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An Extended Hauser-Feshbach Method (EHFM) is developed for light heavy-ionfusion reactions in order to provide a detailed analysis of all the possibledecay channels by including explicitly the fusion-fission phase-space in thedescription of the cascade chain. The mass-asymmetric fission component isconsidered as a complex-fragment binary-decay which can be treated in the sameway as the light-particle evaporation from the compound nucleus instatistical-model calculations. The method of the phase-space integrations forthe binary-decay is an extension of the usual Hauser-Feshbach formalism to beapplied to the mass-symmetric fission part. The EHFM calculations includeground-state binding energies and discrete levels in the low excitation-energyregions which are essential for an accurate evaluation of the phase-spaceintegrations of the complex-fragment emission (fission). In the presentcalculations, EHFM is applied to the first-chance binary-decay by assuming thatthe second-chance fission decay is negligible. In a similar manner to thedescription of the fusion-evaporation process, the usual cascade calculation oflight-particle emission from the highly excited complex fragments is applied.This complete calculation is then defined as EHFM+CASCADE. Calculatedquantities such as charge-, mass- and kinetic-energy distributions are comparedwith inclusive and/or exclusive data for the $^{32}$S+$^{24}$Mg and$^{35}$Cl+$^{12}$C reactions which have been selected as typical examples.Finally, the missing charge distributions extracted from exclusive measurementsare also successfully compared with the EHFM+CASCADE predictions.Comment: 34 pages, 6 Figures available upon request, Phys. Rev. C (to be  published

Extended Hauser-Feshbach method for statistical binary decay of light-mass systems