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 en ergies of the quasi-classical states border on the continuous spectrum limit on two sides and, consequently, these are the matrix elements o f the bound-bound, bound-free and free-free transitions that are consi dered in the review. The analytic formulae are obtained both in the co ntext of and without taking into account the Heisenberg correspondence principle. In the purely Coulomb field a comparison of approximate an d 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 form ulae for transitions between the states of the parabolic basis are con sidered. Quasi-classical results find application in quantitative calc ulations and qualitative estimations when investigating one-photon rad iative transitions, multiphoton excitation and ionization of the Rydbe rg states, including the problems elated to the above-threshold ioniza tion, stabilization and coherent atomic wavepackets.