97-602 Brummelhuis, R. and Ruskai, M.B.

A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization (720K, postscript) Nov 30, 97

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Abstract. We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons $N_{\max}$ satisfies a bound of the form $N_{\max} < 2Z+1 + c \sqrt{B}$ where $Z$ denotes the charge of the nucleus, $B$ the field strength and $c$ is a constant. We follows Lieb's strategy in which convexity plays a critical role. For the case $N=2$ with fractional nuclear charge, we also discuss the critical value $Z_c$ at which the nuclear charge becomes too weak to bind two electrons.

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