Reexamination of nuclear quadrupole moments in39−41K isotopes

Abstract

Nuclear quadrupole moments ($Q$'s) in three isotopes of the potassium atom (K) with mass numbers 39, 40, and 41 are evaluated more precisely in this work. The $Q$ value of ${}^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4{P}_{3/2}$ state. Furthermore, combining this $Q$ value with the measured ratios $Q$(${}^{40}$K)$/Q$(${}^{39}$K) and $Q$(${}^{41}$K)$/Q$(${}^{39}$K), we obtain $Q$(${}^{40}$K)$=\ensuremath{-}0.0764(8)\phantom{\rule{4pt}{0ex}}b$ and $Q$(${}^{41}$K)$=0.0747(7)\phantom{\rule{4pt}{0ex}}b$, respectively. These results disagree with the sub-1$%$ accuracy standard values recently quoted by Pyykk\"o [Mol. Phys. 106, 1965 (2008)]. The calculations were carried out by employing the relativistic coupled-cluster theory at the single, double, and involving important valence triple approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$'s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in a few more excited states are presented. Also, we find that the latest reported experimental hyperfine structure constant results for the $4P$ states in ${}^{39}$K are inconsistent with our calculations.