We have performed ab initio mixed-states and sum-over-states calculations of parity-nonconserving (PNC) electric dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transition amplitudes between $s-d$ electron states of Cs, Fr, ${\mathrm{Ba}}^{+},$ and ${\mathrm{Ra}}^{+}.$ For the lower states of these atoms we have also calculated energies, $E1\mathrm{}$ transition amplitudes, and lifetimes. We have shown that PNC $E1\mathrm{}$ amplitudes between $s-d$ states can be calculated to high accuracy. Contrary to the Cs $6s-7s$ transition, in these transitions there are no strong cancellations between different terms in the sum-over-states approach. In fact, there is one dominating term which deviates from the sum by less than $20\%.$ This term corresponds to an ${s-p}_{1/2}$ weak matrix element, which can be calculated with an accuracy of better than $1\%,$ and a $p_{1/2}{-d}_{3/2}$ $E1\mathrm{}$ transition amplitude, which can be measured. Also, the $s-d$ amplitudes are about four times larger than the corresponding $s-s$ amplitudes. We have shown that by using a hybrid mixed-states–sum-over-states approach the accuracy of the calculations of PNC $s-d$ amplitudes could compete with that of Cs $6s-7s$ if $p_{1/2}{-d}_{3/2}$ $E1\mathrm{}$ amplitudes are measured to high accuracy.

• Received 8 January 2001

DOI:https://doi.org/10.1103/PhysRevA.63.062101