EXCITON OPTICAL STARK SHIFT - LARGE DETUNING EXPANSION AND CORRELATION-EFFECTS

We calculate the large detuning expansion of the exciton optical Stark shift. It appears that the convergence of this expansion is quite slow, the expanding parameter being the square root of the Rydberg-to-detuning ratio and the first two prefactors being quite large. As expected, the so-called Hartree-Fock calculation proposed by Schmitt-Rink and coworkers gives an exact value of the first correction to the large detuning limit (dressed-atom shift). In the next correction, one has to take into account correlation effects although it turns out that their contribution is numerically small at this order. We finally identify in a diagrammatic approach the processes included in the Hartree-Fock approximation and those which are neglected.