Circular Rydberg states of hydrogenlike systems in collinear electric and magnetic fields of arbitrary strengths: an exact analytical classical solution

Abstract

We derived analytical expressions for the energy of classical Circular Rydberg States (CRS) in collinear electric (F) and magnetic (B) fields of arbitrary strengths. Previously published explicit expressions for the energy E were given only for the region of a weak electric field F and only in the limits of $B \to 0$ and $B \to \infty $ . We offered formulas for the dependence of the classical ionization threshold F c (B) and of the energy at this threshold E c (B) valid for the magnetic field B of an arbitrary strength. We also analyzed the stability of the motion by going beyond the CRS. In addition, for two important particular cases previously studied in the literature -- classical CRS in a magnetic field only and classical CRS in an electric field only -- we presented some new results as well.