Statistical Model of Atoms in Intense Magnetic Fields

Abstract

We obtain the dimensions $R$, electron density distributions $n \left(\overrightarrow{\mathrm{r}}\right)$, 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 $Z^{\frac{4}{3}}\ll {10}^{-9\mathrm{}}B\ll 10Z^3$ G; the choice $n\left(\overrightarrow{\mathrm{r}}\right)\sim Z{R}^{-3\mathrm{}}{\sigma }^{\frac{-1\mathrm{}}{4}}\exp (-\sigma )$, $\sigma \equiv \frac{r^2}{R^2}$, gives $E\approx -150\mathrm{}{\left(\frac{B}{{10}^{12}}\right)}^{\frac{2}{5}}{Z}^{\frac{9}{5}}$ eV, for neutral atoms. A crude variational calculation, valid for $B\gg {10}^{10}{Z}^3$, gives $E\approx -13.6N {(Z-\frac{1}{3}N)}^2{\ln }^2\left(\frac{2B}{{10}^{10}}\right)$ eV.