Abstract
A new analytical expression of a previously proposed Klein-Gordon dipole matrix elements in the quasiclassical approach (including quantum defects) is presented. The intermediate state method in the semiclassical Coulomb approximation is used to derive the Klein-Gordon dipole radial integrals corresponding to single-electron nlj to n'l'j' transitions with arbitrary quantum numbers in non-hydrogenic ions. This last approach is extended to the second-order Dirac-Coulomb equation. Similar expressions are obtained in the two electromagnetic field gauges which in the non-relativistic limit give the length and velocity forms of the transition operator. A computational procedure for the evaluation of the Dirac formulae by the use of recursion relations, expressed in terms of Anger's functions, is also described. Numerical applications of the above-mentioned WKB methods, starting from the well known Schrodinger dipole matrix elements, are carried out for the calculation of the lowest 2s1/2-2p1/2,3/2 transitions in the lithium isoelectronic sequence for atomic number Z=3-92. Oscillator strengths for Rydberg 2s1/2-np1/2(Ca17+, n=8-16 and Zr37+, n=3-20) and ns1/2-20p1/2,3/2(Ca17+, Zr37+, W71+, U89+, n=19,20) transitions are also reported. The values obtained are compared and discussed with available experimental and other theoretical treatments.
Published Version
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