Determination of nuclear quadrupole moments of $^{25}$Mg, $^{87}$Sr, and $^{135,137}$Ba via configuration-interaction plus coupled-cluster approach

TL;DR

This work determines nuclear quadrupole moments for $^{25}$Mg, $^{87}$Sr, and $^{135,137}$Ba by combining measured electric quadrupole hyperfine-structure constants with high-precision electric-field gradients computed via a relativistic configuration-interaction plus coupled-cluster approach. The authors compute $q$ for low-lying states in Mg, Sr, and Ba, and extract $Q$ from $B = 234.9648867\, q\, Q$, validating their $q$ and $A$ results against experimental data. Final quadrupole moments are $Q(^{25}$Mg$)=0.203(2)$ b, $Q(^{87}$Sr$)=0.336(4)$ b, $Q(^{135}$Ba$)=0.161(2)$ b, and $Q(^{137}$Ba$)=0.246(4)$ b, with Mg in excellent agreement with muonic X-ray measurements and Sr/Ba results broadly consistent with prior determinations though exhibiting some discrepancies with the 2018 Pekka values. The study demonstrates the reliability of the CI+CC framework for hyperfine-property calculations in alkaline-earth atoms and provides updated, state-averaged $Q$ values that can inform nuclear structure models and related precision measurements.

Abstract

Using the configuration-interaction plus coupled-cluster approach, we calculate the electric-field gradients $q$ for the low-lying states of alkaline-earth atoms, including magnesium (Mg), strontium (Sr), and barium (Ba). These low-lying states specifically include the $3s3p~^3\!P_{1,2}$ states of Mg; the $5s4d~^1\!D_{2}$ and $5s5p~^3\!P_{1,2}$ states of Sr; as well as the $6s5d~^3\!D_{1,2,3}$, $6s5d~^1\!D_{2}$, and $6s6p~^1\!P_{1}$ states of Ba. By combining the measured electric quadrupole hyperfine-structure constants of these states, we accurately determine the nuclear quadrupole moments of $^{25}$Mg, $^{87}$Sr, and $^{135,137}$Ba. These results are compared with the available data. The comparison shows that our nuclear quadrupole moment of $^{25}$Mg is in perfect agreement with the result from the mesonic X-ray experiment. However, there are approximately 10\% and 4\% differences between our results and the currently adopted values [Pyykk$\rm \ddot{o}$, Mol. Phys. 116, 1328(2018)] for the nuclear quadrupole moments of $^{87}$Sr and $^{135,137}$Ba respectively. Moreover, we also calculate the magnetic dipole hyperfine-structure constants of these states, and the calculated results exhibit good agreement with the measured data.