Eikonal cross sections from a time-dependent view

Abstract

Differential cross sections are written in terms of a time autocorrelation function involving the transition operator. Such a formulation is useful when time-dependent approximations are considered. Eikonal theory provides a good example. Using the time autocorrelation function representation, a general eikonal differential cross section is obtained which is parametrised by a momentum. If this parameter is taken as the incoming momentum, then the resulting eikonal differential cross section is found to be complementary to the standard Glauber total cross section, that is, the angular average of the differential cross section is identical to the total cross section. Weak potential limits of these cross sections are Mott cross sections. On the other hand, if the parameter is taken as the average of the incoming and outgoing momenta, then an eikonal differential cross section is produced whose complementary total cross section is not of Glauber form. However, the weak potential limits of these cross sections are the Born cross sections.