On the phase-integral method for the radial Dirac equation

Details On the phase-integral method for the radial Dirac equation On the phase-integral method for the radial Dirac equation

2009-05-06

arxiv.org/abs/0905.0842v2

J.Phys.A42:395203,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, 8 figures. In the new version, the presentation has been improved. A new figure and new references have been added

Scientific paper

10.1088/1751-8113/42/39/395203

In the application of potential models, the use of the Dirac equation in central potentials remains of phenomenological interest. The associated set of decoupled second-order ordinary differential equations is here studied by exploiting the phase-integral technique, following the work of Froman and Froman that provides a powerful tool in ordinary quantum mechanics. For various choices of the scalar and vector parts of the potential, the phase-integral formulae are derived and discussed, jointly with formulae for the evaluation of Stokes and anti-Stokes lines. A criterion for choosing the base function in the phase-integral method is also obtained, and tested numerically. The case of scalar confinement is then found to be more tractable.

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