The band structure of type-I (In,Al)As/AlAs quantum dots with band gap energy exceeding 1.63 eV is indirect in momentum space, leading to long-lived exciton states with potential applications in quantum information. Optical access to these excitons is provided by mixing of the $Gamma$- and X-conduction band valleys, from which control of their spin states can be gained. This access is used here for studying the exciton spin-level structure by resonant spin-flip Raman scattering, allowing us to accurately measure the anisotropic hole and isotropic electron $g$ factors. The spin-flip mechanisms for the indirect exciton and its constituents as well as the underlying optical selection rules are determined. The spin-flip intensity is a reliable measure of the strength of $Gamma$-X-valley mixing, as evidenced by both experiment and theory.
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