The beyond mean field approximation combined with the Gogny interaction is used to analyze the spherical to prolate deformed shape transition in the Neodymium isotopic chain. The vibrator as well as the rotor limits are nicely reproduced while the transitional region is only qualitatively described probably due to the lack of triaxial correlations in the calculations. Our results do not support the interpretation of $^{150}$Nd as a critical point nucleus and question the interpretation of shape changes as nuclear shape phase transitions.
The experimental gamma-ray strength functions (gamma-SFs) of 142,144-151Nd have been studied for gamma-ray energies up to the neutron separation energy. The results represent a unique set of gamma-SFs for an isotopic chain with increasing nuclear deformation. The data reveal how the low-energy enhancement, the scissors mode and the pygmy dipole resonance evolve with nuclear deformation and mass number. The data indicate that the mechanisms behind the low-energy enhancement and the scissors mode are decoupled from each other.
It was recently shown that dielectronic recombination measurements can be used for accurately inferring changes in the nuclear mean-square charge radii of highly-charged lithium-like neodymium [Brandau et al., Phys. Rev. Lett. 100 073201 (2008)]. To make use of this method to derive information about the nuclear charge distribution for other elements and isotopes, accurate electronic isotope shift parameters are required. In this work, we calculate and discuss the relativistic mass- and field-shift factors for the two $2s ^{2}S_{1/2} - 2p ^{2}P^{o}_{1/2,3/2}$ transitions along the lithium isoe…
We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon.
The phenomena of shape evolution and shape coexistence in even-even $^{88-126}$Zr and $^{88-126}$Mo isotopes is studied by employing covariant density functional theory (CDFT) with density-dependent point coupling parameter sets DD-PCX and DD-PC1, and with separable pairing interaction. The results for rms deviation in binding energies, two-neutron separation energy, the differential variation of two-neutron separation energy, and rms charge radii, as a function of neutron number, are presented and compared with available experimental data. In addition to the oblate-prolate shape coexistence i…
The systematic investigation of ground state shape evolution from gamma unstable O(6) to spherical U(5) for Te isotopes has been presented by using the quadrupole moment constrained Hartree Fock Bogoliubov (HFB) method with the Skyrme force SLy4. 124Te has been pointed out as to be the possible critical point nucleus with E(5) symmetry.
Proton inelastic scattering experiments at energy E_p = 200 MeV and a spectrometer scattering angle of 0 degree were performed on 144,146,148,150Nd and 152Sm exciting the IsoVector Giant Dipole Resonance (IVGDR). Comparison with results from photo-absorption experiments reveals a shift of resonance maxima towards higher energies for vibrational and transitional nuclei. The extracted photo-absorption cross sections in the most deformed nuclei, 150Nd and 152Sm, exhibit a pronounced asymmetry rather than a distinct double-hump structure expected as a signature of K-splitting. This behaviour can b…
The goal of this contribution is to analyze the connection between shape coexistence and quantum phase transition, two seemingly unrelated phenomena that share common aspects, namely, the rapid change in the ground state structure along an isotope chain or the presence of several minima at the mean-field level. To illustrate the similarities and differences between both phenomena, we will focus in the Pb region, in particular in Pt and Hg isotopes, as well as in Zr isotopes.
We study the oblate-prolate shape mixing in the low-lying states of proton-rich Kr isotopes using the five-dimensional quadrupole collective Hamiltonian. The collective Hamiltonian is derived microscopically by means of the CHFB (constrained Hartree-Fock-Bogoliubov) + Local QRPA (quasiparticle random phase approximation) method, which we have developed recently on the basis of the adiabatic self-consistent collective coordinate method. The results of the numerical calculation show the importance of large-amplitude collective vibrations in the triaxial shape degree of freedom and rotational eff…
We studied the ground and excited states properties for Zr isotopes starting^M from proton to neutron drip-lines using the relativistic and non-relativistic mean field formalisms with BCS and Bogolyubov pairing. The celebrity NL3 and SLy4 parameter sets are used in the calculations. We find spherical ground and low-lying^M superdeformed excited states in most of the isotopes. Several couples of^M $Ω^π=1/2^{\pm}$ parity doublets configurations are found,^M while analyzing the single-particle energy levels of the superdeformed ^M configurations.
