An integral transform of Green’s function, off-shell Jost solution and T-matrix for Coulomb-Yamaguchi potential in coordinate representation

Abstract

By exploiting the theory of ordinary differential equations together with certain properties of higher transcendental functions, a useful analytical expression for the integral transform of the Green's function for motion in Coulomb-Yamaguchi potential is derived via the r-space approach. This integral transform is applied to construct an analytical expression for off-shell Jost solution in its 'maximal reduced form' involving confluent and Gaussian hypergeometric functions. Corresponding Jost functions automatically follow from this solution. Finally, as another application of the off-shell Jost solution, the off-shell T-matrix is calculated by using a modified relation between offshell physical wave function and T-matrix which does not involve the potential explicitly, thereby avoiding certain difficult integrals, and expressed it in terms of rational functions and simple hypergeometric functions which is in exact agreement with the results given previously by other authors.

Integral Transforms and Their Applications to Scattering Theory

“…In the following we shall verify that for the s-wave case (45) exactly coincides with that of Yamaguchi off-shell Jost solution [22], [32]- [36]. For…”

On the $$\text{p}{-}^{{2}}\text{H}_{{1}} $$ and $$\text{p}{-}^{{16}}\text{O}\,$$ elastic scattering

“…When s = 0, Ḡ(+) M (s, ω) = 0 and we obtain T 2 = 0. The physical solution of the pure Manning-Rosen potential [27][28][29] reads as…”

“…Thus, there is no loss of generality if we get exact solution to investigate the system because a local potential can be replaced distinctly by a separable non-local potential. The problems with Coulomb or Hulthén plus rational separable potentials have been studied at length by various groups [19][20][21][22][23][24][25][26][27][28][29][30][31]. But the problem related to Manning-Rosen plus separable interaction has not yet been treated in the literature.…”

On- and off-shell Jost functions for the Manning-Rosen potential

“…In appendix we shall present detailed derivation of equation (30). As the on-and off-shell Jost functions, ( ) f k and ( ) f k q , , are complex quantities one can write…”