Is perturbative study of ground-state correlations valid?

Perturbative approaches have often been used to include the effects of ground-state correlations in extended theories of the random-phase approximation. Validity of such approaches is investigated for a solvable model where comparison with exact solutions can be made. It is pointed out that there is a case where perturbative approaches give good results in spite of the fact that interaction strength is far beyond a perturbative region.