The shape of a nucleus is one of fundamental nuclear properties. We perform a systematic investigation of bubble nuclei that also exhibit shape coexistence in Hf, W, Os, Pt and Hg even-even isotopes using the deformed relativistic Hartree-Bogoliubov theory in continuum. For a systematic study, we first consider nuclear bubble structures and shape coexistence separately. We confirm that deformations and pairing correlations hinder bubble structures by comparing our results with those from relativistic continuum Hartree-Bogoliubov theory that assumes spherical symmetry in nuclei. We then predict…
The spherical-to-prolate shape transition in neutron-rich Cr isotopes from N = 34 to 42 is studied by solving the collective Schr\"odinger equation for the five-dimensional quadrupole collective Hamiltonian. The collective potential and inertial functions are microscopically derived with use of the constrained Hartree-Fock-Bogoliubov plus local quasiparticle random-phase approximation method. Nature of the quadrupole collectivity of low-lying states is discussed by evaluating excitation spectra and electric quadrupole moments and transition strengths. The result of calculation indicates that …
We have performed tilted-axis-cranked Hartree-Fock-Bogoliubov calculations for a neutron-rich hafnium isotope ($^{182}$Hf) whose proton and neutron numbers are both in the upper shell region. We study whether the shell effects play a role in producing high-$K$ isomers or highly gamma-deformed states at high spin. In particular, the possibility of shape coexistence and the effect of wobbling motion are discussed.
Total Routhian Surface (TRS) calculations have been performed to investigate shape coexistence and evolution in neutron-deficient krypton isotopes ${}^{72,74,76}$Kr. The ground-state shape is found to change from oblate in ${}^{72}$Kr to prolate in ${}^{74,76}$Kr, in agreement with experimental data. Quadrupole deformations of the ground states and coexisting $0^{+}_{2}$ states as well as excitation energies of the latter are also well reproduced. While the general agreement between calculated moments of inertia and those deduced from observed spectra confirms the prolate nature of the low-lyi…
We study ground states and beta decay properties of the proton rich isotope chains Ge, Se, Kr, and Sr. We use a deformed selfconsistent HF+RPA approach with density-dependent effective interactions of Skyrme type. We find that most of the isotopes present two HF minima corresponding to two different shapes. In addition to static quadrupole moments and other ground state band properties, we present results for Gamow-Teller strength distributions, as well as for half-lives and summed strengths. The role of deformation is particularly emphasized.
The critical point nuclei in Sm isotopes, which marks the first order phase transition between spherical U(5) and axially deformed shapes SU(3), have been investigated in the microscopic quadrupole constrained relativistic mean field (RMF) model plus BCS method with all the most used interactions, i.e., NL1, NL3, NLSH and TM1. The calculated potential energy surfaces show a clear shape transition for the even-even Sm isotopes with $N = 82\sim 96$ and the critical point nuclei are found to be $^{148}$Sm, $^{150}$Sm and $^{152}$Sm. Similar conclusions can also be drawn from the microscopic neutr…
Gamow-Teller strength distributions and beta-decay half-lives in neutron-deficient Kr and Sr isotopes are investigated within a deformed quasiparticle random phase approximation. The approach is based on a selfconsistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. A simple two-level model is used to mix the nuclear shapes into the physical ground state. Good agreement with experiment is found with shape mixing coefficients which are consistent with those obtained phenomenologically from mixing of rotational bands.
