QUASI-CLASSICAL DIPOLE MATRIX-ELEMENTS FOR HIGH ATOMIC STATES AND STOCHASTIC DYNAMICS OF HYDROGEN-ATOMS IN MICROWAVE FIELDS

Analytical expressions for dipole matrix elements between high atomic states of non-hydrogenic and perturbed hydrogenic atoms are derived. The theoretical investigation is fulfilled for discrete and continuum atomic states and for the one-dimensional atom. It is shown that the quantal transition probabilities between perturbed atomic states depend on the nature of perturbation, e.g. matrix elements for the hydrogenic atom in an electromagnetic field differ from those of the non-hydrogenic atom. The results obtained generalize and increase the accuracy of some known expressions for the non-hydrogenic atom and extend them for the perturbed hydrogenic atom. Further, the analysis of classical dynamics and the derivation of mapping equations of motion for the one-dimensional atom in a harmonic field is fulfilled. The relationship between the energy change of the classical atom in a harmonic field and expressions for dipole matrix elements is revealed and analysed.