Consistent description of Klein-Gordon dipole matrix elements

Abstract

Relativistic semiclassical radial dipole matrix elements are derived analytically in the length and velocity forms using Klein-Gordon wavefunctions. In contrast to our previous works in which KGWKB matrix elements were derived only in the length form, neglecting the angular displacement of the relativistic trajectory, we have obtained these matrix elements in both length and velocity forms without the above-mentioned approximation. In the latter form, an effective velocity operator has been used. The present approaches lead to two new intermediate states which are discussed. Detailed numerical results obtained through a systematic study of lithium, sodium and copper isoelectronic sequences, starting with the nonrelativistic WKB approaches, enable us to draw inferences as to the improvements and also the limitations of the new relativistic formulae.