Interstellar clouds containing optically thin H2

We consider clouds which contain H2 that is optically thin in the Lyman and Werner bands; and following Black and Dalgarno and towardpitzer and Zweibel, we develop models to explain the observed populations in the excited rotational levels. Observational uncertainties preclude arriving at very precise conclusions, but to achieve good agreement with the measurements we argue that a considerable fraction of all the H2 formed on grains is created with some degree of rotational excitation, and that the formation rate on grains, R, is such that 10-17less than or equal toRless than or equal to3 times10-17 cm3 s-1, but our results are not sufficiently accurate to determine if R does vary. Also, we infer densities within different clouds, and we find that in general n (H) ranges between 10 and 100 cm-3, except that toward zeta Ori there exists a cloud with n (H) =1000 cm-3. We infer the radiation field within clouds and whether the cloud is near an early-type star. For example, the neutral hydrogen observed toward tau Sco is probably at the outer boundary of the H--region surrounding that star