Dependence of pion-nucleus total cross-section on the nuclear density and pion-nucleon off-shell amplitude

Total cross-section forπ ⁺, using the high energy approximation, have been calculated for¹²C and³²S at various energies around the (3, 3) resonance in the free pion-nucleon system. It is observed that the shift in energy of the position of the maximum in the pion-nucleus cross-section with respect to that in the free pion-nucleon system depends sensitively on the shape of the nuclear density. Using the realistic density it is further found that the shift due to the off-shell behaviour of the pion-nucleon scattering amplitude is very small. This observation is different from that reported in the literature by other authors.