Multichannel quantum defect theory for ro-vibrational transitions in ultracold molecule-molecule collisions

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and non-resonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full-close coupling (CC) calculations when spin, hyperfine and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for H$_2$-H$_2$ collisions in full-dimensionality, is shown to adequately reproduce cross sections for quasi-resonant rotational and vibrational transitions in the ultracold (1$\mu$K) and $\sim$ 1-10 K regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$-matrix evaluated in the ultracold regime (1$\mu$K) can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.