  Experimental measurements and theoretical calculations of state-to-state rate
coefficients for rotational energy transfer of CO in collision with H$_2$ are
reported at the very low temperatures prevailing in dense interstellar clouds
(5 - 20 K). Detailed agreement between quantum state-selected experiments
performed in cold supersonic flows using time-resolved infrared -
vacuum-ultraviolet double resonance spectroscopy and close-coupling quantum
scattering calculations confirms the validity of the calculations for
collisions between the two most abundant molecules in the interstellar medium.
