Ab initiomany-body calculation of excitons in solid Ne and Ar

Absorption spectra, exciton energy levels and wave functions for solid Ne and Ar have been calculated from first principles using many-body techniques. Electronic band structures of Ne and Ar were calculated using the $GW$ approximation. Exciton states were calculated by diagonalizing an exciton Hamiltonian, derived from the particle-hole Green function, whose equation of motion is the Bethe-Salpeter equation. Singlet and triplet exciton series up to principal quantum number $n=5$ for Ne and $n=3$ for Ar were obtained. Binding energies and longitudinal-transverse splittings of $n=1$ excitons are in excellent agreement with experiment. Plots of correlated electron-hole wave functions show that the electron-hole complex is delocalized over approximately 70.3em0exa.u. in solid Ar.