Single Particle Potential in Polarized Nuclear Matter

Abstract

The problem of the single particle potential U in isospin and spin polarized nuclear matter, i.e. in nuclear matter with neutron excess and nonvanishing spin, is treated within the frame of the K matrix theory. General expressions for the isospin, spin, and spin–isospin parts of U, Uτ, Uσ, and Uστare obtained with the help of K matrices which depend on two Fermi momenta. The σ and στ parts have scalar and tensor components: Uσs and Uσt, and Uστ,s and Uστ,t These general expressions are specialized for nucleons at the Fermi surface. With suitable approximations, numerical values for Uτ(kF), Uσs(kF), and Uστ,s(kF) are obtained for the Brueckner–Gammel–Thaler and the Reid soft core nucleon–nucleon interactions. The tensor components, Uστ and Uστ,t, are estimated to be much smaller than the corresponding scalar components. The rearrangement effects turn out to be very important. At higher nucleon energies the τ, σ, and στ parts of U are calculated in the phase shift approximation with the Yale and Livermore phase shifts. The agreement of the calculated value of U, with experiment is satisfactory. The calculated values of Uσs and Uστ,s suggest that, in certain cases, a scalar spin–spin part of the optical potential is strong compared to other theoretical estimates, which seems to agree with some of the experimental results.