Research Objectives
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.
Computational Approach
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 3S1 - 3D1 channel, the deuteron, and a virtual state in the 1S0 channel, the di-proton -- gives rise to an additional channel in the optical potential, the deuteron pickup channel.
Accomplishments
We calculated elastic scattering observables for 16O, 40Ca, and 208Pb 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 t-rho 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.
Significance
A long-standing aim of classical nuclear physics has been to apply the nuclear force as obtained from two nucleon data and to predict many body phenomena from it. In recent 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.
Publications
Elster, C., S. P. Weppner, and C. R. Chinn. 1996. Microscopic optical potentials for elastic nucleon-nucleus scattering. In Proceedings of the Specialists' Meeting on the Nucleon-Nucleus Optical Model up to 200 MeV, Bruyeres-le-Chatel, France, November 13-15. http://db.nea.fr/html/science/om200
_____. 1997. Full-folding optical potentials for elastic nucleon-nucleus scattering based on realistic densities. Phys. Rev. C 56:2080. http://xxx.lanl.gov/ps/nucl-th/9611045
Elster, C., and S. P. Weppner. N.d. Energy dependence of the NN t-matrix in the optical potential for elastic nucleon-nucleus scattering. Phys. Rev. C., in press. http://xxx.lanl.gov/ps/nucl-th/9708010
URL
http://plato.phy.ohiou.edu/~elster/nersc97/nersc97.html
The full-folding optical potential for 16O at 200 MeV projectile energy as function of the
momentum transfer q and the nonlocal, orthogonal variable K. The proton-neutron part
corresponding to the Wolfenstein amplitude C is shown, which corresponds to the
imaginary part of the spin-orbit potential.