Statistical Model of Atoms in Intense Magnetic Fields

Abstract

We obtain the dimensions $R$, electron density distributions $n (\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, and total ground-state binding energies $E$ of atoms and positive ions (nuclear charge $Z$, $N$ electrons) in intense magnetic fields. A variationally formulated Thomas-Fermi---like model is valid for ${Z}^{\frac{4}{3}}\ensuremath{\ll}{10}^{\ensuremath{-}9}B\ensuremath{\ll}10{Z}^{3}$ G; the choice $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})\ensuremath{\sim}Z{R}^{\ensuremath{-}3}{\ensuremath{\sigma}}^{\frac{\ensuremath{-}1}{4}}\mathrm{exp}(\ensuremath{-}\ensuremath{\sigma})$, $\ensuremath{\sigma}\ensuremath{\equiv}\frac{{r}^{2}}{{R}^{2}}$, gives $E\ensuremath{\approx}\ensuremath{-}150{(\frac{B}{{10}^{12}})}^{\frac{2}{5}}{Z}^{\frac{9}{5}}$ eV, for neutral atoms. A crude variational calculation, valid for $B\ensuremath{\gg}{10}^{10}{Z}^{3}$, gives $E\ensuremath{\approx}\ensuremath{-}13.6N {(Z\ensuremath{-}\frac{1}{3}N)}^{2}{\mathrm{ln}}^{2}(\frac{2B}{{10}^{10}})$ eV.