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

In this paper, we have calculated parity nonconserving electric dipole transition amplitudes of the hyperfine components for the transitions between the ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin dependent amplitudes from experimental measurements. The wavefunctions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.