On the validity of the random phase approximation for pairing vibrations of closed shell nuclei

The RPA method is applied to two kinds of Hamiltonians. First the pairing force Hamiltonian for two levels is considered. The RPA ground state energy lies below the actual energy whereas the RPA excitation energies are too small. In the case of a more realistic Hamiltonian a potential strength is chosen for which the RPA reproduces the 6.06 MeV 0⁺ level of O¹⁶. By comparison with the (variational) FBCS approximation it is seen that the RPA ground state energy again lies considerably below the variational value. The RPA ground state wave function is calculated. It is shown that the quasi-boson approach of the RPA enhances the spread of the fermi level. The enhancement is proved to become singular when the RPA breaks down. Finally, the class of possible RPA ground state wave functions is discussed.