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

Author(s):  
John A. Adam

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.


2019 ◽  
Vol 10 ◽  
pp. 93
Author(s):  
S. E. Massen ◽  
S. A. Sofianos ◽  
S. A. Rakityansky ◽  
S. Oryu

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.


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