Effects of high-$j$ orbitals, pairing and deformed neutron shells on upbendings of ground-state bands in neutron-rich even-even isotopes $^{170-184}$Hf
The ground-state bands (GSBs) in the even-even hafnium isotopes $^{170-184}$Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hbarω\approx0.5$ MeV observed (predicted) in $^{172}$Hf ($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi1i_{13/2}$ $(1/2^{+}[660])$, $\pi1h_{9/2}$ $(1/2^{-}[541])$ and orbital $\pi1h_{11/2}$ $(7/2^{-}[523])$. The first upbendings of GSBs at low frequency $\hbarω=0.2-0.3$ MeV in $^{170-178}$Hf, which locate below the deformed neutron shell $N=108$, attribute to the alignment of the neutron orbital $\nu1i_{13/2}$. For the heavier even-even isotopes $^{180-184}$Hf, compared to the lighter isotopes, the first band-crossing is delayed to the high frequency due to the existence of the deformed shells $N=108,116$. The upbendings of GSBs in $^{180-184}$Hf are predicted to occur at $\hbarω\approx0.5$MeV, which come from the sharp raise of the simultaneous alignments of both proton $\pi1i_{13/2}$, $\pi1h_{9/2}$ and neutron $\nu2g_{9/2}$ orbitals. The pairing correlation plays a very important role in the rotational properties of GSBs in even-even isotopes $^{180-184}$Hf. Its effects on upbendings and band-crossing frequencies are investigated.
Recent experiments have reached the neutron-rich Cr isotope with N=40 and confirmed enhanced collectivity near this sub-shell. The current data focus on low-spin spectroscopy only, with little information on the states where high-j particles align their spins with the system rotation. By applying the Projected Shell Model, we show that rotation alignment occurs in neutron-rich even-even Cr nuclei as early as spin 8 and, due to shell filling, the aligning particles differ in different isotopes. It is suggested that observation of irregularities in moments of inertia is a direct probe of the def…
Ground state properties of carbon isotopes, including root-mean-square radii, neutron separation energies, single particle spectra, and shapes are systematically studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. The calculations with the effective interaction PK1 reproduce the available data reasonably well. The shell evolution in this isotopic chain is investigated by examining the single particle spectra. The inversion of neutron orbitals $ν2s_{1/2}$ and $ν1d_{5/2}$ compared with the order of neutron orbitals in stable nuclei is revealed in $^{15-20,22}\mathrm{C}…
In this work we studied $β$-decay properties for deformed neutron-rich nuclei in the region Z=36-43. We use the deformed pn-QRPA methods with the realistic CD-Bonn forces, and include both the Gamow-Teller and first-forbidden types of decays in the calculation. The obtained $β$-decay half-lives and neutron-emission probabilities of deformed isotopes are compared with experiment as well as with previous calculations. The advantages and disadvantages of the method are discussed.
Beta-decay properties of neutron-rich Zr and Mo isotopes are investigated within a microscopic theoretical approach based on the proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual separable particle-hole and particle-particle forces are also included in the formalism. The structural evolution in these isotopic chains including both even and odd isotopes is analyzed in terms of the equilibrium deformed shapes. Gamow-Teller strength distributions, beta…
Low-frequency quadrupole vibrations in deformed ${}^{36,38,40}$Mg are studied by means of the deformed Quasiparticle-RPA based on the coordinate-space Hartree-Fock-Bogoliubov formalism. Strongly collective $K^π=0^{+}$ and $2^{+}$ excitation modes (carrying 10-20 W.u.) are obtained at about 3 MeV. It is found that dynamical pairing effects play an essential role in generating these modes. It implies that the lowest $K^π=0^{+}$ excitation modes are particularly sensitive indicators of dynamical pairing correlations in deformed nuclei near the neutron drip line.
