Beyond relativistic mean-field approach for nuclear octupole excitations

Abstract

We report the first beyond-mean-field study of low-lying parity-doublet states in 224 Ra by extending the multireference relativistic energy density functional method to include dynamical correlations related to symmetry restoration and quadrupole-octupole shape fluctuation with a generator coordinate method combined with parity, particle-number, and angular-momentum projections. We clarify full microscopically that the origin of spin-dependent parity splitting in low-spin states is related to the octupole shape stabilization of positive-parity states, the dominated shapes of which drift gradually to that of negative-parity ones. The existence of octupole shaped nuclei in intrinsic frame has been suggested very early from the observed low-lying parity doublets connected with strong electric odd-multipole (Eλ) transition strengths [1,2]. Among them, 224 Ra was recently suggested to be a stable pear shaped nucleus based on the measured Eλ transitions [3]. Nevertheless, as pointed out early [4] and shown in this paper that the effects stemming from static octupole shapes on Eλ transitions can be almost equally well described by including dynamical octupole deformations around the equilibrium shape. Moreover, the spectroscopy of reflection-asymmetric diatomic molecules suggests the existence of a rotational band with alternating parity, which has indeed been found in some candidates of octupole shaped nuclei at high-spin states. However, an evident energy splitting is observed in the odd and even parity states of these nuclei at low-spin region. In particular, this parity splitting is gradually increased with the decrease of spin. This peculiar feature indicates the possible existence of large quantum shape fluctuation in octupole shapes at low-spin states. Therefore, whether atomic nuclei possess dynamical or stable octupole shapes in low-spin states remains an open question, which is relevant not only for deepening our understanding on nuclear structure at low energy, but also in searching for CP-violating Schiff moment which is expected to be amplified in octupole deformed nuclei [5].Numerous studies have been performed to search for octupole deformed nuclei with selfconsistent meanfield approaches [6][7][8][9][10][11][12], and to understand nuclear collective octupole excitations with energy density functional (EDF) based collective Hamiltonian [13][14][15][16], EDF mapped interacting boson model [17], and generator coordinate method (GCM) [18][19][20]. These studies have greatly deepened our understanding on the structure of octupole candidate nuclei. However, the onset of unusual spin-dependent parity splitting has not been clarified.The combination of energy density functional approach with GCM provides a powerful tool to study nuclear shape fluctuations. Unfortunately, angular-momentum projection has not yet been implemented in this framework for octupole nuclei and the stabilization of nuclear octupole shape against rotation remains to be examined.In the meantime, cranked mean-field approaches have also be...

Eclectic flavor groups

“…[64] for the definition of Ω(1) and refs. [65,66] for flavor model building based on this symmetry group. Following the discussion in section 3, the eclectic flavor group Ω (1) is broken spontaneously to various unified flavor subgroups at different points in τ moduli space: As a remark, all of these groups have three-dimensional irreducible representations.…”

Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals

“…Both non-relativistic and relativistic EDFs have successfully been applied to the description of the evolution of single-nucleon shell structures and related nuclear shapes and shape transitions. In the literature one finds a number of detailed self-consistent mean-field studies of nuclei with static or dynamic octupole deformations, e.g., based on the Skyrme [53,54] and Gogny [21][22][23][24][25][26][27]55] effective interactions, and relativistic mean-field (RMF) models [18,20,30,32,33,[41][42][43][44][45][46].…”

“…A straightforward approach is the generator coordinate method (GCM) combined with projection techniques, and recently it has been implemented for reflection-asymmetric shapes, based on both nonrelativistic [27] and relativistic [45,46] EDFs. Using this method, however, it is rather difficult to perform a systematic study of low-lying quadrupole and octupole states in different mass regions, because implementations of GCM are very time-consuming for heavy systems.…”

Octupole deformation in the ground states of even-even Z∼96, N∼196 actinides and superheavy nuclei

“…The generator coordinate method studies taking into account dynamical correlations and quadrupole-octupole shape fluctuations have been undertaken in 224 Ra employing the PC-PK1 functional in Ref. [20]. They revealed rotationinduced octupole shape stabilization.…”