https://doi.org/10.1140/epjd/e2009-00203-9
Bound Dirac states, different Lorentz-type couplings of central potentials and the non-relativistic limit
KTH-Mechanics, Royal Institute of Technology, 10044 Stockholm, Sweden
Corresponding author: a ket@mech.kth.se
Received:
7
April
2009
Revised:
4
June
2009
Published online:
17
July
2009
The analysis of bound radial Dirac states is shown to simplify for problems with an equal mixture of Lorentz vector and Lorentz scalar potentials, thus satisfying a so-called spin symmetry of the energy spectrum. Typical relativistic restrictions on potentials that are singular at the origin then disappear. Such potentials may even be strongly singular at the origin like the well known Lennard-Jones potentials modelling many atom-atom interactions, and they reduce to non-relativistic potentials of identical form. Bound state energies for potentials with equal vector- and scalar couplings are compared with those of a pure vector coupling of the same radial (attractive screened and unscreened Coulomb) shapes, and with non-relativistic results.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 03.65.Pm – Relativistic wave equations / 31.15.-p – Calculations and mathematical techniques in atomic and molecular physics / 36.20.Kd – Electronic structure and spectra
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009
