Tests of the random phase approximation for transition strengths

Details Tests of the random phase approximation for transition strengths Tests of the random phase approximation for transition strengths

2002-11-25

arxiv.org/abs/nucl-th/0211079v2

Phys.Rev. C67 (2003) 044315

Physics

Nuclear Physics

Nuclear Theory

11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rule

Scientific paper

10.1103/PhysRevC.67.044315

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbar\omega$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.

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