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

Abstract

We have calculated the electric dipole (E1) oscillator strengths and spontaneous decay rates for 12 spin-changing P–D transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron. The specific transitions for 4He are [Formula: see text] and [Formula: see text] with n = 2, 3, 4 and n′ = 3, 4. To include the effects of intermediate coupling between pure LS and jj, we used the Breit formulation for the spin–orbit and spin–other-orbit operators and combined the results of the exact diagonalization of the 2 × 2 energy matrix with pseudostate expansions to perform the perturbation sums over intermediate states. We calculated both the length and velocity gauges as a check on numerical accuracy and the validity of the transition operators.

Precision calculation of hyperfine structure and the Zemach radii of $^{6,7}$Li$^+$ ions

“…In calculating the second-order energy, we subtract out the dominant 2 1 P 1 − 2 3 P 1 singlet-triplet mixing term (ignoring for now hyperfine structure for purposes of illustration) and replace it with the energy shift ∆ obtained by exact diagonalization of the corresponding 2 × 2 Hamiltonian matrix, thereby summing the perturbation series for this term to infinity [32][33][34] according to the formula…”