Fission-fragment mass and total-kinetic-energy distributions following fission of the fermium isotopes $^{256,258,260}\text{Fm}$ at low excitation energy have been calculated using the Brownian shape-motion model. A transition from asymmetric fission in $^{256}\text{Fm}$ to symmetric fission in $^{258}\text{Fm}$ is obtained. The total-kinetic-energy distributions for the three isotopes show radically different behaviour due to varying contributions from different fission modes, with a double-humped distribution for $^{258}\text{Fm}$.
We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with exp…
We study the spherical to prolate-deformed shape transition in $^{144-158}$Sm and $^{146-160}$Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr hamiltonian neither the interpretation of the nuclei N=90 as critical points.
Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the Shell Model language. Purpose: We intend to study the importance of configuration mixing in the understanding of the nuclear structure of even-even Po isotopes, where the shape coexistence phenomena are not clear enough. Method: We study in detail a long chain of polonium isotopes, 190-208Po, using the interacting boson model with configuration mixing (IBM-CM). We fix the parameters of the Hamiltonians th…
The ground and first excited 0+ states of the {156-172}Er isotopes are analyzed in the framework of the generator coordinate method. The shape parameter beta is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E2 transition rates up to mod…
The isotopic evolution of the ground-state nuclear shapes and the systematics of one-quasiproton configurations are studied in neutron-rich odd-A Yttrium and Niobium isotopes. We use a selfconsistent Hartree-Fock-Bogoliubov formalism based on the Gogny energy density functional with two parametrizations, D1S and D1M. The equal filling approximation is used to describe odd-A nuclei preserving both axial and time reversal symmetries. Shape-transition signatures are identified in the N=60 isotopes in both charge radii and spin-parities of the ground states. These signatures are a common character…
We study shape coexistence and low-energy excitation spectra in neutron-deficient Pb isotopes using configuration mixing of angular-momentum and particle-number projected self-consistent mean-field states. The same Skyrme interaction SLy6 is used everywhere in connection with a density-dependent zero-range pairing force.
The isotopic evolution of the ground-state nuclear shapes and the systematics of one-quasiproton configurations are studied in odd-A Rubidium isotopes. We use a selfconsistent Hartree-Fock-Bogoliubov formalism based on the Gogny energy density functional with two parametrizations, D1S and D1M, and implemented with the equal filling approximation. We find clear signatures of a sharp shape transition at N=60 in both charge radii and spin-parity of the ground states, which are robust, consistent to each other, and in agreement with experiment. We point out that the combined analysis of these two …
In this paper, we have considered the interplay between phase transitions and configuration mixing of intruder excitations in the 118-128Te isotopes. A transitional interacting boson model Hamiltonian in both IBM-1 and IBM-2 versions which are based on affine Lie Algebra are employed to describe the evolution from spherical to deformed gamma unstable shapes along the chain of Te isotopes. The excitation energies, B(E0) and B(E2) transition rates are rather well reproduced in comparison with experimental counterparts when the weight of SO(6) limit is increased in Hamiltonian. Also our results s…
A novel shape evolution in the Sn isotopes by the state-of-the-art application of the Monte Carlo Shell Model calculations is presented in a unified way for the 100-138Sn isotopes. A large model space consisting of eight single-particle orbits for protons and neutrons is taken with the fixed Hamiltonian and effective charges, where protons in the 1g9/2 orbital are fully activated. While the significant increase of the B(E2; 0+1 -> 2+1) value, seen around 110Sn as a function of neutron number (N), has remained a major puzzle over decades, it is explained as a consequence of the shape evolution …
We investigate ground states properties of Pb isotopes located between neutron and proton drip-lines estimated by two-neutron (two-proton) separation energies and Fermi energies within the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). First, we report some candidates of nuclear shape coexistence in the isotope chain. They are accessed by calculating total energy as a function of the deformation parameter $β_2$, and for the coexistence candidates we take a couple of the deformation region bringing about minima of the energy within energy difference $ΔE < $ 1 MeV. Second,…
Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculations are performed to study the evolution of shapes with the number of nucleons in various chains of Yb, Hf, W, Os, and Pt isotopes from neutron number N=110 up to N=122. Potential energy curves are analyzed in a search for signatures of oblate-prolate phase shape transitions and results from various Skyrme and pairing forces are considered. Comparisons with results obtained with the Gogny interaction as well as with relativistic mean field calculations are presented. The role of the $γ$ degree of freedom is also discussed.
