Velocity-Dependent Forces and Nuclear Structure. I. Central Forces

Abstract

Starting with the assumption that the forces between nucleons inside nuclear matter are the same as between free nucleons, we outline a procedure by which information on the velocity dependence, and other features, in the two-nucleon interaction may be obtained from the level ordering in nuclear shell theory. In this paper we restrict ourselves to the simplest type of velocity-dependent central force, which turns out to be similar to the reduced-mass type of force introduced for the motion in nuclear matter by Brueckner and by Johnson and Teller. If this force is taken with a sign such that the reduced mass is smaller than the mass of the nucleon, it behaves in the long-range approximation as a repulsive Majorana force. In the short-range approximation, the level ordering for the two-particle configuration goes in order of increasing $J$ in the $p_{\frac{3}{2}}$ shell, in the order $J=4, 0, 2$ in the $d_{\frac{5}{2}}$ shell, and in order of decreasing $J$ in all other shells. For a three-particle configuration the ordering goes as $J=\frac{9}{2}, \frac{5}{2}, \frac{3}{2}$ in the $d_{\frac{5}{2}}$ shell and as $J=\frac{9}{2}, \frac{3}{2}, \frac{5}{2}$ in the $f_{\frac{5}{2}}$ shell. We compare this ordering with the experimental one, and obtain restrictions on the strength and range of the velocity-dependent force that may be added to the ordinary one.