The Lipkin model is used to study the transition to a parity-breaking system with the aim of understanding the features of negative parity low-lying levels associated with the octupole degree of freedom. The results of parity projection calculations for the energy splitting between the positive parity ground state and the lowest-lying negative parity state as well as the negative parity transition probability connecting them have been studied and compared to the exact results. A good agreement is observed for not-deformed and for well-deformed systems but at intermediate deformations the parity-projected results strongly differ from the exact ones. By anaylzing the parity-projected energy curves, two characteristic configurations are observed in the problem: the mean-field and the tunneling configurations. By mixing these two configurations, a substantial improvement over the parity projection method is obtained for the two quantities studied in all the regions of deformation. It is suggested that this method could be used in realistic calculations to improve the understanding of the octupole dynamics in opposition to the most powerful but expensive generator coordinate method.

• Received 28 January 1992

DOI:https://doi.org/10.1103/PhysRevC.46.238