The nuclear electric quadrupole moment of $^{87}$Sr from highly accurate molecular relativistic calculations

TL;DR

This study accurately determines the nuclear electric quadrupole moment of $^{87}$Sr using advanced relativistic molecular calculations combined with experimental data, resulting in a value slightly larger than the accepted standard.

Contribution

It introduces a molecular method with high-level relativistic calculations to determine the NQM of $^{87}$Sr, providing a new reference value.

Findings

The NQM of $^{87}$Sr is 0.33666 ± 0.00258 barns.

The new value is about 10% larger than the current standard.

Results are in excellent agreement with recent independent determinations.

Abstract

The nuclear electric quadrupole moment (NQM) of $^{87}$Sr has recently been revisited using high-precision relativistic atomic calculations [B. Lu et al., Phys. Rev. A 100, 012504 (2019)], indicating that the currently accepted value should be revised and that their result may serve as a new reference. In the present work, we determine the NQM of $^{87}$Sr from the molecular method, by combining the experimentally measured nuclear quadrupole coupling constants (NQCCs) of SrO and SrS with highly accurate relativistic calculations of the electric field gradient (EFG) at the Sr nucleus. Electronic correlation is treated at the CCSD(T), CCSD-T and CCSD$\tilde{\text{T}}$ levels. The iterative T contribution of the latter, composite scheme was obtained using a newly implemented parallel scheme where the distributed memory tensor library Cyclops Tensor Framework (CTF) was made available to the DIRAC code for relativistic molecular calculations through TAPP, the new community standard for tensor operations. All correlated calculations are performed using the exact two-component molecular mean-field Hamiltonian (X2C$\mathrm{mmf}$). The Gaunt two-electron interaction is incorporated, an even-tempered optimized quadruple-$\zeta$ quality basis set is employed, and vibrational corrections are accounted for. Our best result is $Q($$^{87}$Sr$) = 0.33666 \pm 0.00258$ b, which is about 10% larger than currently accepted standard value, while it is in excellent agreement with recent determinations [Y.-B. Tang, arXiv:2512.07603 [physics.atom-ph] (2025)].