Semirelativistic Wave Scattering

Aline Djoussi, Falone Fotsing, Celsus Bouri +1 more

Abstract Recently we constructed a semirelativistic and nondipole approach (SRNDA) for Raman scattering of light by hydrogenlike ions, by means of the discrete semirelativistic Coulomb Sturmian basis sets, the direct Foldy-Wouthuysen photon-atom interaction Hamiltonian and the expansion of photon fields in electric and magnetic multipoles [Meyap Soh C et al 2018 Ann. Phys. 395 196]. We also proposed its nonrelativistic version which involves the paramagnetic and diamagnetic terms of the semirelativistic Hamiltonian. Following these treatments, the purpose of this paper is twofold. First, we have completed that previous work with the derivation of the fully relativistic Raman scattering based on the well-known Dirac-Coulomb Sturmians of the first order. The formulas obtained, convenient for computer calculations, make it possible to accurately evaluate cross sections. Second, in an effort to reliably judge the credibility of the SRNDA and to assess its scope of applicability as far as the nuclear charge of atomic systems and the incident photons energy are concerned, we have carried out for concreteness computations of these schemes under the ionization threshold. They allow us to compare the various numerical predictions available, including those existing in the literature.

Fritz Gesztesy

Richard L Hall

It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form , where is a non-local potential with a separable kernel of the form . Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to obtain lower bounds for the energy of the corresponding N -boson problem, with upper bounds provided by the use of a Gaussian trial function.

Bernard A. Lippmann

Rémi Carles, Emmanuel Moulay

The purpose of this paper is to provide higher order Schrödinger equations from a finite expansion approach.These equations converge toward the semirelativistic equation for particles whose norm of velocity vector is below c √ 2and are able to take into account some relativistic effects with a certain accuracy in a sense that we define.So, it is possible to take into account some relativistic effects by using Schrödinger form equations, even if they cannot be considered as relativistic wave equations.

Jean-Marc Lévy-Leblond