Oblate-prolate Shape Coexistence Research Articles

Evidence of oblate-prolate shape coexistence in the strongly-deformed nucleus 119Cs

Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A≈120 nuclei is reported for the first time. One of the four reported bands in 119Cs, built on a 11/2− state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled πh11/2[505]11/2− configuration associated with oblate shape. Together with the decoupled πh11/2[541]3/2− band built on the 11/2− prolate state at 110 keV, for which a half-life of T1/2=55(5)μs has been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A≈120 nuclei, a phenomenon predicted since long time, but not yet observed. Calculations using the particle-number conserving cranked shell model and two dimensional tilted axis cranking covariant density functional theory support and well reproduce the observed oblate and prolate coexisting low-energy states in 119Cs.

Microscopic study of shape evolution and some important ground state properties of 190–210Au isotopes

In this paper, we have examined the nuclear structural properties of 190–210Au isotopes within the framework of the Hartree–Fock–Bogoliubov Model. For the theoretical calculations, we have used the UNEDF2 and SKP interactions. The studies include the shape evolution, quadrupole deformation parameter [Formula: see text], nuclear electric quadrupole moment Q(b), single-particle energy levels, the binding energy per nucleon, nuclear charge radius, neutron rms radius, proton rms radius and neutron skin thickness. To analyze the accuracy of our theoretical results, we have presented the comparative analysis with experimental data and finite-range droplet model calculations. The adequate resemblance with experimental data is supporting our studies. We observe the oblate-prolate shape coexistence for 190Au, 193Au and 195Au using the UNEDF2 interaction.

Shape coexistence revealed in the $$N=Z$$ isotope $$^{72}$$Kr through inelastic scattering

The $N=Z=36$ nucleus $^{72}$Kr has been studied by inelastic scattering at intermediate energies. Two targets, $^{9}$Be and $^{197}$Au, were used to extract the nuclear deformation length, $\delta_\text{N}$, and the reduced $E2$ transition probability, $B(E2)$. The previously unknown non-yrast $2^+$ and $4^+$ states as well as a new candidate for the octupole $3^-$ state have been observed in the scattering on the Be target and placed in the level scheme based on $\gamma-\gamma$ coincidences. The second $2^+$ state was also observed in the scattering on the Au target and the $B(E2;\;2^+_2 \rightarrow 0^+_1)$ value could be determined for the first time. Analyzing the results in terms of a two-band mixing model shows clear evidence for a oblate-prolate shape coexistence and can be explained by a shape change from an oblate ground state to prolate deformed yrast band from the first $2^+$ state. This interpretation is corroborated by beyond mean field calculations using the Gogny D1S interaction.

Microscopic study of shape evolution and ground state properties in even-even Cd isotopes using covariant density functional theory

We have studied the trend of ground state quadrupole deformation and shape transition in even-even 96−136Cd isotopes. Binding energy, two neutrons separation energies, shell closure parameter, rms radii of neutron and proton, charge radii, and nuclear skin thickness have also been studied as a function of the neutron number. We performed the calculations by employing covariant density functional theory with density-dependent meson exchange and point coupling interactions. The ground-state properties are found in good agreement with available experimental data. Our results predict the shape transition from spherical to prolate, prolate to oblate, oblate to prolate, and prolate to spherical in this isotopic mass chain. Besides, the oblate-prolate shape coexistence is also predicted in 110−114Cd isotopes.

Microscopic study of evolution of shape change across even-even mass chain of tellurium isotopes using relativistic Hartree-Bogoliubov model

The density dependent point coupling and meson exchange effective interactions are employed in the relativistic Hartree-Bogoliubov (RHB) model to study the development of ground state deformation and occurrence of shape transitions with change of neutron number in 104−144Te isotopes. Besides this, the systematics of other nuclear structure properties with increasing neutron number are also obtained. The RHB model reproduces well the available experimental data on binding energies, quadrupole deformation parameters, two neutron separation energies and root mean square charge radii. The results of three-dimensional potential energy surfaces predict prolate ground state minima for proton rich and neutron rich tellurium isotopes, oblate minima for 114−124Te, triaxial minima for 126,128Te and spherical minima for 130−134Te. Besides, oblate prolate shape coexistence is predicted in 116−120Te isotopes.

