Energy weighted sums of longitudinal response

Abstract

The energy weighted sums W L( k) of longitudinal response of three- and four-body nuclei and nuclear matter are calculated with realistic nuclear forces and variational wave functions. Results with Faddeev wave functions are also reported for three-body nuclei. The isospin exchange interactions give large contributions to W L( k) and enhance it by 10–80% in the region of interest. We analyze the longitudinal scattering data on 3He, 12C, 40Ca, 48Ca and 56Fe. The W L( k) of 12C, 40Ca, 48Ca and 56Fe are estimated from that of nuclear matter by taking into account its dependence on neutron excess ( N− Z)/ A. The experimental data provide S L( k, ω) at ω < E max, and in the best cases, 3He ( 12C) at k = 350 MeV/ c, it gives only 86% (68%) of the predicted sum. The response at ω > E max is assumed to be given by an exponential or square tail that joins the data at ω < E max, and gives the remainder of W L( k). The contribution of the tail to the longitudinal structure function S L( k) is not too sensitive to its assumed (exponential or square) shape, and greatly improves the agreement between experiment and theory of S L( k).