DIPOLE MATRIX-ELEMENTS IN THE QUASI-CLASSICAL APPROXIMATION

The set of analytic formulae with overlapping areas of applicability, enabling approximate calculation of the dipole matrix elements between any quasi-classical states, is presented. In the Coulomb field the energies of the quasi-classical states border on the continuous spectrum limit on two sides and, consequently, these are the matrix elements of the bound-bound, bound-free and free-free transitions that are considered in the review. The analytic formulae are obtained both in the context of and without taking into account the Heisenberg correspondence principle. In the purely Coulomb field a comparison of approximate and exact results is performed. The non-Coulomb character of the atomic potential at small distances is taken into account by introducing the quantum defects and non-Coulomb phases of scattering. Approximate formulae for transitions between the states of the parabolic basis are considered. Quasi-classical results find application in quantitative calculations and qualitative estimations when investigating one-photon radiative transitions, multiphoton excitation and ionization of the Rydberg states, including the problems elated to the above-threshold ionization, stabilization and coherent atomic wavepackets.