A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization
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چکیده
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 Nmax satisfies a bound of the form Nmax < 2Z + 1 + c √ 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 Zc at which the nuclear charge becomes too weak to bind two electrons. ∗supported by National Science Foundation Grant DMS-94-08903
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تاریخ انتشار 1999