CI-MBPT and Intensity-Based Lifetime Calculations for Th II

Abstract

Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration–interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of J = 1.5 states are strongly mixed, making theoretical predictions unreliable. To solve this problem, a method based on intensities is used. To relate experimental intensities to lifetimes, two parameters, one an overall coefficient of proportionality for transition rates and one temperature of the Boltzmann distribution of populations, are introduced and fitted to minimize the deviation between theoretical and intensity-derived lifetimes. For strongly mixed groups of states, the averaged lifetimes obtained from averaged transition rates were used instead of individual lifetimes in the fit. Close agreement is obtained. Then intensity branching ratios are used to extract individual lifetimes for the strongly mixed states. The resulting lifetimes are compared to available directly measured lifetimes and reasonable agreement is found, considering limited accuracy of intensity measurements. The method of intensity-based lifetime calculations with fit to theoretical lifetimes is quite general and can be applied to many complex atoms where strong mixing between multiple states exists.

Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms

“…However, when the properties over the three levels, such as g-factors, are averaged, the resulting values are in better agreement with the experiment: g exp = 1.0083 vs. g pRCI = 1.0293. This is what was observed in Th II [38]. More mixing and order reversal occurs in higher levels, as expected, due to higher density of states.…”

“…Some uses include cosmological applications [35], nuclear clocks [36], and calibration standards [37]. While the Th II ion is an analog of the La I atom, with three valence electrons above the core, Th II transition lifetime calculations have significant uncertainty [38]. One reason for this is strong mixing between three or more states.…”

“…Figure 1 shows the fit, which for the most part is quite close to the experimental points. From the fit, lifetime values were listed in [38] for J = 2.5 odd states:…”

“…More mixing and order reversal occurs in higher levels, as expected, due to higher density of states. Thus, one conclusion can be made that wavefunctions of 7 lowest states can be used for calculations of atomic properties, while the upper states require some averaging procedure as in [38]. A closed-shell V N−6 potential can be chosen as a starting potential, in which all six valence electrons are removed.…”