Explicit forms of the off-shell Jost solutions for general central potentials

1982 ◽  
Vol 32 (3) ◽  
pp. 344-354 ◽  
Author(s):  
L. Trlifaj
Keyword(s):  
Jost Solutions

scholarly journals Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions

2011 ◽  
Vol 52 (8) ◽  
pp. 083506 ◽  
Author(s):  
M. Boiti ◽  
F. Pempinelli ◽  
A. K. Pogrebkov
Keyword(s):  
Heat Operator ◽  
Jost Solutions

One-Dimensional Jost Solutions: The S-Matrix Revisited

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Boundary Conditions ◽  
Transmission Coefficient ◽  
Radial Equation ◽  
Scattering Problems ◽  
One Dimensional ◽  
S Matrix ◽  
Jost Functions ◽  
Jost Solutions ◽  
Square Well ◽  
Matrix Problems

This chapter examines the properties of one-dimensional Jost solutions for S-matrix problems. It first considers how the left–right transmission and reflections coefficients can be expressed in terms of the elements of the S-matrix for one-dimensional scattering problems on, focusing on poles of the transmission coefficient. It then uses the radial equation to revisit the problem of the square-well potential from the perspective of the Jost solution, with Jost boundary conditions at r = 0 and as r approaches infinity. It also presents the notations for the Jost functions and the S-matrix before discussing the problem of scattering from a constant spherical inhomogeneity.

scholarly journals Effective Interactions: Resonances and Off-Shell Characteristics

2019 ◽  
Vol 10 ◽  
pp. 93
Author(s):  
S. E. Massen ◽  
S. A. Sofianos ◽  
S. A. Rakityansky ◽  
S. Oryu
Keyword(s):  
Inverse Scattering ◽  
Nuclear Reactions ◽  
Bound State ◽  
Inverse Scattering Method ◽  
Wave Functions ◽  
Scattering Method ◽  
Effective Interactions ◽  
Analytical Properties ◽  
Jost Functions ◽  
Jost Solutions

The influence of resonances on the analytical properties and off-shell characteristics of effective interactions has been investigated. This requires, among others, the knowledge of the Jost function in regions of physical interest on the complex kplane when the potentials are given in a tabular form. The latter are encountered in inverse scattering and supersymmetric transformations. To investigate the effects of resonances on the analytical properties of the potential, we employed the Marchenko inverse scattering method to construct, phase and bound state equivalent local potentials but with different resonance spectra. It is shown that the inclusion of resonances changes the shape, strength, and range of the potential which in turn would modify the bound and scattering wave functions in the interior region. This could have important consequences in calculations of transition amplitudes in nuclear reactions, which strongly depend on the behaviour of the wave functions at short distances. Finally, an exact method to obtain the Jost solutions and the Jost functions for a repulsive singular potential is presented. The effectiveness of the method is demonstrated using the Lennard-Jones (12,6) potential.

Sign in / Sign up

Export Citation Format

Share Document