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Structure and dynamics of HD$^+$ in the vicinity of the H$^+$ + D and D$^+$ + H dissociation thresholds: Feshbach resonances and the role of g/u-symmetry breaking

We report on the measurement and analysis of photoionisation, mass-analysed-threshold-ionisation and pulsed-field-ionisation zero-kinetic-energy photoelectron spectra of HD in the vicinity of the dissociative-ionisation thresholds H$^+$ + D(1s) + e$^-$ and H(1s) + D$^+$ + e$^-$. The spectra were recorded via the $v=11$-13 vibrational levels of the $\bar{\rm H}$ and $\bar{\rm B}$ outer wells of the H$\bar{\rm H}$~$^1Σ_g^+$ and B$^{\prime\prime}\bar{\rm B}$~$^1Σ_u^+$ states and provide information on the weakly bound levels of the X$^+$ $^2Σ_g^+$ ground state of HD$^+$ with vibrational quantum numbers $v^+=16$-21 and rotational angular-momentum quantum numbers $N^+=0$-10. The spectra also reveal for the first time shape and Feshbach resonances of HD$^+$ located energetically above the H$^+$ + D(1s) dissociation limit. The structure and dissociation dynamics of the $\bar{\rm H}$ and $\bar{\rm B}$ states of HD and of the X$^+$ $^2Σ_g^+$ and A$^+$ $^2Σ_u^+$ states of HD$^+$ near the dissociation thresholds are strongly influenced by the g/u-symmetry breaking caused by the nuclear-mass asymmetry.