Treatment of inelastic scattering within the separable interaction model

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

“…If ( ) f k r , is decreasing exponentially at infinity for > k Im 0, then one gets a regular square-integrable wave function and consequently an eigen value. Therefore, zeros of the Jost function for > k Im 0 reproduce bound state energies [1,2,[4][5][6][7] while resonant states with zeros in the lower momentum half-plane and negative of the phase of the Jost function gives the scattering phase shift [1,2,[8][9][10][11][12]. This suggests that resonances are indeed bound states with complex energies and therefore decay in time.…”

“…In equation (12) one gets The behaviour of the irregular or Jost solution as  r 0 is termed as the Jost function [3][4][5][6][7][8][9][10]. For the Manning-Rosen we define the Jost function ( )…”

“…Equation ( 19) is the desired expression for the Jost function for motion in the Manning-Rosen potential [6,7]. The onshell Jost function can be obtained by taking near the origin behaviour of the Jost solution ( ) f k r , [3][4][5][6][7][8][9][10]. The zeros of the Jost function in the upper-half of the complex k-plane reproduce the bound states of the respective system.…”

“…In the following we derive the expression for the off-shell Jost function ( ) f k q , by considering its integral representation. The integral representation of the off-shell Jost function [9,10,13,15,31,32] in terms of the on-shell regular solution is written as…”

“…The Hulthén off-shell Jost function [10,22,54]. We made another check, the on-shell limit, on our expression for ( ) f k q , .…”