Four-nucleon scattering:Ab initiocalculations in momentum space

Abstract

The four-body equations of Alt, Grassberger, and Sandhas are solved for $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ scattering at energies below three-body breakup threshold using various realistic interactions including one derived from chiral perturbation theory. After partial wave decomposition the equations are three-variable integral equations that are solved numerically without any approximations beyond the usual discretization of continuum variables on a finite momentum mesh. Large number of two-, three-, and four-nucleon partial waves are considered until the convergence of the results is obtained. The total $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ cross section data in the resonance region is not described by the calculations which confirms previous findings by other groups. Nevertheless the numbers we get are slightly higher and closer to the data than previously found and depend on the choice of the two-nucleon potential. Correlations between the ${A}_{y}$ deficiency in $n\text{\ensuremath{-}}d$ elastic scattering and the total $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ cross section are studied.