Shape coexistence and shape transition in self-conjugate nucleus 72Kr and the tensor force

Oblate-prolate shape-coexistence is well-known in the N = Z nucleus 72Kr. Furthermore, recent experimental data implies that there is a rapid shape transition at very low spins in this nucleus. We reinvestigate this problem by using large-scale shell-model calculations with the monopole interactions derived from the monopole-based universal force that contains the tensor force in the Hamiltonian. We show that in 72Kr, states with nucleon-quartet excitation from the pf shell to the – orbits, which favor large prolate deformation, compete with those having the pf shell as the main configuration with oblate deformation. These shapes can coexist if the two types of states reside closely in excitation energy. In 72Kr the tensor force is found to provide precisely such a coexistence condition near the ground state. As the tensor effect changes dynamically with orbital occupation when the nucleus rotates, a rapid shape transition can occur.

Shape Evolution in Neutron-Rich Krypton Isotopes Beyond N=60: First Spectroscopy of ^{98,100}Kr.

We report on the first γ-ray spectroscopy of low-lying states in neutron-rich ^{98,100}Kr isotopes obtained from ^{99,101}Rb(p,2p) reactions at ∼220 MeV/nucleon. A reduction of the 2_{1}^{+} state energies beyond N=60 demonstrates a significant increase of deformation, shifted in neutron number compared to the sharper transition observed in strontium and zirconium isotopes. State-of-the-art beyond-mean-field calculations using the Gogny D1S interaction predict level energies in good agreement with experimental results. The identification of a low-lying (0_{2}^{+}, 2_{2}^{+}) state in ^{98}Kr provides the first experimental evidence of a competing configuration at low energy in neutron-rich krypton isotopes consistent with the oblate-prolate shape coexistence picture suggested by theory.

Stabilization of prolate deformation at high spin in75Kr

The neutron-deficient nucleus ${}^{75}$Kr has been studied in two EUROBALL experiments. The analysis yielded a considerably extended level scheme including two newly observed excited high spin bands. The results are interpreted in the framework of the cranked Nilsson-Strutinsky approach. The calculations compare well to the experimentally established level scheme and predict the nucleus to be mainly prolate or triaxially deformed at high spin. Evidence for an oblate-prolate shape coexistence could not be found at high spin.

Microscopic approach to large-amplitude deformation dynamics with local QRPA inertial masses

We have developed a new method for determining microscopically the five-dimensional quadrupole collective Hamiltonian, on the basis of the adiabatic self-consistent collective coordinate method. This method consists of the constrained Hartree-Fock-Bogoliubov (HFB) equation and the local QRPA (LQRPA) equations, which are an extension of the usual QRPA (quasiparticle random phase approximation) to non-HFB-equilibrium points, on top of the CHFB states. One of the advantages of our method is that the inertial functions calculated with this method contain the contributions of the time-odd components of the mean field, which are ignored in the widely-used cranking formula. We illustrate usefulness of our method by applying to oblate-prolate shape coexistence in 72Kr and shape phase transition in neutron-rich Cr isotopes around N = 40.

