Effects of the range of the pion-nucleon interaction on pion-nucleus scattering

Abstract

The range of the pion-nucleon interaction is a model-dependent quantity. The range affects the off-shell behavior of the pion-nucleus optical potential that is calculated from it. This will affect the differential cross sections in turn. In this paper, we make an extensive investigation of the effects of varying the range of the pion-nucleon interaction on the differential cross sections of 14C with a first-order and a second-order optical potential. This is done for π + → π +, π + → π 0 and π + → π − reactions at 80, 162 and 292 MeV. It is found that varying the range of the interaction from half to twice its nominal value will produce large differences in the differential cross section including changes in the position of the first minimum. These calculations are performed in momentum space with the optical potential constructed by calculating the Fermi integral. Previous calculations that investigated the effect of the range of the pion-nucleon interaction on the differential cross section, were usually done with a factorized approximation. The results found here are contrary to previous results that agreed with the general argument that the location of the minima should be set by the location of the interaction region in the nucleus. We also investigate taking the infinite-range (zero-range in configuration space) limit. It is found that the differential cross sections change significantly in this limit for the charge-exchange reactions. At 80 and 292.5 MeV it is found that the pion-nucleon P 33 channel still dominates the differential cross section.