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 $0\hbar\omega$ 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.Comment: 11 pages, 7 figures; Appendix added with new proof regarding violation of energy-weighted sum rul

Gamow-Teller transitions and deformation in the proton-neutron random phase approximation

“…The solution with Ω > 0 is associated with the vector ( X, Y ) such that |X| > |Y |, and one chooses a normalization |X| 2 −|Y | 2 = 1; that one can do this also derives from the nonnegative eigenvalues of the stability matrix. The special case Ω = 0 corresponds to invariance of the Hamiltonian under a symmetry, for example, rotation or translation; here the vector ( X, Y ) cannot be normalized, as |X| = |Y |, and one must resort to a different formalism [12,21,24].…”

“…Recently we began to systematically test the RPA against full shell-model diagonalization [19,20,21]. In this paper we describe the generalization to proton-neutron RPA (pnRPA) and compare Gamow-Teller transitions against the full shell-model results.…”

Hartree-Fock-Bogoliubov calculations in coordinate space: Neutron-rich sulfur, zirconium, cerium, and samarium isotopes

“…However, as one approaches the driplines, pairing correlations increase dramatically and it is essential to treat both the mean field and the pairing field selfconsistently within the Hartree-FockBogoliubov (HFB) formalism [13]. While the HF(B) theories describe the ground state properties of nuclei, their * Physics Department, San Diego State University, San Diego, California 92182 excited states can be obtained with the (quasiparticle) random phase approximation (Q)RPA [17,18,19].…”

Scalar ground-state observables in the random phase approximation

“…For example, although the RPA correlation energy has been in the literature for decades, the only tests were in toy models [11]. Recently we compared the RPA correlation energy against exact shell-model results [12]. We found that generally RPA gave very good agreement-albeit with some significant failures which reduce the reliability of RPA binding energies.…”

“…We also show the ratio of correlation energies [12] which is a measure of how well the RPA binding energy tracks the exact binding energy. There appears to be no correspondence: a good RPA value for the binding energy does not correspond to a good RPA expectation value.…”