Oscillator strengths forS-PandP-Dtransitions for singly excited states of two-electron ions viaZ-dependent perturbation theory

Abstract

Oscillator strengths for electric dipole transitions between singly excited S, P, and D states are calculated via Z-dependent perturbation theory. The transition matrix elements through first order are obtained from variational perturbation first-order wave functions. Second-order expansion coefticients for the matrix elements are then estimated with the aid of several approxirnants. These matrix elements, together with accurate transition energies, yield oscillator strengths for transitions between all S-P and P-D transitions between states of two-electron ions with principal quantum number up to 9 and for values of the nuclear charge up to approximately 30.In Z-dependent perturbation theory, the nonrelativistic Hamiltonian for an X-electron atom is given, in charge-M(a, p) y ( y(a)lglq(p) ) m +I =n and where Q = r, cos8) + rzcosOz is the appropriate opera-39 4387

Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence

“…These calculations gave close agreement with those of Refs. [21,22,23,24] when nonrelativistic energies were used but came into agreement with the present calculation when relativistic corrections to the energy were made. Such energy corrections are ambiguous for triplet transitions and not at all possible for intercombination transitions.…”

“…These benchmark calculations were confirmed and extended by Kono and Hattori [22] and by Sandars and Knight [23]. Most recently, Cann and Thakkar [24] have carried out high-precision variational calculations of oscillator strengths for S − P and P − D transitions for ions in the range Z = 2 − 10.…”

“…(23,24), have no effect on the magnetic-multipole potentials, but they do modify electric-multipole potentials. In particular, a gauge transformation of the transverse-gauge potentials using the gauge function,…”

Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

“…Kono and Hattori improved and extended [2] their work on He, and then reported oscillator strengths for 24 P-D transitions [3] in each of the ions from Li+ through N +. A less accurate but much more extensive study was carried out by Sanders and Knight [4), who used Z-dependent, variational perturbation theory of low order to obtain oscillator strengths for 136 S-P and 112 P-D transitions for each of the ions through Z =30.…”

“…(17) from our calculated transition moments M in both the length and velocity forms. We used both differencing and least-squares fitting of M, with Mo and M& constrained to their known values [4]. Our estimated coefficients are listed in Tables X and XI for the S-P and P-D transitions, respectively.…”