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,…
The evolution of quadrupole and octupole collectivity in neutron-deficient Xe, Ba, Ce, and Nd nuclei near the "octupole magic" neutron number $N=56$ is investigated within the mapped $sdf$-IBM framework. Microscopic input is obtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubov calculations, based on the parametrization D1M of the Gogny energy density functional. Octupole-deformed mean-field ground states are predicted for Ba and Ce isotopes near $N=56$. Excitation energies of positive- and negative-parity states as well as electric transition rates are computed with wave fu…
Beta-decay properties of even and odd-A neutron-rich Ge, Se, Kr, Sr, Ru, and Pd isotopes involved in the astrophysical rapid neutron capture process are studied within a deformed proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual interactions in the particle-hole and particle-particle channels are also included in the formalism. The isotopic evolution of the various nuclear equilibrium shapes and the corresponding charge radii are investigated in all…
We expand the triaxial projected shell model basis to include triaxially-deformed multi-quasiparticle states. This allows us to study the yrast and gamma-vibrational bands up to high spins for both gamma-soft and well-deformed nuclei. As the first application, a systematic study of the high-spin states in Er-isotopes is performed. The calculated yrast and gamma-bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-gamma phonon where current…
Low-frequency quadrupole vibrational modes in deformed $^{36,38,40}$Mg close to the neutron drip line are studied by means of the quasiparticle-random-phase approximation based on the coordinate-space Hartree-Fock-Bogoliubov formalism. Strongly collective $K^π=0^{+}$ and $2^{+}$ excitation modes carrying 10-20 Weisskopf units in the intrinsic isoscalar quadrupole transition strengths are obtained at about 3 MeV. There are two reasons for the enhancement of the transition strengths. First, the quasiparticle wave functions generating these modes possess spatially very extended structure. The asy…
The aim of this work is to develop the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) theory based on the point-coupling density functionals and extend it to provide a unified description for all even-even nuclei in the nuclear chart by overcoming all possible challenges. The nuclear superfluidity is considered via Bogoliubov transformation. Densities and potentials are expanded in terms of Legendre polynomials to include the axial deformation degrees of freedom. Sophisticated relativistic Hartree-Bogoliubov equations in coordinate space are solved in the DiracWoods-Saxon…
Background: A global description of the ground-state properties of nuclei in a wide mass range in a unified manner is desirable not only for understanding exotic nuclei but for providing nuclear data for applications. Purpose: We demonstrate the KIDS functional describes the ground states appropriately with respect to the existing data and predictions for a possible application of the functional to all the nuclei by taking Nd isotopes as examples. Method: The Kohn-Sham-Bogoliubov equation is solved for the Nd isotopes with the neutron numbers ranging from 60 to 160 by employing the KIDS functi…
We have investigated the ground-state properties of carbon isotopes in the framework of the relativistic mean-field (RMF) theory. RMF calculations have been performed with the non-linear scalar self-coupling of the $σ$ meson using an axially symmetric deformed configuration. We have also introduced the vector self-coupling of the $ω$ meson for the deformed mean-field calculations. The results show that the RMF predictions on radii and deformations are in good agreement with the available experimental data. It is shown that several carbon isotopes possess a highly deformed shape akin to a super…
We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich $^{36,38,40}$Mg close to the drip line by means of the deformed quasiparticle-random-phase-approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at $E_{x} < 10$ MeV exhausts about $6.0 %$ of the classical Thomas-Reiche-Kuhn dipole sum rule in $^{40}$Mg. We obtained the collective dipole mo…
Low-energy structure of even-even $^{108-116}$Cd isotopes is analyzed using a collective model that is based on the nuclear density functional theory. Spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with parameters determined by the constrained self-consistent mean-field calculations within the relativistic Hartree-Bogoliubov method employing a universal energy density functional and a pairing force. The collective Hamiltonian reproduces the observed quadrupole phonon states of vibrational character, which are based on the moderately deformed eq…
We develop a new framework of the self-consistent deformed proton-neutron quasiparticle-random-phase approximation (pnQRPA), formulated in the Hartree-Fock-Bogoliubov (HFB) single-quasiparticle basis. The same Skyrme force is used in both the HFB and pnQRPA calculations except in the proton-neutron particle-particle channel, where an S=1 contact force is employed. Numerical application is performed for Gamow-Teller (GT) strength distributions and $β$-decay rates in the deformed neutron-rich Zr isotopes located around the path of the rapid-neutron-capture process nucleosynthesis. It is found th…
Electromagnetic properties of the deformed neutron-odd nucleus $^{229}$Th are investigated in the framework of the unified model, with primary emphasis upon the properties of the low-lying isomeric state.
