Shape Coexistence Phenomena Research Articles

Systematic investigation of shape-coexistence in Se,Kr,Sr and Zr isotopes with relativistic mean field theory

The even-even nuclei of Se, Kr, Sr and Zr isotopes are investigated systemically by the constrained relativistic mean field theory with the interactions NL3. The calculated binding energies of ground state for Se, Kr, Sr and Zr isotopes are described fairly well as compared with experiments. By examining the potential energy surfaces obtained by this microscopic approach, it can be found that the shape-coexistence phenomenon is very common in this region. The possible nuclei with shape-coexistence are pointed out systemically and the energy differences between the two minima in the potential energy surfaces for those nuclei are presented as well. In addition, by examining the potential energy surfaces and the microscopic neutron single particle spectra, N=70 are suggested to be a possible neutron magic number in this region.

Experimental study of shape coexistence inTl189

The shape coexistence phenomena in $^{189}\mathrm{Tl}$ are investigated by measuring the lifetimes of the high spin states through the recoil distance LIFETIME measurement technique. For this study, the $^{165}\mathrm{Ho}$($^{28}\mathrm{Si}$, $4n)$$^{189}\mathrm{Tl}$ reaction at a beam energy of 138 MeV was used. In this measurement, the lifetimes of four levels of the negative parity $\ensuremath{\pi}{h}_{9/2}$ band and seven levels of the positive parity $\ensuremath{\pi}{i}_{13/2}$ band are found. The extracted transition quadrupole moments for the positive parity $\ensuremath{\pi}{i}_{13/2}$ band show interesting changes with increasing level spin. This band starts with a small oblate shape (${Q}_{t}=1.1$ $e$ b) at low spin ($17/{2}^{+}$) and attains a strongly deformed prolate shape (${Q}_{t}=8.8$ $e$ b) at high spins ($33/{2}^{+}$). On the other hand, the negative parity $\ensuremath{\pi}{h}_{9/2}$ band shows a stable oblate structure against the increasing spin with an average quadrupole moment (${Q}_{t}$) of \ensuremath{\sim}2.6 $e$ b. To better understand the shape coexistence phenomena in $^{189}\mathrm{Tl}$ nucleus, the experimental results are also compared with the results of the total Routhian surfaces calculations, for the positive parity $\ensuremath{\pi}{i}_{13/2}$ and the negative parity $\ensuremath{\pi}{h}_{9/2}$ bands in this nucleus. The comparison confirms the shape coexistence structure of the $^{189}\mathrm{Tl}$ nucleus in the positive parity $\ensuremath{\pi}{i}_{13/2}$ configuration.

α transitions to coexisting0+states in Pb and Po isotopes

The {alpha}-transitions ({delta}l=0) to ground and first excited 0{sup +} states in neutron deficient Pb and Po isotopes are systematically analyzed by the density-dependent cluster model. The magnitude of nuclear deformation of the coexisting 0{sub 1}{sup +} and 0{sub 2}{sup +} states is extracted directly from the experimental {alpha}-decay energies and half-lives. The phenomenon of shape coexistence around the Z=82 shell closure is clearly demonstrated in our present analysis. The obtained deformation values from Rn {yields} Po {yields} Pb decay chains are generally consistent with both the available experimental and theoretical studies.

Lifetime measurement in 74Kr and 76Kr

Lifetimes of excited states in the ground-state bands of 74Kr and 76Kr were measured using the recoil-distance Doppler-shift and the differential decay curve methods. The states were populated in the 40Ca(40Ca, α2p) and 40Ca(40Ca, 4p) reactions. Gamma rays were detected with the GASP array which was coupled to the Cologne Plunger device. The results resolve discrepancies between earlier lifetime measurements and a recent Coulomb excitation experiment. Experimental transition rates are compared to theoretical calculations. The results support a strong mixing between prolate and oblate configurations for the low-spin states, and represent an important basis for the interpretation and understanding of the shape coexistence phenomenon in this mass region.

Yrast structures in the light Pt isotopes 169–173Pt

The exploitation of the recoil-decay tagging (RDT) technique has reinvigorated experimental investigations of the shape coexistence phenomenon in heavy neutron-deficient nuclei. In a recent experiment using the JUROGAM and GREAT spectrometers in conjunction with the RITU gas-filled separator, excited states have been investigated in the light platinum isotopes. In addition to extending the yrast sequences in 170Pt and 172Pt, the first observation of excited states in the odd-N isotopes, 169Pt and 173Pt, is reported. The bands are discussed in terms of trends in level excitation energies as a function of neutron number.

