Narrow Results

We develop an efficient microscopic method of deriving the five-dimensional quadrupole collective Hamiltonian on the basis of the adiabatic self-consistent collective coordinate method. We illustrate its usefulness by applying it to the oblate-prolate shape coexistence/mixing phenomena and anharmonic vibrations in Se isotopes.

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.

We develop a method of determining microscopically the collective potential and inertial masses in the five-dimensional quadrupole collective Hamiltonian on the basis of the adiabatic self-consistent collective coordinate method. We apply this method to shape coexistence/mixing phenomena in low-lying states of the proton-rich Kr isotopes.

Positive-parity states of ²⁸Si are studied with antisymmetrized molecular dynamics and multi-configuration mixing focusing on clustering and deformations. By superposition of wave functions obtained by energy variation imposing constraints on quadrupole deformation parameter β and distance between α and ²⁴Mg, and ¹²C and ¹⁶O clusters, two oblate bands, two prolate bands and developed α-²⁴Mg band are obtained. It is found that cluster structure components are contained in those bands.

The nuclear potential energies of neutron deficient even–even rare earth nuclei ¹⁵⁸Er and ¹⁶²Hf for the spin range 0–60 are computed within the framework of cranked Nilsson–Strutinsky shell correction method. The potential energy surface diagrams are analyzed in terms of quadrupole deformation and triaxiality parameter. The shape evolution of these isotopes with respect to spin is studied. The spin dependence of nuclear equilibrium potential energy is also verified.

The ground and excited states properties of Zr isotopes are studied from proton to neutron drip lines using the relativistic (RMF) and nonrelativistic (SHF) mean-field formalisms with Bardeen–Cooper–Schrieffer (BCS) and Bogoliubov pairing, respectively. The well-known NL3* and SLy4 parameter sets are used in the calculations. We have found spherical ground and low-lying large deformed excited states in most of the isotopes. Several couples of Ω^π = 1/2^± parity doublets configurations are noticed, while analyzing the single-particle energy levels of the large deformed configurations.

The nuclear potential energies of Lu isotopes with neutron number $N=90-98$ up to high spins are computed within the framework of the unpaired cranked Nilsson–Strutinsky method. The potential and the macroscopic Lublin–Strasbourg drop (LSD) energy-surface diagrams are analyzed in terms of quadrupole deformation and triaxiality parameter. The shape evolution of these isotopes with respect to angular momentum, as well as the neutron number is studied.

In this paper, we have studied the shape coexistence in the ${}^{180-190}$Hg isotopes. The SO(6) representation of eigenstates and a transitional Hamiltonian in the Interacting Boson Model (IBM) are used to consider the evolution from prolate to oblate shapes for systems with total boson number $N=9-12$. Parameter free (up to overall scale factors) predictions for energy spectra and quadrupole transition rates are found to be in good agreement with experimental counterparts. The results for the control parameter of transitional Hamiltonian offer a combination of spherical and deformed shapes in these Hg isotopes and also more deviation from SO(6) limit is observed when the quadrupole deformation is decreased. Also, there are some suggestions about the expectation values of the ${\widehat{n}}_d$ operator which are determined in the first state of ground, beta and gamma bounds and the control parameter of model.

A systematic search of the shape phase transitions and isotopic shift of the neutron-rich barium (Ba; $Z=56$) isotopes, as a candidate for transitional nuclei, is done within the covariant density functional theory (CDFT). The relativistic Hartree–Bogoliubov (RHB) formalism with separable pairing and relativistic mean-field (RMF) with BCS pairing are used. The constraint calculations assuming the axial symmetry as well as triaxial symmetry clearly manifest the shape coexistence and the transitional behavior in these nuclei. A strong shell closure is observed at $N=82$ and weaker shell/subshell closure is observed at $N=88$. Shape transition below and above the shell closure location at $N=82$ (from prolate to spherical to prolate) is there. The candidates for $E(5)$ and $X(5)$ dynamical symmetries are found to be ${}^{134}$Ba, ${}^{136}$Ba and ${}^{140}$Ba, ${}^{142}$Ba nuclei, respectively. The calculated results are compared with the available experimental data and are in good agreement. We have investigated the model dependence as well as dependence on various model parameters. A comparison is made with other theoretical models: infinite nuclear matter (INM) model, macro–microscopic finite-range droplet model (FRDM) and the self-consistent Hartree–Fock–Bogoliubov (HFB) model. Overall good agreement is found within the different models used and between the calculated and experimental results.

