N-d SCATTERING WITH LOCAL POTENTIALS BELOW BREAKUP THRESHOLD USING VARIOUS SEPARABLE EXPANSIONS

Abstract

Publisher Summary This chapter discusses N–d scattering with local potentials below breakup threshold using various separable expansions. The chapter illustrates the three-boson model N–d scattering calculations with the local Hulthen potential V(r) = –s/(er–1) below breakup threshold for a value of the interaction strength parameter s = 1.447 that generates a two-body bound state with energy –0.05. The Mitra–Faddeev equations were reduced to a system of coupled one-dimensional Fredholm integral equations by the use of separable expansions of the local interaction. The chapter explains the Weinberg expansion and the unitary pole expansion (UPE). N–d phases for 1 > 1 are given by one separable term in both the cases. The results using the Weinberg expansion were better than the one using the unitary pole expansion. However, it is incorrect to say that one separable approximation is better than the other. The chapter illustrates the calculations for three-nucleon N–d scattering below threshold, with spin-isospin factors taken into account.