Raymond Brummelhuis, Mary Beth Ruskai
A One-Dimensional Model for Many-Electron Atoms 
 in Extremely Strong Magnetic Fields: Maximum Negative Ionization
(138K, latex2e, with 5 figs (fig. 2 in 2 parts))

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 follow 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.