New Formula for Calculations of Scattering Cross-Sections According to Quantum Mechanics

Abstract

We have calculated the general elastic and inelastic scattering differential and total cross-sections using a simple general solution of radial Schrödinger equation for a particle or particle current in a central field, generally. Before, we have obtained the general simple formulas of the scattering amplitudes and elastic, inelastic (no-elastic) and total scattering cross-sections. After, we have made some applications, numerically. In these applications, the barrier potentials are assumed to have centrifugal plus Coulomb potentials. With these potentials, the elastic, inelastic (absorption, radiation, particle detachment, particle capture, etc.) and total scattering cross-sections of different targets were calculated. Scattering cross-sections for   particles of three different energies on many targets, from , are calculated. The calculated results are compared with experimental results. The results calculated have given satisfactory agreement with the available experimental results. Then, when the experimental elastic and reaction cross sections are known, we calculated the width of the potential barrier and the coefficient of transmission of potential barrier. By taking thermal neutrons as incoming particles, the potential barrier transmission coefficients and barrier widths were calculated for many nuclei as examples.