Low-energy theorem for a composite particle in mean scalar and vector fields

Abstract

For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction satisfying a low-energy theorem pointed out by Wallace, Gross and Tjon. The other does not vanish at zero-momentum and involves a ``polarisability" of the particle by the scalar field. The first of these contributions is independent of the details of the structure of the particle and the couplings of its constituents to the external fields. The appearance of such a piece in the central nucleon-nucleus potential thus would support the existence of strong scalar fields in nuclei, without requiring the use of a Dirac equation for the nucleon.