Dynamic toroid polarizability of atomic hydrogen: A. Costescu. Department of Physics, University of Bucharest, P.O. Box Mg-11, Bucharest, Romania; and E. E. Radescu. International Center for Theoretical Physics, Trieste, Italy, and Institute of Atomic Physics, P.O. Box Mg-6, Bucharest, Romania

Abstract

Abstract The concept of toroid polarizability introduced in previous work is examined within the familiar context of nonrelativistic quantum Coulomb systems, in a way unbiased by approximations. The dynamic (i.e., frequency (ω) dependent) toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless, ground-state) hydrogenlike atom is calculated analytically in terms of (essentially) one Gauss hypergeometric function. The static result takes on the simple form γ(ω = 0) = 23 60 α 2 Z −4 a 0 5 (α = fine structure constant, Z = nucleus charge number, a0 = Bohr radius). γ(ω) characterizes the linear response of the system to a conduction and/or displacement (time dependent) external current. The method of calculation (based on the use of the integral representation for the nonrelativistic Coulomb Green's function) is presented in detail. The imaginary part of γ(ω) above ionization threshold is also computed in a simple closed form. Comparing γ(ω = 0) with the already known (exact) results for the electric multipole polarizabilities (for which, as a byproduct, we present in an Appendix a considerably simplified expression, to our knowledge the simplest reported as yet), one sees that although for H-like atoms the toroid effects appear as very small indeed, they are however increasing with Z. A comparison with analogous (but, this time, only order of magnitude) evaluations for (charged) pions, indicates that the role of the induced toroid moments (as against that of the usual electric ones) increases drastically when passing from atomic to hadron physics; it is argued that this trend might continue further, at the sub-hadronic level.