Covariant separable interaction for the neutron-proton system in $^3S_1$-$^3D_1$ partial-wave state

TL;DR

This paper develops a covariant, separable interaction model for the neutron-proton system in the coupled $^3S_1$-$^3D_1$ state, fitting experimental data and testing deuteron electrodisintegration predictions.

Contribution

It introduces a rank-six covariant separable kernel with two methods for relativistic generalization, fitting phase shifts, scattering length, and deuteron properties.

Findings

Successfully fits phase shifts and deuteron properties

Calculates deuteron magnetic moment accurately

Predicts deuteron electrodisintegration cross sections

Abstract

Within a covariant Bethe-Salpeter approach a rank-six separable neutron-proton interaction kernel for the triplet coupled $^3S_1$-$^3D_1$ partial-wave state is constructed. Two different methods of a relativistic generalization of initially nonrelativistic form factors parametrizing the kernel are considered. The model parameters are determined by fitting the elastic $^3S_1$ and $^3D_1$ phase shifts and the triplet scattering length as well as the asymptotic $D/S$ ratio of the deuteron wave functions and the deuteron binding energy. The $D$-state probability constraints 4-7\% are taken into account. The deuteron magnetic moment is calculated. The half-off-shell properties are further demonstrated by the Noyes-Kowalski functions. The first test of the constructed kernel is performed by calculating the deuteron electrodisintegration at three different kinematic conditions.