Microscopic Calculations of Nuclear Scattering:

`Full-Folding' Optical Potentials for Elastic Nucleon-Nucleus Scattering.

Charlotte Elster
Associate Professor, Department of Physics and Astronomy
Ohio University, Athens, OH 45701

I. Research Description

A long standing aim of `classical' nuclear physics has been the application of the nuclear force as obtained from two nucleon data and the prediction of many body phenomena therefrom. During the last years the PI and collaborators have made considerable progress towards this goal in the area of proton and neutron scattering from nuclei at intermediate energies. This progress has partially been due to the rapid developments in high performing computing technologies.

An important goal in the application of multiple scattering theory to nuclear systems is to determine the nonrelativistic optical potential for elastic nucleon-nucleus scattering within the framework of the Spectator Expansion of multiple scattering theory. A consistent ab-initio calculation of the first order term of this expansion implies the construction of `full-folding' optical potentials from realistic single particle wave functions (describing the ground state of the target nucleus) convoluted with nucleon-nucleon (NN) t-matrices (derived from nuclear forces based on meson exchange) as well as the modification of the optical potential through the nuclear medium.

The exact calculation of the optical potential requires a three dimensional integration, in which the integration variable is coupled to the energy of propagation of the projectile and target nucleon. This very fact leads to a full-folding optical potential which treats the off-shell behavior and the energy dependence of the NN t-matrix when carrying out the integration. When integrating to negative energies, the pole structure of the NN t-matrix has to be taken carefully into account. This pole structure, a true bound state in the tex2html_wrap_inline65Stex2html_wrap_inline67-tex2html_wrap_inline65Dtex2html_wrap_inline67 channel, the deuteron, and a virtual state in the tex2html_wrap_inline73Stex2html_wrap_inline75 channel, the `di-proton', give rise to an additional channel in the optical potential, the deuteron pickup channel.

We calculated elastic scattering observables for tex2html_wrap_inline77O, tex2html_wrap_inline79Ca, and tex2html_wrap_inline81Pb at projectile energies ranging from 65 to 200 MeV projectile energy and compared the full calculation to calculations in which the energy of the NN t-matrix is fixed at half the projectile energy. We found that this fixed energy prescription describes the full calculation remarkably well for proton scattering at 200 MeV projectile energy. For energies below 200 MeV we found that the influence of the deuteron and di-proton state slowly gains importance as lower energies are approached.

We also tested the validity of the factorized off-shell `tex2html_wrap_inline83' approximation in the energy regime between 65 and 400 MeV and found that this approximation, which only retains the non-locality given through the NN t-matrix is even at lower energies a very good representation of the full-folding calculation based on a fixed energy in the NN t-matrix as far as the elastic nucleon-nucleus observables are concerned.

In summary, we performed calculations of the first order optical potential for nucleon-nucleus scattering consistent within the first order spectator expansion of multiple scattering theory. Within this first order term, the effect of the nuclear medium is taken into account by including the coupling of the struck target nucleon to the residual nucleus via the same mean field force from which the nuclear density matrix is derived. One of the most noteworthy results is the correct prediction of the spin observables for elastic proton scattering from light (tex2html_wrap_inline77O) as well as heavy (tex2html_wrap_inline87Zr, tex2html_wrap_inline81Pb) nuclei as low as 65 MeV. Another important result is the correct prediction of total cross section measurements for neutron scattering from light (tex2html_wrap_inline91C, tex2html_wrap_inline77O) as well as heavy (tex2html_wrap_inline87Zr, tex2html_wrap_inline81Pb) nuclei in the energy regime between 75 and 600 MeV. In the calculation of the full-folding optical potential the off-shell structure of the NN t-matrix enters as crucial ingredient. However, realistic, on-shell equivalent NN potentials have a very similar off-shell structure close to the on-shell condition, so that off-shell differences cannot be seen in the elastic observables for nucleon-nucleus scattering.

