Predicting total and total reaction cross sections using a simple functional form

Total reaction cross sections have been predicted for neucleons scattering from nuclei ranging in mass 6 to 238 and for projectile energies from just above noticeable giant resonance excitation to 300 MeV. So also have been the mass variations of those cross sections at selected energies when they have been calculated using coordinate space optical potentials formed by full folding effective two-nucleon (NN) interactions with one body density matrix elements (OBDME) of the nuclear ground states. Good comparisons with data result when effective NN interactions defined by medium modification of free NN t matrices are used. However, there is a simple three parameter functional form that reproduces the partial wave total reaction cross section values determined from those optical potential calculations; a functional form also maps the total scattering cross section partial wave elements. Adjusting the theoretical defined parameter values has enabled us to fit the actual measured data values from scattering involving (15) nuclei spanning the mass range from 9Be to 238U and for proton energies from 10 to 300 MeV. Likewise total cross sections for neutron cross sections for neutron scattering from various nuclei can be equally well reproduced. Of import is that the three parameter values vary smoothly with mass and energy.

P. K. Deb, K. Amos · 2004