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We develop an efficient computational technique to calculate compositeexcitonic states in photoexcited semiconductors through the stochasticvariational method (SVM). Many-body interactions between an electron gas andthe excitonic state are embodied in the problem through Fermi holes in theconduction band, introduced when electrons are pulled out of the Fermi sea tobind the photoexcited electron-hole pair. We consider the direct Coulombinteraction between distinguishable particles in the complex, theexchange-induced band-gap renormalization effect, and electron-hole exchangeinteraction between an electron and its conduction-band hole. We provideanalytical expressions for potential matrix elements, using a technique thatallows us to circumvent the difficulty imposed by the occupation of low-energyelectron states in the conduction band. We discuss the computational steps oneshould implement in order to perform the calculation, and how to extractkinetic energies of individual particles in the complex, average inter-particledistances, and density distributions.

Turning many-body problems to few-body ones in photoexcited semiconductors using the stochastic variational method in momentum space, SVM-k