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.

DESCRIPTION OF SHAPE COEXISTENCE BY MEAN-FIELD AND BEYOND MEAN-FIELD METHODS

In this talk, we present a method which allows the introduction of correlations beyond a Skyrme Hartree-Fock calculation by symmetry restoration and configuration mixing on the axial quadrupole moment. A first application to 240 Pu is discussed, to show the potential of the method. As an example of the shape coexistence phenomenon in Pb isotopes, results for collective spectra and transition probabilities are then presented for 188 Pb .

Application of the Adiabatic Self-Consistent Collective Coordinate Method to a Solvable Model of Prolate-Oblate Shape Coexistence

The adiabatic self-consistent collective coordinate method is applied to an exactly solvable multi-O(4) model that is designed to describe nuclear shape coexistence phenomena. The collective mass and dynamics of large amplitude collective motion in this model system are analyzed, and it is shown that the method yields a faithful description of tunneling motion through a barrier between the prolate and oblate local minima in the collective potential. The emergence of the doublet pattern is clearly described.

Shape coexistence in the relativistic Hartree-Bogoliubov approach

The phenomenon of shape coexistence is studied in the relativistic Hartree-Bogoliubov framework. Standard relativistic mean-field effective interactions do not reproduce the ground-state properties of neutron-deficient Pt-Hg-Pb isotopes. It is shown that, in order to consistently describe binding energies, radii, and ground-state deformations of these nuclei, effective interactions have to be constructed, which take into account the sizes of spherical shell gaps.

An algebraic approach to shape coexistence: new symmetries and applications

We study the phenomenon of shape coexistence at or near single-closed shells. For that purpose, we describe multi-particle-hole intruder excitations on equal footing with regular excitations in the interacting boson model, by introducing the particle-hole degree of freedom, through a new quantum number, called I(ntruder)-spin. The resulting horizontal classification scheme of multi-particle-hole intruder excitations in terms of I-spin multiplets is useful to interpret data and to describe global properties of intruder excitations throughout a mass region. On the other hand, the creation and annihilation of particle-hole pairs, using a non-compact algebraic structure U(6,6), allows to account for local properties associated with mixing between regular and intruder excitations. We will illustrate the model by discussing a particular series of isotopes where shape coexistence may be present, 192–210Po.

Shape coexistence and the effective nucleon-nucleon interaction

The phenomenon of shape coexistence is discussed within the self-consistent Hartree-Fock method and the nuclear shell model. The occurrence of the coexisting configurations with different intrinsic shapes is traced back to the properties of the effective Hamiltonian.

Shape competition and shape coexistence in75Br

High-spin states in ${}^{75}\mathrm{Br}$ were populated to investigate shape competition and shape coexistence phenomena in the single and three-quasiparticle regions. The thin-target experiment ${}^{48}\mathrm{Ti}{(}^{30}\mathrm{Si}{,p2n)}^{75}\mathrm{Br}$ at 90 MeV was performed using the FSU Tandem-LINAC accelerator facility, and the FSU-PITT array of 10 Compton-suppressed Ge detectors for the collection of $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence data. Construction of level schemes and assignments of decays, excitation energies, spins, and parities were achieved through examination of coincidence data, relative intensity measurements, and angular correlation analysis. A rotational sequence with band-head spin-parity ${J}^{\ensuremath{\pi}}={\frac{9}{2}}^{+}$ was found and is compared to a similar band in ${}^{77}\mathrm{Br}.$ A negative-parity three-quasiparticle band exhibiting rigid rotation was also discovered. In total, 65 new transitions and 36 new excitation states were added to the level scheme. Cranked-shell, Hartree-Fock-Bogoliubov, and particle-rotor coupling models are used in the interpretation.

Shape coexistence phenomena in medium mass nuclei

We review the theoretical interpretation of experimental results on low and high spin states in some even mass A=60−80 nuclei within the complex versions of the Excited Vampir and Fed Vampir variational approaches. The coexistence of oblate and prolate deformed configurations and their mixing at low spin are found to be responsible for the irregular sequences of states and the isomeric decays identified at low excitation energy in even-even nuclei. This behaviour is determined essentially by the isoscalar neutron-proton interaction. At higher spins the coexistence of states with different deformations causes complicated multiple band structures and strong fragmentation of the B(E2) strengths. It also influences the occurence of almost identical bands at normal deformation in some even mass nuclei. In some odd-odd nuclei the shape coexistence furthermore suggests a possible mechanism to populate high spin isomeric states. For the ground state properties of N=Z nuclei the competition between neutron-proton and like-nucleon isovector pairing plays an important role. With increasing angular momentum the neutron-proton alignment dominates the like-nucleon one in the ground bands of odd-odd N=Z nuclei while in the doubly even N=Z nuclei both types of alignment are of comparable importance.

