Magnetic dipole hyperfine interactions in ${}^{137}{\mathrm{Ba}}^{+}$ and the accuracies of the neutral weak interaction matrix elements

The relativistic coupled-cluster method is applied to calculate the magnetic dipole hyperfine constant $“A”$ of the ${6s}_{1/2},$ ${6p}_{1/2},$ ${6p}_{3/2},$ and ${5d}_{3/2}$ states of singly ionized barium. After the inclusion of two-body correlation effects into the computation of the hyperfine matrix elements, the accuracy of the obtained values was significantly increased compared to earlier computations. Based on these numbers and earlier calculations of the electric dipole transitions and excitation energies, an estimate for the accuracy of the $|\left[{5p}^6\right]{6s}_{1/2}\overrightarrow{〉}|\left[{5p}^6\right]{5d}_{3/2}〉$ parity-nonconserving electric dipole transition amplitude is carried out. The results suggest that for the first time, to our knowledge, a precision of better than 1% is feasible for this transition amplitude.