There are basically two ways to determine precision values for nuclear quadrupole moments (Q): Measurements for stable or reasonably long-lived (mostly ground) states by atomic and molecular spectroscopy and measurements for much shorter-lived excited states using nuclear condensed matter techniques like Mössbauer (MS) or perturbed angular distribution (PAD) (and correlation, PAC) spectroscopy. In all cases the direct experimental result is the product of the electric field gradient (efg) at the nuclear site with Q. The efg for atomic and simple molecular systems can now generally be obtained from theory with good accuracy, while the present status of density functional calculations for the solid-state systems used with short-lived excited states limits the accuracy to the 10 to 20% level. 

For Cd and Hg we have overcome this problem by measuring isolated linear molecules with PAC [1]. Similar experiments are in preparation for the PAC state in 204Pb. For the MS state in 119Sn [2] such an approach is practically impossible. Analysis of all now available information shows, however, that the presently accepted value of Q is about 20% too large, thus confirming an earlier ISOLDE result [3].

[1] H. Haas et al., Phys. Rev. Letters 216, 103001 (2021)

[2] P. Pyykkö, Mol. Phys. 116, 1328 (2018)

[3] H. Haas et al., Hyperfine Interact. 15, 215 (1983)