Prediction of deformed halo nuclei $^{43,45}$Si from multiple criteria based on structure and reaction analyses
Anhui Normal University（安徽师范大学）；Beihang University（北京航空航天大学）；Peking University（北京大学）；Fuzhou University（福州大学）；Institute for Basic Science（韩国基础科学研究所）；Kyungpook National University（庆北国立大学）；China Academy of Engineering Physics（中国工程物理研究院）
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 extend the ab initio coupled-cluster effective interaction (CCEI) method to deformed open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei $^{20}$Ne and $^{24}$Mg we reproduce…
We calculate the binding energy, root-mean-square radius and quadrupole deformation parameter for the recent, possibly discovered superheavey element Z=122, using the axially deformed relativistic mean field (RMF) and non-relativistic Skyrme Hartree-Fock (SHF) formalisms. The calculation is extended to include various isotopes of Z=122 element, strarting from A=282 to A=320. We predict highly deformed structures in the ground state for all the isotopes. A shape transition appears at about A=290 from a highly oblate to a large prolate shape, which may be considered as the superdeformed and hype…
First calculations for deformed nuclei with the Fayans functional are carried out for the uranium and lead isotopic chains. The ground state deformations and deformation energies are compared to Skyrme-Hartree-Fock-Bogolyubov results of HFB-17 and HFB-27 functionals. For the uranium isotopic chain, the Fayans functional predictions are rather similar properties compared to HFB-17 and HFB-27. However, there is a disagreement for the lead isotopic chain. Both of the Skyrme HFB functionals predict rather strong deformations for the light Pb isotopes which does not agree with the experimental data…
The Coriolis matrix elements responsible for mixing of the $1^+ K=1$ and $1^+ K=0$ states are calculated in the framework of the Quasiparticle Phonon Model for several Gd and Dy isotopes. In many considered cases these matrix elements are equal to several tens of keV and are comparable with energy distances between the mixed levels. The results obtained indicates that Gd isotopes could be more suitable for finding deviations from Alaga rules in M1 transitions from $1^+$ state to the states of the ground band.
The properties of the collective low-lying states of Zr isotopes which include excitation energies and $E2$ reduced transition probabilities indicate that some of these states are mainly spherical and the other are mainly deformed ones. We investigate the properties of the low-lying collective states of $^{92-102}$Zr and their evolution with increase of the number of neutrons based on the five-dimensional Geometrical Quadrupole Collective Model. The quadrupole-collective Bohr Hamiltonian with a potential having spherical and deformed minima, is applied. The relative depth of two minima, height…
The particle-number conserving (PNC) method in the framework of cranked shell model (CSM) is developed to deal with the reflection-asymmetric nuclear system by applying the $S_x$ symmetry. Based on an octupole-deformed Nilsson potential, the alternating-parity bands in \element{236,238}{U} and \element{238,240}{Pu} are investigated. The experimental kinematic moments of inertia (MoI) and the angular momentum alignments of all studied bands are reproduced well in the PNC-CSM calculations. The striking difference of rotational behaviors between U and Pu isotopes can be linked to the strength of …
Shape-phase transition in neutron-rich Cr isotopes around N=40 is investigated by employing the collective Hamiltonian approach. The inertial functions for large-amplitude vibration and rotation are evaluated by the local normal modes along the axial quadrupole collective coordinate using the Skyrme and pairing energy density functionals. The time-odd components of the mean fields are fully included in the derived masses. The low-lying spectra obtained by requantizing the collective Hamiltonian show an excellent agreement with the recent experimental data. Gradual change from spherical to axia…
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…
Bulk and decay properties, including deformation energy curves, charge mean square radii, Gamow-Teller (GT) strength distributions, and beta-decay half-lives, are studied in neutron-deficient even-even and odd-A Hg and Pt isotopes. The nuclear structure is described microscopically from deformed quasiparticle random-phase approximation calculations with residual interactions in both particle-hole and particle-particle channels, performed on top of a self-consistent deformed quasiparticle Skyrme Hartree-Fock basis. The observed sensitivity of the, not yet measured, GT strength distributions to …
A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the study of neutron halos in deformed nuclei and the halo phenomenon in deformed weakly bound nuclei is investigated. Magnesium and neon isotopes are studied and some results are presented for the deformed neutron-rich and weakly bound nuclei 44Mg and 36Ne. The core of the former nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurr…
The available data for E2 transition strengths in the region between neutron-deficient Hf and Pt isotopes are far from complete. More and precise data are needed to enhance the picture of structure evolution in this region and to test state-of-the-art nuclear models. In a simple model, the maximum collectivity is expected at the middle of the major shell. However, for actual nuclei, this picture may no longer be the case, and one should use a more realistic nuclear-structure model. We address this point by studying the spectroscopy of Hf. We remeasure the 2^+_1 half-lives of 172,174,176Hf, for…