New transitions in neutron rich ${}^{96}$Y have been identified by analyzing the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ coincidence data from the spontaneous fission of ${}^{252}$Cf at the Gammasphere detector array. Shell model calculations were performed and are found in good agreement with experimental data. The ground state is nearly spherical but a new excited band has large deformation.

The Po isotopes show the presence of coexisting structures having different deformations with increasing neutron number within the macroscopic–microscopic Nilsson–Strutinsky formalism. The model is based on the Lublin Strasbourg Drop (LSD) method for the macroscopic energy calculation. We study the shape evolution in a long chain of polonium isotopes, ${}^{178-200}$Po.

We present a systematic description of the exotic features in the ground states of light nuclei from the stable valley to the drip lines. A study with the even and odd isotopes of Ne, Mg, Si, S and Ar has been performed using theoretical formalisms (i) Relativistic mean-field plus state-dependent BCS approach and (ii) Macroscopic–Microscopic (MM) approach using the triaxially deformed Nilsson–Strutinsky Method. The computed binding energies and one- and two-neutron separation energies using both the theories show magic character of $N=14,20,28$ and 40. The neutron and proton radii and the neutron densities show a well-developed neutron skin in the neutron-rich isotopes. The exotic phenomena such as weakly bound structures and the central density depletion characterized as bubble effect are explored. Our calculations for the single particle levels, density profiles and the charge form factors indicate bubble-like structures. Few new candidates of bubble nuclei are identified. Most of the nuclei in this region are found deformed with mostly prolate shape and few triaxial shapes while many nuclei exhibit the phenomenon of shape coexistence. Our results display a reasonable agreement between both the theories and the available experimental data.

In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the ${}^{114}$Cd, ${}^{112}$Cd and ${}^{110}$Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of different energy levels indicates that there is a close relationship between ground and excited-state quantum phase transitions (ESQPTs).

Excited states of ¹¹⁷Sn have been populated using the fusion-evaporation reaction ¹¹⁴Cd(⁷Li, 1p3n) at a beam energy of 48MeV. A total of nine new transitions have been identified and added into the level scheme of ¹¹⁷Sn. Based on the systematical comparisons with the neighboring Sn isotopes and the configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations, a collective structure and two isomers are proposed to exist in ¹¹⁷Sn. The phenomenon of shape coexistence has been extended to A = 117 in odd-A Sn isotopes for the first time.

The ground state shapes and properties of even–even ${}^{98-132}$Cd isotopes have been studied in the framework of relativistic Hartree–Bogoliubov model with two effective interactions that are density-dependent meson exchange and point coupling. The theoretical results on the binding energies, charge radii and two neutron separation energies are presented in this paper in comparison to experimental data and a reasonable agreement is found between the two. Both the interactions predict spherical to axially prolate, prolate to triaxial, triaxial to prolate and prolate to spherical transitions in cadmium isotopic mass chain. In addition, the present calculations confirm the existence of shape coexistence observed in ${}^{110,112}$Cd. The comparison of calculated ground state properties with the results based on PC-PK1 functional shows that PC-PK1 employed in the deformed relativistic Hartree–Bogoliubov theory in continuum has the lowest root mean square deviation for average binding energies and two neutron separation energies.

