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Summary form only given.Optical processes with strong coupling and quantum coherence are opening various new possibilities beyond the limit of conventional optical processes. Recently, we have extended these optical processes to a high-density solid medium using solid hydrogen for stimulated Raman scattering (SRS) process. We have found that the strong-coupling in high-density solid-medium results in a new phenomenon of self-induced phase-matching in which the parametric anti-Stokes generation process self-organizes the phase-matching without the strict restriction of the refractive-index dispersion of the medium. In order to assess the mechanism of the self-induced phase-matching, the essential issue should be to measure the coherence decay time for the Raman transition quantitatively. The purpose of this work is to report on this issue using solid hydrogen crystal of nearly pure parahydrogen. The coherence decay for the Raman transition was measured by using time-resolved coherent anti-Stokes Raman scattering.