Resonance cross-section formula for low-energy elastic scattering

Abstract

A simple analytical formula for partial wave cross section describing low-energy elastic scattering in the presence of a shape resonance located near the elastic threshold is proposed. The formula is based on the extension of the regularized method of analytical continuation in the coupling constant (RAC) recently proposed by Hor\'a\ifmmode \check{c}\else \v{c}\fi{}ek and co-workers. The RAC method provides the complex energies of resonances and virtual states requiring as input information a set of real bound state energies of a perturbed system for which standard highly sophisticated numerical codes may be employed. No scattering calculations are needed. These parameters define the low-energy partial wave resonance scattering cross section. Cross sections are calculated for the $2{s}^{2}\ensuremath{\varepsilon}p\phantom{\rule{0.16em}{0ex}}^{2}P^{0}$ state of beryllium and $3{s}^{2}\ensuremath{\varepsilon}p\phantom{\rule{0.16em}{0ex}}^{2}P^{0}$ of magnesium. The results compare well with recently published data.