Pipit: A momentum space optical potential code for pions☆

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⁺ → π⁰ 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 P₃₃ channel still dominates the differential cross section.

A model for the resonant pion-nucleon D- and F-waves is developed which assumes that the pion-plus-nucleon couples to a resonance and that the resonance can serve as a doorway to the inelastic channels. With the use of simple form factors, the model is capable of reproducing the pion-nucleon phase shifts up to an energy of T_π = 1.4 GeV if the coupling of the elastic channel to the inelastic channels is taken from data as input into the model. A value for the mass of the resonance that would result in the absence of the coupling to decay channels is extracted from the data utilizing the model. This is the mass that is most easily modeled by bag models. For the non-resonant D- and F-wave channels a separable potential model is used. This model, like the resonance model, is developed utilizing the invariant amplitude which is free of kinematic singularities and uses invariant norms and phase spaces. The model is also applied to the S-wave channels. A relation between the resonance model and the Chew-Low model is discovered and used to derive an extended Chew-Low model which is applied to the P₁₃, P₃₁, and P₃₃ channels. Implications of the model for understanding the range of the pion-nucleon interaction and the dynamic structure of the interaction are presented.

Pion-nucleus elastic scattering and single- and double-charge exchange to analog states are computed from a momentum- space optical potential. The optical potential is calculated with an exact performance of the fermi averaging integral and with fully relativistic kinematics by utilizing relativistic three-body recoupling coefficients.