Reflection asymmetric, octupole shapes in nuclei are a prominent aspect of nuclear structure, and have been recurrently studied over the decades. Recent experiments using radioactive-ion beams have provided evidence for stable octupole shapes. A variety of nuclear models have been employed for the related theoretical analyses. We review recent studies on the nuclear octupole shapes and collective excitations within the interacting boson model. A special focus is placed on the microscopic formulation of this model by using the mean-field method that is based on the framework of nuclear density functional theory. As an illustrative example, a stable octupole deformation, and a shape phase transition as a function of nucleon number that involves both quadrupole and octupole degrees of freedom are shown to occur in light actinides. Systematic spectroscopic studies indicate enhancement of the octupole collectivity in a wide mass region. Couplings between the octupole and additional degrees of freedom are incorporated in a microscopic manner in the boson system, and shown to play a crucial role in the description of the related intriguing nuclear structure phenomena such as the shape coexistence.

The β-decay spectroscopy with a spin-polarized nucleus is a powerful tool, which unambiguously assigns spins and parities of the daughter levels by measuring the asymmetric β-decay of the polarized parent nucleus. This method has been applied to structure investigations of neutron-rich Mg isotopes. In our recent study of ³¹Mg, which is located at a border of the region of the N = 20 “island of inversion”, we firmly assigned spins of all positive-parity excited states below the neutron separation energy at 2.3 MeV. This results clearly showed the shape coexistence in ³¹Mg. Following the results on ³¹Mg, we plan to apply this method to neutron-rich ³¹Al and ³³Al.

The adiabatic self–consistent collective coordinate (ASCC) method is applied to the pairing-plus-quadrupole (P + Q) model Hamiltonian including the quadrupole pairing, and the oblate–prolate shape coexistence phenomena in proton-rich nuclei, ⁶⁸Se and ⁷²Kr, are investigated. It is shown that the collective path connecting the oblate and prolate local minima runs along a triaxial valley in the (β, γ) plane. Quantum collective Hamiltonian is constructed and low-lying energy spectra and E2 transition probabilities are calculated for the first time using the ASCC method. Basic properties of the shape coexistence/mixing are well reproduced. We also clarify the effects of the time-odd pair field on the collective mass (inertial function) for the large–amplitude vibration and on the rotational moments of inertia about three principal axes.

A large variety of shapes may be observed in Sr and Zr nuclei of the A = 100 region when the number of neutrons increases from N = 58 to N = 64. The lighter isotopes are rather spherical. It is also well established that three shapes co-exist in the transitional odd-A, N = 59, Sr and Zr nuclei. For N > 59, strongly deformed axially symmetric bands are observed. Recently, a new isomer of half-life 1.4(2) µs was observed in ⁹⁵Kr, the odd-odd ⁹⁶Rb has been reinvestigated and a new high spin isomer observed in the even-even ⁹⁸Zr. Beyond N = 60 nuclei, the neutron-rich Mo isotopes represent well deformed nuclei, but at the same time, the triaxial degree of freedom plays an important role. We have re-investigated the odd ¹⁰⁵Mo and ¹⁰⁷Mo and found that odd and even Mo in the neutron range N = 62-66 have comparable quadrupole and triaxial deformation. These nuclei were studied by means of prompt γ-ray spectroscopy of the spontaneous fission of ²⁴⁸Cm using the EUROGAM 2 Ge array and/or measurements of µs isomers produced by fission of ^239,241Pu with thermal neutrons at the ILL (Grenoble).

We extend the quark-meson coupling model to study the ground-state properties of axially deformed even-even nuclei. For this purpose, we introduce ω-N tensor coupling to the model Lagrangian and obtain the parameters from fits to the experimental data for finite nuclei. The present work is mainly focused on the nuclei in the rare-earth region. The ground-state binding energies, quadrupole deformations, shape coexistence, two-neutron separation energies and the root-mean-square charge radii are calculated and compared with the experimental data. It is shown that this extended quark-meson coupling model can give a reasonable description of the axially deformed nuclei.