Abstract
We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities.
Similar content being viewed by others
References
V. S. Lisitsa, Usp. Fiz. Nauk 153, 379 (1987) [Sov. Phys. Usp. 30, 927 (1987)].
H. Friedrich, Theoretical Atomic Physics, Springer-Verlag, Berlin (1991).
P. A. Braun, Rev. Mod. Phys. 65, 115 (1993).
H. J. Silverstone, Phys. Rev. A 18, 1853 (1978).
T. P. Grozdanov and H. S. Taylor, J. Phys. B 19, 4075 (1986).
M. R. M. Witwit and J. P. Killingbeck, J. Phys. B 26, 1599 (1973).
V. M. Vainberg, V. A. Gani, and A. E. Kudryavtsev, Zh. Éksp. Teor. Fiz. 113, 550 (1998) [JETP 86, 305 (1998)].
J.-H. Wang and C.-S. Hsue, Phys. Rev. A 52, 4508 (1995).
Yu. P. Kravchenko, M. A. Liberman, and B. Johansson, Phys. Rev. A 54, 287 (1996).
E. A. Solov’ev, Zh. Éksp. Teor. Fiz. 82, 1762 (1982) [Sov. Phys. JETP 55, 1017 (1982)].
T. P. Grozdanov, L. Andric, C. Manescu, and R. McCarroll, Phys. Rev. A 56, 1865 (1997).
V. D. Ovsiannikov, Phys. Rev. A 57, 3719 (1998).
N. L. Manakov, V. D. Ovsyannikov, and L. P. Rapoport, Phys. Rep. 141, 319 (1986).
V. D. Ovsiannikov and S. V. Goossev, Phys. Scr. 57, 56 (1998).
S. V. Goossev and V. D. Ovsiannikov, J. Phys. B 28, 5251 (1995).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd ed., Pergamon Press, Oxford (1977), § 39.
A. Erdélyi, Higher Transcendental Functions (Bateman Project) Vol. 1, McGraw-Hill, New York (1953), Chap 5; Vol. 2, Chap. 10.
D. Delande and J. C. Gay, J. Phys. B 17, L335 (1984).
S. P. Alliluev and I. A. Malkin, Zh. Éksp. Teor. Fiz. 66, 1283 (1974) [Sov. Phys. JETP 39, 627 (1974)].
Author information
Authors and Affiliations
Additional information
Zh. Éksp. Teor. Fiz. 116, 838–857 (September 1999)
Rights and permissions
About this article
Cite this article
Ovsyannikov, V.D., Khalyov, K.V. Third-order diamagnetic susceptibilities of hydrogenlike atoms. J. Exp. Theor. Phys. 89, 444–453 (1999). https://doi.org/10.1134/1.559002
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.559002