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We analyzed a thousand visible spectra of Fulcher-$\alpha$ band measured fordivertor plasmas in Large Helical Device. With a coronal model and Baysianinference, the population distribution of hydrogen molecule in the electronicalground state were estimated. The non-thermal population distribution wasrecovered with a two-temperature model, which has two sets of rotational andvibrational temperatures, as well as their mixture coefficient. The lowerrotational temperature significantly changes according to the plasmaparameters. Its nearly linear dependence on the electron density was found,which is consistent with previous works. The lower vibrational temperature alsoshows a small density dependence, as reported by a previous work. On the otherhand, the higher rotational and vibrational temperatures as well as the mixturecoefficient only show slight changes over the broad range of plasma parameters.These population parameters show a significant correlation; with higherelectron density, all the temperatures and the fraction of thehigher-temperature component increase simultaneously. This suggests that theelectron-impact plays an important role to determine the populationdistribution.

Plasma-Parameter Dependence of Ro-Vibrational Temperatures for $\mathrm{H}_2$ in LHD Divertor