  We develop an efficient computational technique to calculate composite
excitonic states in photoexcited semiconductors through the stochastic
variational method (SVM). Many-body interactions between an electron gas and
the excitonic state are embodied in the problem through Fermi holes in the
conduction band, introduced when electrons are pulled out of the Fermi sea to
bind the photoexcited electron-hole pair. We consider the direct Coulomb
interaction between distinguishable particles in the complex, the
exchange-induced band-gap renormalization effect, and electron-hole exchange
interaction between an electron and its conduction-band hole. We provide
analytical expressions for potential matrix elements, using a technique that
allows us to circumvent the difficulty imposed by the occupation of low-energy
electron states in the conduction band. We discuss the computational steps one
should implement in order to perform the calculation, and how to extract
kinetic energies of individual particles in the complex, average inter-particle
distances, and density distributions.