Acknowledgment
This work was performed in part under the auspices of the U. S. Department of Energy under contract No. DE-FG02-93ER40756 with Ohio University. We thank the Ohio Supercomputer Center (OSC) for the use of their facilities under Grant No. PHS206, the National Energy Research Supercomputer Center (NERSC) for the use of their facilities under the FY1996 and FY1997 Massively Parallel Processing Access Program, the Pittsburgh Supercomputer Center (PSC) for the use of their facilities under Grant No. PHY950010P. We also thank the Arctic Region Supercomputing Center (ARSC) for the use of their resources, which were made available through the metacenter regional alliance project funded by the Advanced Scientific Computing Program of the National Science Foundation, Award number ASC-9418357.
The calculations were mostly performed on Cray T3E (and earlier on Cray T3D) Massively Parallel Systems. A smaller fraction was carried out on the Cray YMP8/64 at OSC.

II. Selected Relevant Publications

A.
Off-Shell Structures of Nucleon-Nucleon t-matrices and their Influence on Nucleon-Nucleus Elastic Scattering Observables, S.P. Weppner, Ch. Elster, D. Hüber, Phys. Rev. C57, 1378 (1998). (http://xxx.lanl.gov/ps/nucl-th/9712001 ).

B.
`Energy Dependence of the NN t-matrix in the Optical Potential for Elastic Nucleon-Nucleus Scattering', by Ch. Elster and S.P. Weppner, Phys. Rev. C57, 189 (1998) (http://xxx.lanl.gov/ps/nucl-th/9708010 ).

C.
`Full-Folding Optical Potentials for Elastic Nucleon-Nucleus Scattering based on Realistic Densities.' by Ch. Elster, S.P. Weppner, and C.R. Chinn, Phys. Rev. C56, 2080 (1997) (http://xxx.lanl.gov/ps/nucl-th/9611045).

D.
`Microscopic Optical Potentials for Elastic Nucleon-Nucleus Scattering', by Ch. Elster, S.P. Weppner, and C.R. Chinn, Proceedings of the Specialists' Meeting on the Nucleon-Nucleus Optical Model up to 200 MeV, Bruyeres-le-Chatel, France, 13.-15. November 1996, http://db.nea.fr/html/science/om200 .

E.
`Propagator Modifications in Elastic Nucleon-Nucleus Scattering within the Spectator Expansion', C.R. Chinn, Ch. Elster, R.M. Thaler, S.P. Weppner, Phys. Rev. C52, 1992 (1995) (http://xxx.lanl.gov/ps/nucl-th/9503027).

F.
Image of the full folding optical potential for tex2html_wrap_inline77O at 200 MeV projectile energy as function of the momentum transfer q and the nonlocal, orthogonal variable K.
The image can be found at:
http://plato.phy.ohiou.edu/~ elster/research/ffO16.html
Please use Netscape to view the image.

G.
Oral contributions at professional meetings:
  1. American Physical Society meeting, April 1997, `Sensitivity of Nucleon-Nucleus Scattering Observables to the Off-Shell Behavior of Realistic NN Potentials.' S.P. Weppner, Ch. Elster, Bull. Amer. Phys. Soc. 42, 925 (1997).
  2. American Physical Society, Ohio Section, November 1996, `Sensitivity of Nucleon-Nucleus Scattering Observables to the Off-Shell Behavior of realistic NN Potentials.' S.P. Weppner, Ch. Elster.
  3. American Physical Society meeting, Division of Nuclear Physcis, October 1996, `Application of Multiple Scattering Theory to Elastic Nucleon-Nucleus Scattering.', Ch. Elster, Bull. Amer. Phys. Soc. 41, 1262 (1996).

H.
Ph.D Thesis: S.P. Weppner, `Microscopic Calculations of First Order Optical Potentials for Nucleon-Nucleus Scattering', Ohio University, August 1997.



Charlotte Elster
Sun Dec 28 19:27:33 EST 1997