Polarons Bound in a Coulomb Potential. II.2P-State Zeeman Effect

Abstract

Approximate polaron effective-mass trial functions are constructed to describe $2P$ hydrogenic polaron levels in weak magnetic fields. Breakdown of the effective-mass description due to level crossing of the $2P$ effective-mass states with $1S$ one-phonon states [denoted ($1S,1$)] necessitates admixture of ($1S,1$) states to the initial effective-mass state in order to achieve lowest cariational energy. The effect of mixing in the ($1S,1$) states is to produce, effectively, a double-values $2P$ energy and to reduce considerably the linear Zeeman splitting near the point of level crossing. Level crossings with ($1S,n$) states for $n>\mathrm{}1\mathrm{}$ are expected, on the basis of a heuristic argument, to produce similar discontinuities near the respective crossing energies. Perturbation theory is used to find expressions in the weak-coupling limit for the Zeeman splitting in the limit of weak binding, and, for stronger binding, near the ($1S,1$) level crossing.