Hydrogen atom in a magnetic field: electromagnetic transitions of the lowest states

TL;DR

This paper investigates the lowest energy states of a hydrogen atom in a strong magnetic field, calculating electromagnetic transition properties with high accuracy using a variational method.

Contribution

It introduces a simple, physically motivated trial function for the variational method applicable across a wide range of magnetic fields, improving accuracy in energy and transition calculations.

Findings

Accurate ionization energies across magnetic field strengths.

Good agreement with previous results for dipole and oscillator strengths.

Deviations up to 30% for certain oscillator strengths at high magnetic fields.

Abstract

A detailed study of the lowest states $1s_0, 2p_{-1}, 2p_0$ of the hydrogen atom placed in a magnetic field $B\in(0-4.414\times 10^{13} {\rm G})$ and their electromagnetic transitions ($1s_{0} \leftrightarrow 2p_{-1}$ and $ 1s_{0} \leftrightarrow 2p_{0}$) is carried out in the Born Oppenheimer approximation. The variational method is used with a physically motivated recipe to design simple trial functions applicable to the whole domain of magnetic fields. We show that the proposed functions yield very accurate results for the ionization (binding) energies. Dipole and oscillator strengths are in good agreement with results by Ruder {\em et al.} \cite{Ruderbook} although we observe deviations up to $\sim 30%$ for the oscillator strength of the (linearly polarized) electromagnetic transition $1s_{0} \leftrightarrow 2p_{0}$ at strong magnetic fields $B\gtrsim 1000$ a.u.