Classical Stark and Zeeman Effects of Axially-symmetric Circular Rydberg States of He and He-like Ions

Introduction: Circular Rydberg States (CRS) were studied theoretically and experimentally in numerous works. In particular, in the previous paper by one of us, there were derived analytical expressions for the energy of classical CRS in collinear electric (F) and magnetic (B) fields of arbitrary strengths imposed on a hydrogenic system (atom or ion). For the magnetic field B of any strength, the author of that study gave formulas for the dependency of the classical ionization threshold Fc(B) and the energy at this threshold Ec(B). He 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 – some new results were also presented in that paper, especially concerning the Stark effect. Objective: In the present paper, we study analytically axially-symmetric CRS of a heliumic system (He atom or He-like ion) subjected to an electric or magnetic field of arbitrary strength. Methods: In this investigation, analytical techniques were applied. Results: We showed that in the case of the Stark effect, the difference in the unperturbed structure of the heliumic systems (compared to hydrogenic systems), i.e., the non-negligible size, causes the decrease of the classical ionization threshold, as well as increases the energy and the orbit radius of the outer electron at the ionization threshold. Also, the allowance for the non-negligible size of the internal subsystem increases the maximum possible absolute value of the induced electric dipole moment. In the case of the Zeeman effect, we demonstrated that the non-negligible size of the inner system increases the energy and the orbit radius of the outer electron. Conclusion: The allowance for the non-negligible size of the internal subsystem can strongly affect the properties of the axially symmetric circular states. We believe that our results are of fundamental importance.