Nuclear-spin-dependent parity-nonconserving transitions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ba</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ra</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

An experiment to observe parity nonconservation using the $|{5p}^{6}6s{〉}_{1/2}\ensuremath{\rightarrow}|{5p}^{6}5d{〉}_{3/2}$ transition in ${\mathrm{Ba}}^{+}$ has been proposed [N. Fortson, Phys. Rev. Lett., 70, 2383 (1993)]. We have carried out relativistic configuration-interaction calculations to explore whether the $|{5p}^{6}6s{〉}_{1/2}\ensuremath{\rightarrow}|{5p}^{6}5d{〉}_{5/2}$ and $|{6p}^{6}7s{〉}_{1/2}\ensuremath{\rightarrow}|{6p}^{6}6d{〉}_{5/2}$ transitions in ${\mathrm{Ba}}^{+}$ and ${\mathrm{Ra}}^{+}$ respectively are good candidates for carrying out similiar experiments to measure the nuclear anapole moment. Our results suggest that ${\mathrm{Ra}}^{+}$ might be a good candidate for such an experiment.