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

TL;DR

The study determines the nuclear electric quadrupole moment of $^{87}\mathrm{Sr}$ by combining experimental NQCCs for SrO and SrS with high-accuracy EFGs computed at relativistic CC levels within an X2Cmmf framework, including Gaunt corrections and vibrational effects. By systematically evaluating CCSD(T), CCSD-T, and CCSD$\tilde{\mathrm{T}}$ schemes and performing extensive basis-set and active-space convergence tests, the authors identify CCSD(T) as the most balanced approach, yielding a final $Q(^{87}\mathrm{Sr})=0.33666\pm0.00258$ b (two-molecule average from SrO and SrS). The results are in excellent agreement with recent atom-centered determinations (e.g., $Q(^{87}\mathrm{Sr})=0.336\pm0.004$ b by Tang) and suggest a revision relative to older accepted values, demonstrating the robustness of the molecular approach and the importance of triple-excitation correlation and relativistic effects in accurate EFG calculations. The work also demonstrates a first implementation of massively parallel tensor operations for high-order CC calculations in DIRAC via TAPP-CTF, enabling scalable, accurate molecular property computations on HPC platforms.

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-$ζ$ 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)].

Figures (1)

• Figure 1: Electric field gradient (EFG) of the SrO molecule as a function of the virtual orbital energy cutoff, computed at the equilibrium geometry at the DCG-CCSD level.