Abstract
AbstractThe problem of a multi‐electron atom in a strong magnetic field is treated within the framework of a new statistical model. Here, the charge density n is required to have axial symmmetry. The partial factorization ansatz, n(ϱ, z) = nϱ(ϱ) · nz(ϱ;z), when introduced into Kadomtsev's equation, leads to a second‐order, non‐linear partial differential equation for nz that is valid over an important range of field strengths. Analytical solutions for two limiting approximations are consistent with earlier qualitative studies. Some illustrative, numerical solutions for a less restrictive approximation reveal atomic structures analogous to accurate hydrogenic results, already in the literature.
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