Light nuclei near neutron and proton drip lines in relativistic mean-field theory

We have made a detailed study of the ground-state properties of nuclei in the light-mass region with atomic numbers Z = 10–22 in the framework of the relativistic mean-field (RMF) theory. The nonlinear σω model with scalar self-interaction has been employed. The RMF calculations have been performed in an axially deformed configuration using the force NL-SH. We have considered nuclei about the stability line as well as those close to proton and neutron drip lines. It is shown that the RMF results provide good agreement with the available empirical data. The RMF predictions also show reasonably good agreement with those of the mass models. It is observed that nuclei in this mass region are found to possess strong deformations and exhibit shape changes all along the isotopic chains. The phenomenon of shape coexistence is found to persist near the stability line as well as near the drip lines. It is shown that the magic number N = 28 is quenched strongly, thus enabling the corresponding nuclei to assume strong deformations. Nuclei near the neutron and proton drip lines in this region are also shown to be strongly deformed.

Microscopic aspects of identical bands in 78Sr and 78Rb

Recent investigations of the shape transition and shape coexistence phenomena dominating the structure of the even-even N ≃ Z nuclei in the A ≃ 80 mass region are extended to the odd-odd nucleus 78Rb. Special attention is paid to the structure of some “identical” bands which have been recently identified in 78 Sr and 78Rb. The ground band of78 Sr and the yrast as well as excited negative parity bands in 78Rb are studied within the EXCITED VAMPIR approximation using complex Hartree-Fock-Bogoliubov transformations in a relatively large model space. The results are compared with the available experimental data. The emerging picture reveals the role played by the strong quadrupole deformation on the appearance of identical bands as well as the influence of the shape coexistence on their evolution. Predictions for the electromagnetic and alignment properties of the bands are presented.

Shape coexistence and shape transition in nuclei from krypton to molybdenum

Abstract The recent investigations of the shape coexistence phenomena dominating the structure of even-even and odd-odd nuclei in the A ∼ 70 mass region are extended to N ⋍ Z nuclei ranging from krypton to molybdenum. Positive-parity states with even angular momenta in 72 Kr, 76 Sr, 78 Sr, 80 Zr and 84 Mo are investigated within the EXCITED VAMPIR approximation using essentially complex Hartree-Fock-Bogoliubov transformations and a relatively large model space. The results are compared with the available experimental data. We obtain an oblate ground band and strong oblate-prolate mixing for N = Z = 36, almost pure prolate and oblate bands, with the yrast one being prolate in 76 Sr, maximum prolate deformation in 76,78 Sr and 80 Zr with very high-lying non-yrast bands and decreased prolate quadrupole deformation for the N = Z = 42 system. Predictions for the electromagnetic properties of the investigated states are presented, too.

New Algorithm for Hartree-Fock Variational Equation

Aiming at microscopically understanding the shape-coexistence phenomena, a new algorithm for obtaining many self-consistent Hartree-Fock states is developed. In contrast with the conventional numerical method of the constrained Hartree-Fock equation, which gives the most energetically favorable state under a given constrained condition, it can find many high-lying Hartree-Fock states as well as many continuous constrained Hartree-Fock solutions by dictating their configurations through some reference state. Numerical calculation is performed by using the Skyrme III.

Shape coexistence in the A ∼ 70 region including neutron-proton interaction and unnatural-parity correlations in the mean field

The recent investigations of the shape-coexistence phenomena dominating the structure of the even-even nuclei in the A ∼ 70 mass region are extended by introducing neutron-proton and unnatural-parity correlations in the mean field, while keeping the time-reversal invariance and the axial-symmetry restrictions. Selected low-lying states in 68Ge, 72Ge and 72Kr nuclei are investigated within the FED VAMPIR or EXCITED FED VAMPIR approaches. The results obtained using real and complex mean fields in a relatively large model space are compared with the experimental data. Similar qualitative features are obtained with both real and complex calculations concerning the evolution of the shape transition and shape coexistence with increasing spin and excitation energy. The results obtained indicate the importance of the new type of correlations introduced by the complex mean fields.