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The unoccupied states of complex materials are difficult to measure, yet playa key role in determining their properties. We propose a technique that canmeasure the unoccupied states, called time-resolved Compton scattering, whichmeasures the time-dependent momentum distribution (TDMD). Using anon-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to alattice in a pump-probe setup. We find a direct relation between temporaloscillations in the TDMD and the dispersion of the underlying unoccupiedstates, suggesting that both can be measured by time-resolved Comptonscattering. We demonstrate the experimental feasibility by applying the methodto a model of MgB$_2$ with realistic material parameters.

Mapping of the unoccupied states and relevant bosonic modes via the time dependent momentum distribution