Spherical model of the Stark effect in external scalar and vector fields

TL;DR

This paper develops a relativistic quasi-classical model for the Stark effect considering scalar and vector external fields, providing analytical formulas for resonance energies and widths with implications for quantum systems under external influences.

Contribution

It introduces a relativistic quasi-classical approach to the Stark effect in scalar and vector fields, deriving analytical expressions for resonance parameters and wave function asymptotics.

Findings

Resonance width a0a0a0 depends strongly on energy and mixing constant a0a0a0.

Analytical formulas for Dirac wave function asymptotics at zero and infinity.

The model generalizes classical quantization rules to relativistic scalar and vector potentials.

Abstract

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.