Half-shellT matrix for Coulomb-modified Graz separable potential

Laha, U.; Talukdar, B.

doi:10.1007/bf02846549

Cited by 21 publications

(12 citation statements)

References 11 publications

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“…Section 3 is devoted to construct an exact analytical expression for off-shell Jost solution f CY (k, q, r) for motion in Coulomb-Yamaguchi potential. The result for Coulomb-Yamaguchi Jost function f CY (k, q) has appeared in a number of publications [8][9][10], while the result for f CY (k, q, r) has only been discussed in the literature in the recent past [6]. The offshell Jost function f CY (k, q) automatically follows from f CY (k, q, r).…”

Section: Introductionmentioning

confidence: 87%

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

Laha

2009

Pramana - J Phys

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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.

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Section: Introductionmentioning

confidence: 87%

“…represent the on-and off-shell Jost solutions and Jost functions[6,8,10] respectively.The basic aim here is to express eq. (38) in the form of eq.…”

mentioning

confidence: 99%

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

Laha

2009

Pramana - J Phys

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“…The physical Green's function for Graz separable potential satisfies the inhomogeneous differential equation [21] …”

Section: Off-shell Jost Solution-integral Transform Of Green's Functionmentioning

confidence: 99%

“…Having the expression for off-shell physical solution one can identify the corresponding off-shell Jost solution by exploiting the following relation [21] …”

mentioning

confidence: 99%

Integral Transforms and Their Applications to Scattering Theory

Bhoi¹,

Laha²

2014

IJAPM

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Closed form analytical expressions for integral transforms of the free particle Green's functions by the form factors of the separable potential and Hankel function are evaluated by adopting various approaches to the problem to construct off-shell Jost/irregular solution of inhomogeneous Schrödinger type equation for motion in Graz separable potential. Off-shell Jost function is also computed numerically.

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“…(9) and its on-shell version. Equations (14) and (15) are derived only by rewriting the differential equations and their particular integrals for f (k, q, r) together with transposed operator relation. Note that eqs (14) and (15) are applicable both for short-range and Coulomb potentials.…”

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confidence: 99%

On the integral representations of the Jost function and Coulomb off-shell Jost solution

Laha

2006

Pramana - J Phys

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The integral representations of the Jost function (on-and off-shell) are rederived by the judicious use of the transposed operator relation on the particular integrals for Jost solution and using one of these particular integrals an analytical expression for the Coulomb off-shell Jost solution is presented in the maximal reduced form.It is well-known that in charged-particle scattering the long range of Coulomb interaction is a source of special difficulties due to 1/r behaviour of the potential at large distances. These difficulties are observed both in classical and quantum scattering. The scattering wave functions for charged-particle scattering exhibit an essentially different (logarithmic) behaviour at large distances compared to scattering wave functions for short-range potentials. This leads to a discontinuity in the behaviour of half-and off-shell functions for the Coulomb and Coulomb-like interactions at the energy shell. The characteristic Coulomb discontinuity arises from the fact that a long-range potential distorts not only the scattering wave but also the incident plane wave [1]. However, in such a situation, one can extract physical information by introducing suitable Coulombian asymptotic states [2].The behaviour of the irregular solution f (k, r) of the radial Schrödinger equation near the origin determines the Jost function [3] f (k) which has an important role in examining the analytic properties of partial wave scattering amplitude. The Jost function has two integral representations [4]: one in terms of irregular solution f (k, r) and the other in terms of the regular solution φ (k, r). The integral representation associated with irregular solution f (k, r) follows directly from the integral equation for f (k, r). Contrary to this, the other integral representation is derived with particular emphasis on the asymptotic behaviour of regular solution φ (k, r).The off-shell Jost function [5] f (k, q), with q, an off-shell momentum, is also determined from the irregular solution f (k, q, r) of an inhomogeneous Schrödinger 357

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Half-shellT matrix for Coulomb-modified Graz separable potential

Cited by 21 publications

References 11 publications

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

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

Integral Transforms and Their Applications to Scattering Theory

On the integral representations of the Jost function and Coulomb off-shell Jost solution

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