On the Alpha-Carbon-12 Elastic Scattering

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

“…The Manning-Rosen potential, generally used in molecular dynamics, can also be applied successfully in nuclear systems [6,7]. Within the Jost function formalism one is able to treat both bound and scattering states quite efficiently [4][5][6][7][8][9][10][11]. Our expressions for the off-shell Jost function and half-shell T-matrix are in maximal reduced form and are suitable for numerical treatment.…”

“…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.…”

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

“…The phase function, however, may be stated in a straightforward mathematical form for a separable nonlocal potential using some integrals of the regular and irregular solutions to the parent nonlocal interaction. Separable nonlocal interactions have been employed successfully in a variety of physics applications because of how easily they can be calculated analytically [4,5,11,[13][14][15][16][17][18][19][20]. A fair description of nucleon-nucleon and nucleon-nucleus elastic scatterings is explained by the Graz model [4,5,[14][15][16][17][18] of separable interaction.…”