Convergence properties of the perturbation expansion for the effective two-particle interaction in mass-18 nuclei in a doubly partitioned Hilbert space

The theory for calculating the effective interaction ov for finite nuclei in a doubly partitioned Hubert space is discussed and then applied to the calculation of ov through third order in the nuclear reaction matrix G for the J = 0, T = 1 states in mass-18 nuclei. The G-matrix elements were computed using the technique of Barrett, Hewitt and McCarthy, which allowed an acccurate treatment of the Pauli projection operator. Calculations were first performed using the standard procedure for computing ov. These calculations were then repeated employing the double-partition procedure, and its results were compared with those from the standard procedure. The convergence of the perturbation expansion for ov through third order in G was improved in the double-partition approach but was not conclusive. However, the double-partition procedure allows the possibility of performing much more sophisticated and accurate calculations of ov than the standard procedure. All calculations were performed as a function of the starting energy ω of G, which is related to constant shifts between the energy levels of the occupied and unoccupied single-particle states. For all calculations a value of ω was found at which the 0⁺ ground state agreed with experiment. A procedure is proposed for determining in advance the value of ω at which G and ov should be computed.