Rational function approximation of nuclear scattering cross-section function

Abstract

The one-variable scattering cross-section function f(eta) proposed by Lindhard, Nielsen and Scharff (LNS) is approximated by a rational function using the minimax algorithm in this work. Taking an ingenious transformation ion of the variable eta, this approximation is about one order of magnitude faster than other approximations in the literature. To maintain a reasonable accuracy, we divide the wide variable range into two regions. In addition, an adaptive integration method is adopted to compute the scattering angle and the nuclear stopping power in order to get accurate f(eta) data.