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Relativistic Impulse Approximation


The relativistic treatment of the quasifree nucleon-nucleus scattering has been described in [SRM86], [HoI86], [HoM88], [HiD94] and in particular for charge exchange reactions in [HoP93]. The method generally employed uses a relativistic random phase approximation to the Walecka model. In the Walecka model the nn interaction is mediated by the exchange of isoscalar scalar and vector mesons, and in the mean-field approximation these meson fields are replaced by their classical expectation value. In the mean-field approximation strong scalar and vector mean-fields will cause large shifts in the in-medium mass and energy of nucleons in the nucleons:

where is the mean scalar field and is the free(in-medium) nucleon mass.

The modified mass of the nucleon is in itself a reasonable explanation for the lack of enhancement because the reduced value of the nucleon mass should have a significant effect on the longitudinal spin-isospin response. An RPA calculation of the pion dimesic function [DaP91] gives the effective coupling constant in the nuclear medium as [HoP93]

If the pion coupling constant is reduced in-medium one would expect that pionic correlations will play a diminished role in an RPA calculation of the nuclear responses. Therefore, the spin-longitudinal response, which was primarily mediated by pion exchange, will be smaller relative to the nonrelativistic case.

There is also another effect due to the change in effective nucleon mass. The peak of the quasifree distribution, , will be shifted relative to a naive Fermi gas model, and the distribution will broaden, before any correlations are considered. Therefore, attractive pion correlations will act on an uncorrelated case which is already ``hardened'' (moved to higher energy) and the overall effect of the pion correlations much smaller than without the relativistic corrections.

Michael A. Lisa
Tue Apr 1 08:52:10 EST 1997