Sum rules of the transverse response functions of A =2, 3 and 4 nuclei

Abstract

The non-energy- and energy-weighted sum rules of the transverse response functions of ²H, ³H, ³He and ⁴He are calculated using the realistic Argonne v₁₄ and Urbana model-VII three-nucleon interactions, exact (A = 2) or variational (A = 3 and 4) wave functions and one-body currents. The Monte Carlo method for the three- and four-body nuclei, and standard numerical techniques for the deuteron are employed to evaluate, without any approximation, the ground-state expectation values. The non-energy-weighted sum rule S_T^N(k) is significantly affected by nucleon-nucleon correlations, particularly the long-range ones induced by the tensor component of the nuclear force. The strong spin-, isospin- and momentum-dependent terms of the interactions give large contributions to the energy-weighted sum rule W_T^N(k), and enhance it by 25–300% in the momentum transfer region of interest. We analyse the transverse scattering data on ²H, ³H, ³He and ⁴He. S_T^N(k) and W_T^N(k) are used to estimate, in the quasi-elastic region of the transverse response, the contributions given by two- (or many-)body currents and the interference between one- and two(or many-)body currents. Although these “non-nucleonic” contributions are small in ²H, ³H and ³He, they are found to be quite large in ⁴He. Some of the implications of this fact are discussed.