Quasi-resonant transitions in ultracold collisions of hydrogen isotope dimers: zero-energy resonances in vibration space

The quasi-resonant rotation-rotation (QRRR) mechanism is studied theoretically in ultracold H$_2$, D$_2$, and HD self-collisions as a function of initial vibrational level $v$. In the QRRR mechanism, the collision partners swap internal rotational excitation resulting in large cross sections and scattering lengths. The efficiency of the QRRR mechanism is a consequence of conservation of total system internal rotational angular momentum and near conservation of internal energy. Extending to high vibrational excitation, we find that the QRRR mechanism identified for H$_2$($v=1$)+H$_2$($v'=0$) by Qu\'em\'ener {\it et al.} [1] persists with scattering lengths, both real and imaginary, varying smoothly with $v$. However, exceptions occur at select high values of $v$ where the scattering lengths are enhanced by orders of magnitude corresponding to the location of a zero-energy resonance in ``vibration space." Similar trends are seen for D$_2$ and HD self-collisions. If the QRRR mechanism operates in other ultracold dimer-dimer collision systems, then vibrational excitation may be used to ``tune" the interaction strength similar to methods which use external fields or theoretical variation of the reduced mass.\\[4pt] [1] G. Qu\'em\'ener et al., {\it Phys. Rev.} A {\bf 77}, 030704(R) (2008).