Rayleigh-Schroedinger coefficients for singular perturbations in a discrete spectrum

Calculation of perturbation matrix element together with related additional point perturbation was conducted for singular perturbations λ(x)-ν of even retarding potential. It is shown that matrix elements exist at 0<ν<3/2 for even nonperturbed functions. Series for Rayleigh-Schroedinger coefficients of all orders converge for the same ν values independently of the form of retarding potential. ν value limitations for odd states are weaker as compared to even ones