# Analytic fits to the rate coefficients

The functional fit to the rate coefficients for collisional de-excitation takes the form

where , and a value of was adopted in all the fits. This last parameter prevents divergence of the rate coefficients as .

Three files are included, for de-excitation of para-H2 and ortho-H2 (merged into a single file) by H, He, ortho- and para-H2; these files are called, respectively, qh1h2.dat , qheh2.dat , qoh2h2.dat and qph2h2.dat   In each file, the first line specifies the total number of transitions.  Subsequent lines contain, in 5 successive columns: an index identifying the initial (upper) state; an index identifying the final (lower) state; value of a; value of b; value of c.  The ordering (and identification) of the levels is according to energy, commencing with the lowest J=0, v=0 state of H2.  For transitions induced by collisions with H, He, and para-H2, the 49 lowest energy levels are all included, i.e. up to and including J=6, v=3.  In addition, levels 52 (J=7, v=3) and 54 (J=8,v=3) are present, as they were incorporated in the collisional basis sets. For transitions induced by collisions with ortho-H2, a smaller basis of 39 energy levels was used.   The energetic ordering of the pairs of values of (J,v) is to be found in the file: labelling.energy_levels