Nonadiabatic Dynamics and Rotational Coupling in $\mathrm{HeH^+}$ Dissociative Recombination and Resonant Ion-Pair Formation

We present a time-dependent wave-packet study of dissociative recombination (DR) and resonant ion-pair (RIP) formation in $\mathrm{HeH^+}$ isotopologues. Nuclear dynamics are treated on a manifold of 23 coupled electronic states of $^2Σ$, $^2Π$, and $^2Δ$ symmetries, including rotational couplings between different symmetries. The results reveal that inclusion of a large manifold of resonant states and rotational couplings significantly enhances the DR cross section relative to earlier theoretical studies. In the diabatic representation, $^2Σ$ states dominate the recombination dynamics, while in the adiabatic representation, $^2Π$ and $^2Δ$ states contribute significantly at low collision energies. For RIP formation, two different diabatization schemes yield systematically larger cross sections than previous models, highlighting the sensitivity of ion-pair production to electronic coupling structure. Isotopic effects are examined, showing a clear inverse dependence of cross section magnitude on reduced mass. Thermal rate coefficients are computed over $10^{2}$ to $2\times 10^4$ K thermal electron temperatures. Isotopic effects are examined, showing a clear inverse dependence of cross section magnitude on reduced mass. The results are compared with rotational-state-resolved experimental and theoretical results. The present results highlight the importance of multistate coupling and rotational interactions in electron-driven fragmentation processes relevant to primordial and astrophysical plasmas.