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.

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Note that al has the dimension (fm)2l+1 and that rl has the dimension (fm)1−2l. Sometimes a1 (or −a1) is called the scattering volume.
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Here we follow the convention of Hamilton.3 Some authors define Kl in a different way, by taking the real part of the right hand side of Eq. (3.4) for real γ. Then Re(h(γ)) is often called g(γ), or confusingly h(γ).
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