Brummelhuis, R. and Ruskai, M.B.
A One-Dimensional Model for Many-Electron Atoms
in Extremely Strong Magnetic Fields: Maximum Negative Ionization
(720K, postscript)
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.