Microscopic description of large-amplitude shape-mixing dynamics with inertial functions derived in local quasiparticle random-phase approximation

On the basis of the adiabatic self-consistent collective coordinate method, we develop an efficient microscopic method of deriving the five-dimensional quadrupole collective Hamiltonian and illustrate its usefulness by applying it to the oblate-prolate shape coexistence/mixing phenomena in proton-rich $^{68,70,72}\mathrm{Se}$. In this method, the vibrational and rotational collective masses (inertial functions) are determined by local normal modes built on constrained Hartree-Fock-Bogoliubov states. Numerical calculations are carried out using the pairing-plus-quadrupole Hamiltonian including the quadrupole-pairing interaction within the two major-shell active model spaces both for neutrons and protons. It is shown that the time-odd components of the moving mean-field significantly increase the vibrational and rotational collective masses in comparison with the Inglis-Belyaev cranking masses. Solving the collective Schr\"odinger equation, we evaluate excitation spectra, quadrupole transitions, and moments. The results of the numerical calculation are in excellent agreement with recent experimental data and indicate that the low-lying states of these nuclei are characterized as an intermediate situation between the oblate-prolate shape coexistence and the so-called $\ensuremath{\gamma}$ unstable situation where large-amplitude triaxial-shape fluctuations play a dominant role.

PHENOMENOLOGICAL ANALYSIS OF THE OBLATE-PROLATE SYMMETRY BREAKING IN TRIAXIAL DEFORMATION DYNAMICS

From a viewpoint of oblate-prolate symmetry and its breaking, we propose a simple model based on the quadrupole collective Hamiltonian to study dynamics of triaxial deformation in shape coexistence phenomena. The numerical results suggest that the oblate-prolate symmetry breaking in the rotational moments of inertia can play an important role for the oblate-prolate shape coexistence as well as that in the collective potential.

A Model Analysis of Triaxial Deformation Dynamics in Oblate-Prolate Shape Coexistence Phenomena

From a viewpoint of oblate-prolate symmetry and its breaking, we adopt the quadrupole collective Hamiltonian to study dynamics of triaxial deformation in shape coexistence phenomena. It accommodates the axially symmetric rotor model, the $\gamma$-unstable model, the rigid triaxial rotor model and an ideal situation for the oblate-prolate shape coexistence as particular cases. Numerical solutions of this model yield a number of interesting suggestions. (1) The relative energy of the excited 0+ state can be a signature of the potential shape along the $\gamma$ direction. (2) Specific E2 transition probabilities are sensitive to the breaking of the oblate-prolate symmetry. (3) Nuclear rotation may induce the localization of collective wave functions in the ($\beta, \gamma$) deformation space.

Collective path connecting the oblate and prolate local minima in proton-rich N = Z nuclei around 68Se

By means of the adiabatic self-consistent collective coordinate method and the pairing-plus-quadrupole interaction, we have for the first time obtained a self-consistent collective path connecting the oblate and prolate local minima in 68Se and 72Kr. This self-consistent collective path is found to run approximately along the valley connecting the oblate and prolate local minima in the collective potential energy landscape. The result of this calculation clearly indicates the importance of triaxial deformation dynamics in oblate-prolate shape coexistence phenomena.

Collective Paths Connecting the Oblate and Prolate Shapes in 68Se and 72Kr Suggested by the Adiabatic Self-Consistent Collective Coordinate Method

By means of the adiabatic self-consistent collective coordinate method and the pairing-plus-quadrupole interaction, we have obtained the self-consistent collective path connecting the oblate and prolate local minima in 68Se and 72Kr for the first time. The self-consistent collective path is found to run approximately along the valley connecting the oblate and prolate local minima in the collective potential energy landscape. This result of calculation clearly indicates the importance of triaxial deformation dynamics in oblate-prolate shape coexistence phenomena.

Collective Path Connecting the Oblate and Prolate Local Minima in 68Se

By means of the adiabatic self-consistent collective coordinate method and the pairing plus quadrupole interaction, we have obtained the selfconsistent collective path connecting the oblate and prolate local minima in 68Se for the first time. Along the collective path, the triaxial deformation parameter (gamma) changes between 0 and 60 (degree) keeping the axially symmetric deformation parameter (beta) approximately constant, indicating the importance of triaxial deformation dynamics in the oblate-prolate shape coexistence phenomena.