Study of the Sasakawa Approach to Two-Particle Scattering

It is shown that the Kowalski formulation of the Sasakawa approach to potential scattering can be used as the basis for a momentum-space formulation of the theory of the Jost function. Two examples are presented for which the Kowalski equations can be solved in closed form. One example is a separable potential, and the other is the exponential potential. The separable potential illustrates the fact that the series obtained by iterating Kowalski's equations does not always converge. The exponential potential provides a verification of Coester's proof that the iteration series does converge for a certain class of local potentials of arbitrary strength. The practicality of Kowalski's equations are demonstrated by using them to calculate the phase shifts and half-off-shell $T$ matrix that are produced by the Reid potential in some of the uncoupled states of the two-nucleon system.