Transition form factor of the hydrogen Rydberg atom

Abstract

The form factor for the transition between the hydrogenic states with parabolic quantum numbers n 1 n 2 m and n 1 Јn 2 ЈmЈ is obtained in a closed analytic form. The asymptotic limit of the transition form factor at large parabolic quantum numbers is derived, and a comparison with exact quantum calculations shows that the asymptotic limit is accurate in a wide region of parabolic quantum numbers and the momentum p transferred to electrons. A simple quasiclassical formula for the transition probability is given, and the range of quantum numbers corresponding to quasiclassically forbidden transitions are defined.

Half-cycle-pulse-train induced state redistribution of Rydberg atoms

“…where t r is the period of the pulse train and H = −1/2n 2 is the unperturbed Hamiltonian of the system. The applicable form factor has been analytically calculated for hydrogenic Stark states with parabolic quantum numbers n 1 , n 2 , m, and n = n 1 + n 2 + |m| + 1 where the atomic quantization axis and the HCP electric field polarization are parallel [18]. In this configuration the only applicable selection rule is ∆m = 0.…”

Alternative implementation of atomic form factors

“…In conclusion, we note two important publications that offer other methods for evaluation of atomic form factors not discussed in this article. In [55] the parabolic quantum numbers and the corresponding wave functions were used. Calculation of the form factor in the parabolic basis is less complicated than in the spherical one.…”

Electron beam from oriented Rydberg atoms irradiated by a half-cycle pulse

“…We want to estimate the matrix element T f i in the semiclassical approximation as well. The semiclassical wavefunction of the initial state in the parabolic coordinates is given by [20]…”