Effect of high-lying states on the ground state and few low-lying excited O+energy levels of some closed-shell nuclei

Abstract

The ground state and some excited O+(J=0, T=0 positive parity) energy levels of closed-shell nuclei are examined, in an oscillator basis using matrix techniques. The effect of states outside the mixed (0+2h(cross) omega ) model space in 4He (namely configurations at 4h(cross) omega excitation) are taken into account by renormalisation using the generalised Rayleigh-Schrodinger perturbation expressions for a mixed multi-configurational model space, where the resultant non-symmetric energy matrices are diagonalised. It is shown that the second-order renormalised O+ energy spectrum is close to the corresponding energy spectrum obtained by diagonalising the O+2+4h(cross) omega 4He energy matrix. The effect, on the ground state and the first few low-lying excited O+ energy levels, of renormalising certain parts of the model-space energy matrix up to second order in various approximations is also studied in 4He and 16O. It is found that the low-lying O+ energy levels in these various approximations behave similarly in both 4He and 16O.