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In this paper, we have calculated parity nonconserving electric dipoletransition amplitudes of the hyperfine components for the transitions betweenthe ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$using sum-over-states technique. The results are presented to extract theconstants associated with the nuclear spin dependent amplitudes fromexperimental measurements. The wavefunctions to calculate the most dominantpart of the sums are constructed using highly correlated coupled-cluster theorybased on the Dirac-Coulomb-Gaunt Hamiltonian.

$E1$ PNC transition amplitudes of the hyperfine components for $^2S_{1/2}$ $-$ $^2D_{3/2}$ transitions of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$