The evolution of the ground-state shape along the triaxial landscape of several isotopes of Yb, Hf, W, Os, and Pt is analyzed using the self-consistent Hartree-Fock-Bogoliubov approximation. Two well reputed interactions (Gogny D1S and Skyrme SLy4) have been used in the study in order to asses to which extent the results are independent of the details of the effective interaction. A large number of even-even nuclei, with neutron numbers from N=110 up to N=122 has been considered, covering in this way a vast extension of the nuclear landscape where signatures of oblate-prolate shape transitions…
Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the Shell Model language or equivalently to nuclear shapes with different deformation. Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it. Method: We study in detail a long chain of mercury isotopes, $^{172-200}$Hg, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least square fit …
We study Gamow-Teller strength distributions in the neutron-deficient even isotopes (184-194)Pb in a search for signatures of deformation. The microscopic formalism used is based on a deformed quasiparticle random phase approximation (QRPA) approach, which involves a self-consistent quasiparticle deformed Skyrme Hartree-Fock (HF) basis and residual spin-isospin forces in both the particle-hole and particle-particle channels. By analyzing the sensitivity of the Gamow-Teller strength distributions to the various ingredients in the formalism, we conclude that the beta-decay of these isotopes coul…
We show how the shape evolution of the neutron-rich exotic Si and S isotopes can be understood as a Jahn-Teller effect that comes in part from the tensor-driven evolution of single-particle energies. The detailed calculations we present are in excellent agreement with known experimental data, and we point out of new features that should be explored in new experiments. Potential energy surfaces are used to understand the shape evolutions. The sub-shell closed nucleus, $^{42}$Si, is shown to be a perfect example of a strongly oblate shape instead of a sphere through a robust Jahn-Teller mechanis…
The shape coexistence in the nuclei $^{182-192}$Pb is analyzed within the Hartree-Fock-Bogoliubov approach with the effective Gogny force. A good agreement with the experimental energies is found for the coexisting spherical, oblate and prolate states. Contrary to the established interpretation, it is found that the low-lying prolate and oblate $0^+$ states observed in this mass region are predominantly characterized by neutron correlations whereas the protons behave as spectators rather than playing an active role.
The isovector giant dipole resonance (IVGDR) in even-even Nd isotopes from A=124 to A=160 is studied in the framework of time-dependent Hartree-Fock (TDHF) with Skyrme forces SkI3, SVbas, SLy5 and SLy6. The dipole strength is calculated and compared with the experimental data on photon absorption cross section $σ_γ$. An overall agreement between them is obtained. The dipole strengths in $ ^{124-140}\text{Nd}$ and $^{152-160}\text{Nd} $ are predicted. In addition, the correlation between the quadrupole deformation parameter $β_{2}$ and the splitting $ΔE/ \bar{E}_{m}$ of the giant dipole resonan…
The deformation energy of the even-even nuclei of the Cerium isotopic chain is investigated by means of the Macroscopic-Microscopic method with a semi-classical shell correction. We consider axially symmetric shapes. Binding energy and two neutron separation energy are also evaluated. For the sake of clarity several important details of the calculations are also given. It turns out that all these nuclei have prolate equilibrium shape. The regions of maximum deformation are obtained around N=64 and N=102. There is no critical-point of quantum phase transition in this isotopic chain.
