Isospin dependent nucleon-nucleus optical potential with Skyrme interactions

Abstract

In this paper, the isospin dependent nucleon-nucleus optical potential theory is introduced on the basis of the effective Skyrme interactions. From the view of the many-body theory, the nucleon optical potential can be identified with the mass operator of the one-particle Green function. The first and second order mass operators of the one particle Green function in nuclear matter are derived, and the real and imaginary parts of the optical potential for finite nuclei are obtained as usual by applying a local density approximation. Our results, in most cases, can be derived and expressed analytically. From an extensive comparison with experimental data of various quantities of interests, it is concluded that for certain versions of Skyrme interactions without parameter adjusting the agreement between theory and experiments can be obtained satisfactorily. We define the ratio of the difference and summation of the neutron and proton nonelastic cross sections as the isospin effect value. The calculated results show that the isopin effect value decreases as the incident energy increases and increases as the asymmetric parameter ${\ensuremath{\alpha}}_{0}=(N\text{\ensuremath{-}}Z)/A$ of the target nucleus increases.