Velocity dependent nuclear forces and their effect in nuclear matter

Abstract

The object of this paper is to investigate whether it is possible to replace the hard core in current nucleon-nucleon potentials by a non-singular but velocity-dependent potential. This is considered in two stages. Firstly, sucho a non-singular velovity-dependent potential is adjusted to fit the experimental phase-shifts in the four states singlet, even and odd, and triplet, even and odd. The results show that a rough fir can be obtained comparable to the Gammel-Thaler fit with hard-core potentials. These data therefore do not offer a sensitive method of distinguishing the two types of potentials. Secondly, the potentials so obtained are used to calculated the energy of infinite nuclear matter by applying ordinary perturbation theory. With first-order perturbation theory it is possible to get saturation at densities in the neighbourhood of the experimental value, but with an energy that is too positive. However, it isshown that the next term in the series, which is always negative, is by no means negligible, and so must also be considered, if an accurate value of the energy is required. Even so, these terms are still sufficiently small to indicate reasonable convergence of the series.