We discuss shape coexistence in the neutron-deficient Kr72-Kr78 isotopes in the framework of configuration mixing calculations of particle-number and angular-momentum projected axial mean-field states obtained from self-consistent calculations with the Skyrme interaction SLy6 and a density-dependent pairing interaction. While our calculation reproduces qualitatively and quantitatively many of the global features of these nuclei, such as coexistence of prolate and oblate shapes, their strong mixing at low angular momentum, and the deformation of collective bands, the ordering of our calculated …
In this paper, we have studied the shapes coexistence in the 180-190Hg isotopes. The SO(6) representation of eigenstates and a transitional Hamiltonian in the Interacting Boson Model 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 i…
The ground-state deformations of the Ge isotopes are investigated in the framework of Gogny-Hartree-Fock-Bogoliubov (HFB) and Skyrme Hartree-Fock plus pairing in the BCS approximation. Five different Skyrme parametrizations are used to explore the influence of different effective masses and spin-orbit models. There is generally good agreement for binding energies and deformations (total quadrupole moment, triaxiality) with experimental data where available (i.e., in the valley of stability). All calculations agree in predicting a strong tendency for triaxial shapes in the Ge isotopes with only…
We study the role of intruder states and shape coexistence in the even-even $^{190-206}$Po isotopes, through an interacting boson model with configuration mixing calculation. We analyzed the results in the light of known systematics on various observable in the Pb region, paying special attention to the unperturbed energy systematics and quadrupole deformation. We find that shape coexistence in the Po isotopes behaves in very much the same way as in the Pt isotopes, i.e., it is somehow hidden, contrary to the situation in the Pb and the Hg isotopes.
We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (sphe…
Bohr-Mottelson Hamiltonian with octic potential applied to the $^{106-116}$Cd isotopes
Department of Theoretical Physics, "Horia Hulubei" − - National Institute for R&D in Physics and Nuclear Engineering（希里亚·胡卢贝伊理论物理系，核物理与核工程研发国家研究所）；Academy of Romanian Scientists（罗马尼亚科学家学院）
The oblate-prolate shape coexisting/mixing phenomena in proton-rich 68,70,72Se are investigated by means of the adiabatic self-consistent collective coordinate (ASCC) method. The one-dimensional collective path and the collective Hamiltonian describing the large-amplitude shape vibration are derived in a fully microscopic way. The excitation spectra, B(E2) and spectroscopic quadrupole moments are calculated by requantizing the collective Hamiltonian and solving the collective Schroedinger equation. The basic properties of the coexisting two rotational bands in low-lying states of these nuclei …
In this work, the ground-state properties of the platinum isotopic chain, 160-238Pt, are studied within the covariant density functional theory. The calculations are carried out for a large number of even-even Pt isotopes by using the density-dependent point-coupling and the density dependent meson-exchange effective interactions. All ground-state properties such as the binding energy, separation energy, two-neutron shell gap, rms-radii for neutrons and protons and quadrupole deformation are discussed and compared with available experimental data, and with the predictions of some nuclear model…
The properties of the low-lying states, especially the relevant shape coexistence in $^{80}$Ge close to one of most neutron-rich doubly magic nuclei at $N=50$ and $Z=28$ have been investigated within the framework of the proton-neutron interacting model (IBM-2). Based on the fact that the relative energy of the $d$ neutron boson is different from proton bosons', the calculated energy levels of low-lying states, $E2$ transition strengths can reproduce the experimental data very well. Particularly, the first excited state 0$^+_2$ is reproduced quite nicely, which is intimately related with the s…
Five-dimensional collective Hamiltonian based on the covariant density functional theory has been applied to study the the low-lying states of even-even $^{148-162}$Gd isotopes. The shape evolution from $^{148}$Gd to $^{162}$Gd is presented. The experimental energy spectra and intraband $B(E2)$ transition probabilities for the $^{148-162}$Gd isotopes are reproduced by the present calculations. The relative $B(E2)$ ratios in present calculations are also compared with the available interacting boson model results and experimental data. It is found that the occupations of neutron $1i_{13/2}$ orb…
The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate-oblate transition, the smooth…
