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A coupled transport-rate theory of free photoexcited carrier densities and band-gap trap states in direct-gap semiconductors with fast band-to-band recombination rates is presented. The rate equations are decoupled and solved analytically by means of an adiabatic principle which leads to time gating of photothermal emission and capture transport processes between trap states and bandedges occurring with time constants much longer than the recombination lifetime. This theory exploits the adiabatic character of photoexcitation of nonequilibrium excess free carriers which attains steady-state distribution at times very short compared to trap emission and capture effects induced by thermal transport to and from the bandedges of the semiconductor. The theory accounts for the absorption of a sub-band-gap probe laser beam by free carriers (both electrons and holes) photogenerated by a super-band-gap laser beam, as well as absorption by nonequilibrium trapped carriers in the band-gap states due to thermal emission and capture events. The theory forms the basis of a new two-laser-beam deep level photothermal spectroscopy (DLPTS). The latter was implemented and tested on semi-insulating (SI)-GaAs. DLPTS and photocarrier radiometric signals were used to validate the theory. The generated experimental temperature-scanned photothermal spectra and time-resolved transients were fitted with the multiple-trap theory and yielded superpositions of energy levels and capture cross sections. It was found that the one-trap theory commonly used in conventional deep level transient spectroscopy based techniques, such as photoinduced transient spectroscopy, does not give a good fit to the experimental DLPTS spectrum. The methodology encompassing the adiabatic theory and combined DLPTS time-scanned transients and temperature-scanned spectra amounts to an analytical quantitative photothermal spectroscopy capable of noncontact all-optical probing of band-gap defect/impurity state energy distrib- utions and capture cross sections in direct-gap semiconductors, and SI-GaAs in particular.