Shape evolution of krypton isotopes calculated with axially deformed relativistic Hartree-Bogoliubov approach
Advanced Energy Science and Technology, Guangdong Laboratory（广东实验室先进能源科学与技术）；CAS Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics , Chinese Academy of Sciences（中国科学院近代物理研究所高精度核谱学重点实验室）；Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Department of Physics, Zhejiang Sci-Tech University（浙江理工大学物理学院量子态调控与光场操控浙江省重点实验室）；Astrophysical Big Bang Laboratory, Pioneering Research Institute, RIKEN（理化学所先驱研究院天体物理大爆炸实验室）；Physik-Department der Technische Universität München（慕尼黑工业大学物理系）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与核技术国家重点实验室）
Background: The $γ$ vibrational mode of excitation is an acknowledged collective mode in deformed nuclei. The collectivity depends on the details of the shell structure around the Fermi levels, in particular the presence of the orbitals that have the enhanced transition matrix elements of the non-axial quadrupole excitation. Quite recently, a sudden decrease in the excitation energy of the $γ$ vibration was observed at RIKEN RIBF for the neutron-rich Dy isotopes at $N=106$. Purpose: In the present work, by studying systematically the microscopic structure of the $γ$ vibration in the neutron-ri…
Low-frequency $K^π=0^{+}$ states in deformed neutron-rich nuclei are investigated by means of the quasiparticle-random-phase approximation based on the Hartree-Fock-Bogoliubov formalism in the coordinate space. We have obtained the very strongly collective $K^π=0^{+}$ modes not only in neutron-rich Mg isotope but also in Cr and Fe isotopes in N=40 region, where the onset of nuclear deformation has been discussed. It is found that the spatially extended structure of neutron quasiparticle wave functions around the Fermi level brings about a striking enhancement of the transition strengths. It is…
We have developed an {\it ab initio} deformed in-medium similarity renormalization group (IMSRG) for open-shell nuclei. This is a single-reference IMSRG in deformed Hartree-Fock (HF) basis. Deformed wave functions are more efficient in describing deformed nuclei. The broken spherical symmetry needs to be restored by angular momentum projection, which is computational expensive. The angular momentum mainly capture the static correlations and can be estimated by the projection of the HF state. In this work, we do deformed IMSRG calculation and add the correlation energy from projected HF as a le…
Beta-decay properties of neutron-rich Ca, Ti, and Cr isotopes are studied within a deformed proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual spin-isospin interactions in the particle-hole and particle-particle channels are also included in the formalism. The energy distributions of the Gamow-Teller strength, the beta-decay feedings, the beta-decay half-lives, and the beta-delayed neutron emission probabilities are discussed and compared with other …
We study the breathing oscillations in bose-fermi mixtures with Yb isotopes in the largely prolate deformed trap, which are realized by Kyoto group. We choose the three combinations of the Yb isotopes, Yb170-Yb171, Yb170-Yb173 and Yb174-Yb173, whose boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive. The collective oscillations in the deformed trap are calculated in the dynamical time-development approach, which is formulated with the time-dependent Gross-Pitaevskii and the Vlasov equations. We analyze the results in the time-development approach with t…
The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for the $pf$-$g_{9/2}$-$d_{5/2}$ model space. Experimental energy levels are reproduced well by a single fixed Hamiltonian. Intrinsic shapes are analyzed for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate and gamma-unstable shapes are seen including shape fluctuations, $E$(5)-like situation, the magicity of doubly-magic $^{56,68,78}$Ni, and the coexistence of spherical and strongly deformed shapes. Regarding the last …
The alpha and cluster decay properties of the $132-138$^Nd, $144-158$^Gd, $176-196$^Hg and $192-198$^Pb even-even isotopes in the two mass regions A = 130-158 and A = 180-198 are analysed using the Coulomb and Proximity Potential Model. On examining the clusters at corresponding points in the cold valleys (points with same A_2) of the various isotopes of a particular nucleus we find that at certain mass numbers of the parent nuclei, the clusters emitted are getting shifted to the next lower atomic number. It is interesting to see that the change in clusters appears at those isotopes where a ch…
Photoabsorption cross sections of Nd and Sm isotopes from spherical to deformed even nuclei are systematically investigated by means of the quasiparticle-random-phase approximation based on the Hartree-Fock-Bogoliubov ground states (HFB+QRPA) using the Skyrme energy density functional. The gradual onset of deformation in the ground states as increasing the neutron number leads to characteristic features of the shape phase transition. The calculation well reproduce the isotopic dependence of broadening and emergence of a double-peak structure in the cross sections without any adjustable paramet…
We calculate the binding energy and deformation parameter for light nuclei with and without pairing using a deformed relativistic mean field model. The role of BCS-type pairing effect is analyzed for Ne and F isotopes. The calculated odd-even staggering and the deformation parameters argue strongly against the role of pairing in the light nuclei.
