Analysis of π± – 12C Elastic Scattering Data at 100 MeV Using Inverse Scattering Theory and Klein-Gordon Equation

Abstract

Our optical potential, determined from available phase shifts within the framework of inverse scattering theory using the full Klein-Gordon equation, is used successfully in this study. This potential is inserted in the radial part of Klein-Gordon equation which is solved numerically using Numerouv integration method. The logarithmic derivatives of the inner and outer solutions are matched at the nuclear surface and phase shifts are obtained for each partial wave. As such, scattering amplitudes and cross sections can easily be calculated. The reliability and success of our potential are examined by accounting for the measured elastic differential cross sections, especially at very large angles, and reaction cross sections for π± – 12C at 100 MeV. The use of full Klein-Gordon equation, and not the truncated one, is very important in explaining large and very large angle data.