The core polarization effect for the electric quadrupole moment of the neutron-rich $^{31}$Al, $^{33}$Al and $^{35}$Al isotopes in the vicinity of the island of inversion are investigated by means of the microscopic particle-vibration coupling model in which the Skyrme Hartee-Fock-Bogoliubov and quasiparticle-random-phase approximation are used to calculate the single-quasiparticle wave functions and the excitation modes. It is found that the polarization charge for the proton $1d_{5/2}$ hole state in $^{33}$Al is quite sensitive to coupling to the neutrons in the $pf$-shell associated with the pairing correlations, and that the polarization charge in $^{35}$Al becomes larger due to the stronger collectivity of the low-lying quadrupole vibrational mode in the neighboring $^{36}$Si nucleus.
Shell model calculations with the neutron effective charge as single free parameter describe well the \bet and \bef rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a pseudo SU3 symmetry, which remains of heuristic value in the latter, though the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. For $N\ge 64$ quadrupole dominance is accentuated in the Cd isotopes and gives way to seniority dominance…
We present systematic calculations on the spectroscopy and transition properties of even-even Te isotopes by using the large-scale configuration interaction shell model approach with a realistic interaction. These nuclei are of particular interest since their yrast spectra show a vibrational-like equally-spaced pattern but the few known E2 transitions show anomalous rotational-like behavior, which cannot be reproduced by collective models. Our calculations reproduce well the equally-spaced spectra of those isotopes as well as the constant behavior of the $B(E2)$ values in $^{114}$Te. The calcu…
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…
The longstanding problem of characterization of the $0^+_2$ states in Gd isotopes is revisited by adopting the Nilsson$+$BCS mean field and the random-phase approximation. The interband electric quadrupole transition strengths varying almost two orders of magnitude are nicely reproduced at the same time as other observables. These results indicate that the $0^+_2$ states, in particular, those in lighter isotopes are well described as $β$ vibrations excited on top of deformed ground states without recourse to the shape-coexistence picture.
The electric quadrupole response in $^{112,114}$Sn isotopes is investigated by energy-density functional (EDF) and three-phonon quasiparticle-phonon model (QPM) theory with special emphasis on 2$^+$ excitations located above the first collective quadrupole state and below 5 MeV. Additional quadrupole strength clustering as a sequence of states similar to the recently observed pygmy quadrupole resonance in $^{124}$Sn is found. The spectral distributions and transition densities of these 2$^+$ states show special features being compatible with oscillations of a neutron skin against the isospin-s…
Effect of ground-state deformation on the Isoscalar Giant Monopole Resonance and the first observation of overtones of the Isoscalar Giant Quadrupole Resonance in rare-earth Nd isotopes
The recent RCNP $(α, α')$ data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in $^{92,94,96,98,100}$Mo are analyzed within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) approach with Skyrme interactions, in which pairing correlations and possible axial deformations are taken into account. The Skyrme sets SkM*, SLy6, SVbas and SkP$^δ$, that explore a diversity of nuclear matter properties, are used. We discuss the connection between the line shape of the monopole strength ISGMR and the deformation-induced coupling be…
Spectroscopic properties that characterize the shape phase transitions in krypton isotopes with the mass $A\approx80$ region are investigated within the framework of the nuclear density functional theory. Triaxial quadrupole constrained self-consistent mean-field calculations that employ relativistic energy density functionals and a pairing interaction are carried out for the even-even nuclei $^{76-86}$Kr. The spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with the ingredients, i.e., the deformation-dependent moments of inertia and mass paramet…
A key question concerning the spherical-vibrator attributes of states in Cadmium isotopes is addressed by means of a boson Hamiltonian encompassing U(5) partial dynamical symmetry. The U(5) symmetry is preserved in a segment of the spectrum and is broken in particular non-yrast states, and the resulting mixing with the intruder states is small. The vibrational character is thus maintained in the majority of low-lying normal states, as observed in $^{110}$Cd.
[Background] The BE2 rates of the Sn isotopes for $N\le 64$ exhibit enhancements hitherto unexplained. The same is true for the Cd isotopes. [Purpose] Describe the electromagnetic properties of the Sn and Cd isotopes [Method] Shell model calculations with a minimally renormalized realistic interaction, supplemented by Quasi and Pseudo-SU3 symmetries and Nilsson-SU3 selfconsistent calculations. [Results for $N\le 64$] Shell model calculations with the neutron effective charge as single free parameter describe well the BE2(2>0) and BE2(4>2) rates for $N\le 64$ in the Cd and Sn isotopes. The form…
One neutron triaxial halo candidates in aluminum isotopes from reaction observables
School of Physics, Beihang University（北京航空航天大学物理学院）；National Key Laboratory of Neutron Science and Technology, Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics（中国工程物理研究院核物理与化学研究所中子科学与技术国家重点实验室）；Baoding Hospital of Beijing Children’s Hospital（北京儿童医院保定医院）
In this work the excited energy levels, reduced transition probabilities, $B(E2)\uparrow$, intrinsic quadrupole moments and deformation parameters have been calculated for $^{62-68}$Zn isotopes with neutrons (N=32,34,36 and 38 ). Nushellx code has been applied for all energy states of (fp-shell) nuclei. Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the lp$_{3/2}$, 0f$_{5/2}$ and lp$_{1/2}$ orbits outside doubly-magic closed "56Ni"core nucleus. By using (f5p) model space and (f5pvh) interaction, the theoretical results have been obtain…
The structure of even-even $^{108-116}$Cd isotopes is investigated based on the self-consistent mean-field approach. By mapping the quadrupole-$(β,γ)$ deformation energy surface, obtained from the constrained self-consistent mean-field calculations with a choice of the Skyrme force and pairing property, onto the Hamiltonian of the interacting boson model with configuration mixing, the strength parameters of the Hamiltonian are determined. The low-lying excitation spectra and electric quadrupole transition rates for the considered Cd nuclei are computed by the resultant Hamiltonian, and are com…
Microscopic description of quadrupole-hexadecapole coupling in radium, thorium, uranium and plutonium isotopes with the Gogny energy density functional
In this work, Na isotopes with mass varying from $A=$ 20 to 31 have been studied using DJ16A, JISP16 and N3LO microscopic effective interactions in the $sd$-shell. These effective interactions are derived for $sd$-shell using no-core shell model wavefunctions and a unitary transformation method. We have also performed calculation with IMSRG effective interactions targeted for a particular nucleus. The studies include a detailed analysis of ground state binding energy, low-lying spectra, and electromagnetic properties such as reduced electric quadrupole transition strengths, quadrupole and magn…
In the random-interaction ensembles, electromagnetic moments of Cd $I^π=11/2^-$ isomers predominately present linear systematics as changing the neutron number, which has been reported in realistic nuclear system. Quadrupole-like and $δ$-like $pn$ interaction are responsible for such linear systematics of quadrupole and magnetic moments, respectively.
The lowest positive- and negative-parity bands of $^{20}$Ne and neutron-rich even-even Ne isotopes are investigated using a theoretical framework based on energy density functionals. Starting from a self-consistent relativistic Hartree-Bogoliubov calculation of axially-symmetric and reflection-asymmetric deformation energy surfaces, the collective symmetry-conserving states are built using projection techniques and the generator coordinate method. Overall a good agreement with the experimental excitation energies and transition rates is obtained. In particular, the model provides an accurate d…
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 …
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…
Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbo…
Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -- the number of nucleons -- theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and $E2$ reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuit…
