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