Oscillator strengths and radiative decay rates for spin-changing S–P transitions in helium: finite nuclear mass effects

Abstract

We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for 24 spin-changing transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron augmented by the recently derived Pachucki term. The specific transitions for 4He are and with and for For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on both numerical accuracy and validity of the transition operators. The corrections for the nuclear mass and the electron anomaly tend to cancel, indicating that if one is included, then so should be the other. The tables give mass- and anomaly-dependent coefficients permitting the easy generation of results for the other isotopes of helium.

Oscillator strengths for spin-changing P–D transitions in He I including the effect of a finite nuclear mass and intermediate coupling

“…All these are within one part in 10 8 or less of the latest recommended values of the fundamental constants [7]. Tables 1 to 4 As described in Paper III [3], Pachucki [14] identified an additional interaction proportional to a e due to the magnetic component of the radiation field. The extra contribution to the length matrix element ∆ǫM L is…”

“…These calculations summed the spin-dependent Breit interaction as a first-order perturbation over all intermediate states, but assumed infinite nuclear mass. In Paper III [3] we applied the same perturbation analysis to 24 S-P transitions and included the electron anomaly and the true nuclear mass, which partially cancel each other so it is important to include both. The present paper extends those results to 12 P-D transitions with corrections to the wave functions and operators for the nuclear mass and electron anomaly and the operators for the electron anomaly.…”

“…In Sections 2 and 3 below we repeat the theoretical discussion in Paper III [3] for the true nuclear mass and the electron anomaly and show how the summation over intermediate states is modified to use the exact diagonalization of the 1 D 2 and 3 D 2 states. We use reduced atomic units in which we relate lengths r and energies ǫ to laboratory values by R = a 0 (m e /µ)r and E = α 2 m e c 2 (µ/m e )ǫ.…”

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium

“…[33] In 2008, Bo et al merely obtained the splitting of fine energy levels 2 3 𝑃 o 1 -2 3 𝑃 o 0 and 2 3 𝑃 o 2 -2 3 𝑃 o 0 , using the multi-configuration Dirac-Fock (MCDF) method. [34] A few years later, the fine structure and transition including the relativistic effect and the influence of finite nuclear mass were further studied by Morton et al [27,29] using the relativistic many-body perturbation theory (RMBPT). In 2020, the electric dipole (E1) oscillator strengths of 1𝑠2𝑝 states were investigated by G lowacki [30] using the configuration interaction Dirac-Fock (CIDF) approach.…”

“…In 2020, the electric dipole (E1) oscillator strengths of 1𝑠2𝑝 states were investigated by G lowacki [30] using the configuration interaction Dirac-Fock (CIDF) approach. Although there are a lot of works [4,6,29] about magnetic quadrupole (M2) transition, it is still meaningful to study systematically the electric quadrupole (E2) and M2 transitions.…”