at high 
important difference between these interactions is the density. The Paris potential, on the other hand, is 
strength of their high-q repulsion. The central less repulsive at high-q and tends to underpredict the 
interactions are compared, as functions of density and high-q cross section. The Paris potential analyzing 
momentum transfer, in Fig. 4. The inelastic cross power predictions do not become sufficier~tly negative. 
Paris Hamada - Johnston 
Therefore, we conclude that the high-q repulsion in the 
isoscalar spin-independent central component of the 
two-nucleon effective interaction based on the ILT 
potential is too strong while that of the Paris 
potential is too weak. This high-q repulsion arises 
from the core of the nucleon-nucleon potential. 
Therefore, we conclude that the core of the 
nucleon-nucleon potential should be intemediate 
I I I betweer1 the extreme hard core of the HJ and the soft 
1 I I I I I I I I 
I 2 3 I 2 3 core of the Paris potentials. ( f i - 9  
Figure 4. Modulus of the isoscalar spin-independent 
central interaction. For the interactions based on the 
Paris and HJ potentials, the long (short) dashed curves 
represent the low (saturation) density limits. The 
~ o v e - ~ r a n e ~ ~  free t-matrix is shown on both sides as 
the solid curve. 
1) J. Kelly, Ph.D. Thesis, M.I.T. (1981); J. Kelly 
et al., preprint. 
2) F. Ajzenberg-Selove, Nucl. Phys. A320, 1 (1979). 
3) J. Kelly et al., Phys. Rev. Lett. 45, 2012 (1980). 
4) F.A. Brieva and J.R. Rook, Nucl. Phys. A291 
299, 317 (1977), and A297, 206 (1978). 
section predictions are similar at low q and then begin 
to diverge at the minimum of the central contribution. 
The HJ potential tends to overpredict the high-q cross 
section, particularly for surface transitions that are 
5) H.V. von Geramb, "Table of Effective Density and 
Energy Dependent Interactions for Nucleons", 
unpublished. 
6) W.G. Love and M.A. Franey, Phys. Rev. C 24, 1073 
(1981). 
dominated by the low density limit of the effective 7) W. Bauhoff, H.V. von Geramb, and G. Palla, to be 
published. 
135 MeV PROTON SCATTERING FROM 3~ 
S.F. Collins, B.M. Spicer, G.G. Shute and V.C. Officer 
University of Melbourne, Parkville, Victoria, 3052, Australia 
D.W. Devins, D.L. Friesel and W.P. Jones 
Indiana University Cyclotron Facility, Bloomington, Indiana, 47405 
The data from the 13~(p,p') reaction, reported in elucidating the structure, and its nature, at about 12 
the 1980 Annual Report, has been supplemented in two MeV in excitation. The second of these used a polar- 
short experiments, both of which were aimed at ized proton beam, and it is expected that the asymmetry 


Proton Elastic and Inelastic Scattering at Intermediate Energies from Isotopes of Oxygen and 9-Be as Part of a Unified Study of these Nuclei

https://scholarworks.iu.edu/dspace/bitstream/2022/2743/1/iucf_1981_10-13.pdf

Proton Elastic and Inelastic Scattering at Intermediate Energies from Isotopes of Oxygen and 9-Be as Part of a Unified Study of these Nuclei

Abstract

Similar works

Full text

Available Versions

IUScholarWorks