Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Abstract

Although nuclear energy density functionals are determined primarily by fitting to ground state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random phase approximation (QRPA). Here we test the Skyrme functionals SkM * and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with γ-vibrational states, but our results are not perfect and indicate the presences of multi-particle-hole correlations that are not included in the QRPA. The Skyrme functional SkM * performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with "β-vibrational" states than with the γ-vibrational states.

Shape evolution of giant resonances in Nd and Sm isotopes

“…This result is close to the one obtained in Ref. [54], where the authors obtained the γ -vibrational state at 2.5 and at 2. agreement with the measurements, and the quality is at the same level found in Ref. [14].…”

Many-body correlations of quasiparticle random-phase approximation in nuclear matrix elements of neutrinolessdouble−βdecay

“…Those dimensions are determined from our experiences with separation of the spurious solutions and convergence of sum rules in the mass region of A ≈ 150 [35,36] [37]. The QRPA with the setup in this paper is better near the center of the well-deformed rare-earth region (A 164) [36]. However, the fact that the QRPA energy is higher than the experimental data implies that the QRPA solutions are far from the breaking point of the QRPA.…”

“…The dimensions of the four modes of K = 0,1 and π = ± are much larger than those of the other (Kπ) values because the former (Kπ) modes have spurious solutions [19] in QRPA calculations based on the deformed mean and pair fields; the translational invariance is also broken by the nuclear wave functions. Those dimensions are determined from our experiences with separation of the spurious solutions and convergence of sum rules in the mass region of A ≈ 150 [35,36] [37]. The QRPA with the setup in this paper is better near the center of the well-deformed rare-earth region (A 164) [36].…”

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

“…In such systems, nuclear pairing correlation can play an essential role [24][25][26][27]. However, compared * E-mail: toishi@phy.hr † E-mail: npaar@phy.hr with the electric dipole (E1) and quadrupole (E2) modes [28][29][30][31][32][33][34], the knowledge on the pairing effect on magnetic modes, as well as on unnatural-parity states, is rather limited [10][11][12]20]. In studies of nuclear modes of excitation, the sum rules associated to the transition strength and energyweighted sum rules, represent an essential tool for the analyses of the excitations, not only as benchmark tests of the theoretical frameworks involved, but also to inspect the completeness of the experimental data [35][36][37][38][39][40][41][42][43][44][45][46][47][48].…”