The mass region with A~100 and Z~40 is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even 94-110Zr nuclei and, moreover, to obtain information about wave…
The newly developed multi-quasiparticle triaxial projected shell-model approach is employed to study the high-spin band structures in neutron-deficient even-even Ce- and Nd-isotopes. It is observed that gamma-bands are built on each intrinsic configuration of the triaxial mean-field deformation. Due to the fact that a triaxial configuration is a superposition of several K-states, the projection from these states results in several low-lying bands originating from the same intrinsic configuration. This generalizes the well-known concept of the surface gamma-oscillation in deformed nuclei based …
Quadrupole moments and charge radii in cadmium isotopes are studied from a microscopic perspective. The results obtained from self-consistent deformed Hartree-Fock+BCS calculations with Skyrme forces are compared with isomer and isotope shifts measured from high resolution laser spectroscopy experiments. The microscopic calculations reproduce fairly well the main features observed in those isotopes that include the linear increase with the neutron number of the quadrupole moments of the 11/2- isomers, as well as the parabolic behavior of the mean-square charge radii difference between isomers …
Isotope-dependence of measured reaction cross sections in scattering of $^{28-32}$Ne isotopes from $^{12}$C target at 240 MeV/nucleon is analyzed by the double-folding model with the Melbourne $g$-matrix. The density of projectile is calculated by the mean-field model with the deformed Wood-Saxon potential. The deformation is evaluated by the antisymmetrized molecular dynamics. The deformation of projectile enhances calculated reaction cross sections to the measured values.
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.
Whereas previous works for B(E2)'s in the even-even Ti isotopes focused on yrast transitions we here also consider inter-band transitions to a second group i.e. states like 1_{1} , 2_{2}, 3_{1} , 4_{2} , 5_{1}e.t.c.. We focus on variations from one even-even Ti isotope to the next. We make a qualitative comparison with similar transitions in a heavier deformed nucleus.
Masses, deformations, radii, and single-particle properties of the very neutron-rich Sulfur isotopes are investigated in the framework of the selfconsistent mean-field theory. The stability of the N=28 magic gap around $^{44}$S is discussed.
The symmetry energy, the neutron pressure and the asymmetric compressibility of deformed neutron-rich even-even nuclei are calculated on the examples of Kr and Sm isotopes within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for isotopic chains of these nuclei in the framework of the self-consistent Skyrme-Hartree-Fock plus BCS method. Resul…
The potential energy surfaces of even-even $^{142-156}$Ba are investigated in the constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. It is shown that for the ground states, $^{142}$Ba is near spherical,$^{156}$Ba well quadrupole-deformed, and in between $^{144-154}$Ba octupole deformed. In particular, the nuclei $^{148,150}$Ba with $N=92,94$ have the largest octupole deformations. By including the octupole degree of freedom, energy gaps $N=88$, $N=94$ and $Z=56$ near Fermi surfaces for the single-particle levels in $^{148}$Ba with $β_2\sim 0.26$ and $β_3…
A study of the shape transition from spherical to axially deformed nuclei in the even Ce isotopes using the nucleon-pair approximation of the shell model is reported. As long as the structure of the dominant collective pairs is determined using a microscopic framework appropriate to deformed nuclei, the model is able to produce a shape transition. However, the resulting transition is too rapid, with nuclei that should be transitional being fairly well deformed, perhaps reflecting the need to maintain several pairs with each angular momentum.
