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We investigate the formation of molecular hydrogen (H_2) in a primordial H+He gas cloud irradiated by a power-law UV flux. We find that at high densities (>1 cm^{-3}) and low temperatures (<10^4 K), the background radiation enhances the formation of H_2 and results in molecular cooling dominating over photoionization heating. This process could accelerate the collapse and fragmentation of dense objects at high redshifts.

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