Tests of the random phase approximation for transition strengths

Abstract

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hslash \omega$ 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.

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

References in corpus (6)

• Neutron-Proton Correlations in an Exactly Solvable Model
• Weak Interaction Rates Of sd-Shell Nuclei In Stellar Environment Calculated in the Proton-Neutron Quasiparticle Random Phase Approximation
• Missing and Quenched Gamow Teller Strength
• RPA vs. exact shell-model correlation energies
• Scalar ground-state observables in the random phase approximation
• Mean field theory for global binding systematics

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• Comparison of Gamow-Teller strengths in the random phase approximation
• QRPA calculations for M1 transitions with the noniterative finite amplitude method and the application to neutron radiative capture cross sections
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