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Results of semiempirical, adiabatic hyperspherical calculations are presented for the photodetachment cross section of the process H- 2p2 (3Pe)+γ→H(n=2)+ e- at photon energies in the range from threshold to 0.125 a.u. above. We find the detachment cross section to have a maximum value of 482 Mb at 25.7 meV above threshold, in good agreement with results of close-coupling calculations by Jacobs, Bhatia, and Temkin [Astrophys. J. 242, 1278 (1980)]. In contrast to the close-coupling results, however, we find that the detachment cross section rises by a factor of more than 400 from its threshold value to its maximum.