Finite sum expressions for elastic and reaction cross sections

Nuclear cross section calculations are often performed by using the partial wave method or the Eikonal method through Glauber theory. The expressions for the total cross section, total elastic cross section, and total reaction cross section in the partial wave method involve infinite sums and do not utilize simplifying approximations. Conversely, the Eikonal method gives these expressions in terms of integrals but utilizes the high energy and small angle approximations. In this paper, by using the fact that the lthlth partial wave component of the T  -matrix can be very accurately approximated by its Born term, the infinite sums in each of the expressions for the differential cross section, total elastic cross section, total cross section, and total reaction cross section are re-written in terms of finite sums plus closed form expressions. The differential cross sections are compared to the Eikonal results for 16O+16O,12C+12C16O+16O,12C+12C, and p+12Cp+12C elastic scattering. Total cross sections, total reaction cross sections, and total elastic cross sections are compared to the Eikonal results for 12C+12C12C+12C scattering.