Ultracold vibrational relaxation of H$_2$ molecules*

The success in creating Bose-Einstein condensates of molecules has spurred much interest in atom-molecule and molecule-molecule collisions at cold and ultracold temperatures. To understand the effect of rotational and vibrational relaxation in molecular collisions at ultracold temperatures we have performed quantum scattering calculations taking the H$_2$-H$_2$ system as an illustrative example. We have used a time-independent quantum formalism based on Jacobi coordinates in space fixed frame implemented in a new quantum scattering code [1] that includes all six internal degrees of freedom. Elastic and inelastic cross sections including state-to-state cross sections in cold and ultracold H$_2$(v=1,j=0) + H$_2$(v=0,j=0) and H$_2$(v=1,j=0) + H$_2$(v=1,j=0) collisions will be presented. \footnotesize{ [1] R. V. Krems, TwoBC - quantum scattering program, University of British Columbia, Vancouver, Canada, (2006) }