Premium
On the validity of the Landé interval rule in the alkaline earth atoms
Author(s) -
Langhoff Stephen R.,
Bauschlicher Charles W.,
Partridge Harry
Publication year - 1984
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560260842
Subject(s) - valence (chemistry) , metastability , chemistry , atomic physics , radiative transfer , hamiltonian (control theory) , ab initio , physics , quantum mechanics , mathematical optimization , mathematics , organic chemistry
Ab initio spin–orbit matrix elements 〈 3 P 2 | H so | 3 P 2 〉 and 〈 3 P 1 | H so | 1 P 1 〉 have been computed for Mg, Ca, and Sr by using large Slater basis sets and the microscopic spin–orbit Hamiltonian. Results obtained at the valence, core‐valence, and singles‐plus‐doubles configuration interaction level demonstrate the importance of including core‐valence correlation. Oscillator strengths for the dipoleallowed 1 P 1 – 1 S 0 transition computed at the core‐valence level are also in excellent agreement with experiment. Combining these results leads to radiative lifetimes for the 3 P 1 metastable states of 4.16 ms for Mg, 0.34 ms for Ca, and 21.2 μs for Sr. These are in good accord with experiment if the class of longer lifetimes is selected for Mg and the class of shorter lifetimes is selected for Ca. The present theoretical study establishes the following two points. First, that deviations from the Landé interval rule are an accurate reflection of the 〈 3 P 1 | H so | 1 P 1 〉 matrix element for the heavier alkaline earths (Sr and Ba), but not for Mg, where spin–spin effects are comparable. Second, that the inclusion of direct relativistic effects is not necessary for quantitative agreement with the observed 3 P 1 lifetimes. Thus it appears that one is justified in using the Breit interaction as a first‐order perturbation to describe radiative transitions occurring through off‐diagonal mixing with intermediate states.