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

Abstract

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s 2, 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

Exponentially Correlated Hylleraas–Configuration Interaction Studies of Atomic Systems. III. Upper and Lower Bounds to He-Sequence Oscillator Strengths for the Resonance 1S→1P Transition

“…She pointed out that, for light atoms (using C III as an example), the relativistic correction is important for a precise energy but the line strength (and hence the oscillator strength) is close to the non-relativistic one. Helium is the simplest multi-electron atom and there exists a recent high-precision multiconfiguration Dirac-Hartree-Fock (MCDHF) calculation (using the GRASP2K [54][55][56] program 9 ) of the 1 S → 1 P transition [28]. Two lines in the data for He I in the table (the LLWQ lines [28]) are from this study and are included here to ascertain the magnitude of the relativistic effects for the He I transition, which turn out to be ≈0.00003 (≈0.01%) and indeed show relativistic effects to be small.…”

“…Helium is the simplest multi-electron atom and there exists a recent high-precision multiconfiguration Dirac-Hartree-Fock (MCDHF) calculation (using the GRASP2K [54][55][56] program 9 ) of the 1 S → 1 P transition [28]. Two lines in the data for He I in the table (the LLWQ lines [28]) are from this study and are included here to ascertain the magnitude of the relativistic effects for the He I transition, which turn out to be ≈0.00003 (≈0.01%) and indeed show relativistic effects to be small. Note that all of the high-precision studies (all correlated wave function calculations) are in agreement that the oscillator strength is 0.27616.…”

“…Specifically, we know from the 3040 × 2888 result that the 1088 × 960 and 1520 × 1444-term results are in error in the seventh decimal digit, but the bounds suggest that the results are only good to three decimal places. We recommend the NR oscillator strength to be 0.2761 647 (28) for He I.…”

“…6 Multi-configuration Hartree-Fock [62]. 7 Liu, Li, Wang and Qu [28]. 8 Multi-configuration Dirac-Hartree-Fock [63][64][65].…”

“…For a detailed treatment of line strengths (proportional to transition rates), see Morton et al [27], where the corrections are shown to be less than 0.1% for helium, and Liu et al [28], where they are shown to be ≈0.01% for helium.…”