Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei with octupole correlations

Abstract

Background: Predictions of spectroscopic properties of low-lying states are critical for nuclear structure studies. Theoretical methods can be particularly involved for odd-mass nuclei because of the interplay between the unpaired nucleon and collective degrees of freedom. Only a few models have been developed for systems in which octupole collective degrees of freedom play a role.Purpose: We aim to predict spectroscopic properties of odd-mass nuclei characterized by octupole shape deformation, employing a model that describes single-particle and collective degrees of freedom within the same microscopic framework.Method: A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed, which includes collective excitations of even-mass core nuclei and single-particle states of the odd nucleon, calculated using a quadrupole-octupole collective Hamiltonian combined with a constrained reflection-asymmetric relativistic Hartree-Bogoliubov model.Results: Model predictions for low-energy excitation spectra and transition rates of odd-mass radium isotopes 223,225,227 Ra are shown to be in good agreement with available data.Conclusions: A microscopic CQC model based on covariant density functional theory has been developed for odd-mass nuclei characterized by both quadrupole and octupole shape deformations. Theoretical results reproduce data in odd-mass Ra isotopes and provide useful predictions for future studies of octupole correlations in nuclei and related phenomena.

Pear-shaped atomic nuclei

“…The values of intrinsic octupole moments, Q 3 , for radium isotopes, deduced from the measured transition matrix element falsefalse⟨0+||scriptMfalse(E3false)||3−falsefalse⟩, are compared with various theoretical calculations in figure 7. The calculations are from macroscopic–microscopic (MacMic) [37], relativistic mean-field (RMF) (NL1 variant) [38], cluster model [39], Gogny Hartree–Fock–Bogoliubov (Gogny) (D1S variant) [40], relativistic Hartree–Bogoliubov + interacting boson model (RHIBM) [41], quadrupole–octupole collective Hamiltonian (QOCH) [42] and Skyrme Hartree–Fock–Bogoliubov (Skyrme) (UNEDF0 variant) [43] calculations. All of these models except for the cluster model predict a maximum around N=136--138.…”

Model for collective motion

“…Just as in the case of the 5DCH model, all the collective parameters are calculated from the self-consistent solutions of constrained reflectionasymmetric CDFT, using cranking formulas [50]. As an illustrative example, the CDFT-based QOCH is used to calculate the lowenergy excitation spectra and electromagnetic transitions of Ra isotopes [51]. In Fig.…”

“…Fig. 11 Deformation energy surfaces of the nuclei 222−228 Ra[51] in the β 2 -β 3 plane calculated with the CDFT, using the PC-PK1 functional[42]. For each nucleus the energies are normalized with respect to the binding energy of the global minimum.…”

Refined description of the positive-parity bands and the extent of octupole correlations in Ba120

“…In order to understand this surprising behavior of the experimental B(E 1)/B(E 2) ratios, we performed calculations using the quadrupole and octupole collective Hamiltonian based on the relativistic Hartree-Bogoliubov (QOCH-RHB) model [16], employing the DD-PC1 density functional [17]. The B(E 1) values are calculated as follows: first, we perform a constrained relativistic Hartree-Bogoliubov (RHB) calculation to obtain the intrinsic dipole moments D 0 in the (β 2 , β 3 ) plane using the dipole moment operator D = e N A r p − e N A r n (Eq.…”

“…The previously known negative-parity band [8] is considerably extended to high spin. The configurations of the observed bands are assigned based on the analysis of the alignment properties of the bands, on the comparison with the oddeven neighboring 119 Ba and 119 Cs nuclei, on systematics, as well as on cranked Nilsson-Strutinsky (CNS) [9][10][11][12], particle number conserving cranked shell model (PNC-CSM) without octupole deformation [13,14] and with octupole deformation included [15], as well as quadrupole and octupole collective Hamiltonian based on the relativistic Hartree-Bogoliubov (QOCH-RHB) [16] calculations using the DD-PC1 density functional [17].…”