Breaking space-inversion symmetry in the dynamics of the doubly excited Q21Πu(1) state of HD

A set of cross sections for the formation of a pair of $2p$ atoms on an absolute scale is determined against the incident photon energy in the double photoexcitation of the isotopomers ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$, incorporating the same cross sections of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ obtained in our recent experiments [K. Hosaka et al., Phys. Rev. A 93, 063423 (2016)], and the oscillator strengths for the formation of a pair of $2p$ atoms from the precursor ${Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state, ${f}_{2p2p}^{{\text{H}}_{2}/\text{HD}/{\text{D}}_{2}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, are determined from the cross sections. The oscillator strength of HD, ${f}_{2p2p}^{\text{HD}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, is found to be larger than the value expected from ${f}_{2p2p}^{{\text{H}}_{2}/{\text{D}}_{2}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, considering the same decay mechanism for ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ molecules photoexcited to the ${Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state, a mechanism which was revealed in our recent experiments for ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ mentioned above. The origin of the enhancement in the oscillator strength for HD is discussed and we show that the enhancement is attributed to nonadiabatic transitions between a gerade electronic state and an ungerade one through a term neglected in the Born-Oppenheimer approximation that vanishes in the homonuclear isotopomers (${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$) but does not vanish in the heteronuclear isotopomer (HD). It turns out that approximately 10--20 % of ${f}_{2p2p}^{\text{HD}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$ originates from such nonadiabatic transitions due to the breaking of the space-inversion symmetry for electrons.