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Proposal to improve the behaviour of self-energy contributions to the S-matrix

100%
Tóth G.
Open Physics
|
2010
|
vol. 8
|
issue 4
527-541
EN
A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.
2
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Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

100%
Chen C.-Y., Lu F.-L., Sun D.-S.
Open Physics
|
2008
|
vol. 6
|
issue 4
884-890
EN
In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.
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