T matrix and effective range function for Coulomb plus rational separable potentials especially for I=1

Abstract

The off-shell l=1 T matrix in the momentum representation for the pure Coulomb potential and for the Coulomb plus a rational plus a rational separable potential of the Yamaguchi type is obtained in closed form. The amplitude, the effective range function, and the effective range parameters are derived from the T matrix and are given in closed form. For a large number of rational separable potentials we prove thar the effective range function is real analytic at zero energy. We give, however, an axample of potential for which this effective range function has a pole at the orign. From t hese effective range functions a certain function W is extracted which does not depend either or l or on the particular potential. This function W is studied in detail. We indicate howe the result s of this paper can be generalized to arbitrary values of l and to all Coulomb plus rational separable potentials.