How to take excited H2 levels into account

Case 1: 50 < Tk < 500 K

Hydrogen molecules (H2) exist in two isomeric forms: para-hydrogen with total nuclear spin I = 0 and ortho-hydrogen with I = 1. In the ground electronic and vibrational state¹, the rotational levels of para-H2 have even values of the angular momentum j while the levels of ortho-H2 have odd j values. The ground-state of ortho-H2 (j = 1) lies 170 K above the ground-state of para-H2 (j = 0).

In cold environments where the kinetic temperature Tk is lower than ~50 K and in the absence of radiative pumping, only the ground-state of the two nuclear spin isomers are significantly populated so that only para-H2 (j = 0) and ortho-H2 (j = 1) need to be considered as collision partners. Moreover, the rate coefficients for ortho-H2 (j = 1) are generally larger than those for para-H2 (j = 0), by up to an order of magnitude

At higher kinetic temperatures Tk < 50 K or in the presence of radiative pumping, H2 molecules in excited levels j = 2, 3, etc. can become significant new colliders. It has been generally found, however, that the dominant collisional rate coefficients for H2 (j > 1) differ by less than 20-30% from those for H2 (j = 1) (e.g. Daniel et al. 2014 and references therein). This result holds for targets in their ground vibrational state and for target rotational levels or kinetic temperatures below ~500 K, i.e. below the opening of the H2 level j = 2 at 510 K. In these conditions, rotation-rotation transfers between the target species and H2 are negligible so that H2 remains mostly in the same rotational state during the collision (i.e. j → j).

EMAA provides de-excitation rate coefficients (in cm3s-1) due to collisions with 'para-H2' and 'ortho-H2' which in practice correspond to H2 (j = 0 → 0) and H2 (j = 1 → 1), respectively (except otherwise stated). In order to include excited levels of H2, rate coefficients for e.g. H2 (j = 2 → 2) can be assumed to be approximately equal to those for H2 (j = 1 → 1). Thus, in radiative transfer calculations, the volume density (in cm-3) affected to the 'para-H2' collider should be that of H2 (j = 0) while the volume density affected to the 'ortho-H2' collider should be that of the sum of all levels of H2 with j > 0. A simple solution to estimate the H2 level populations is to further assume that these levels are thermalized at the kinetic temperature, with a fixed or thermalized ortho-to-para ratio.


Daniel F., Faure A., Wiesenfeld L., Roueff E., Lis D. C, Hily-Blant P., MNRAS 444 2544-2554 (2014)
Faure A., Lique F., Wiesenfeld L., MNRAS 460 2103-2109 (2016)

1The first vibrational level of H2 opens at 4161.2 cm-1