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J. Xiang

Publications and source records attributed to J. Xiang.

At least 19 recordsLinked to original sources
arXiv2026

Low-lying states of neutron-rich $N=50$ isotones in multi-reference covariant density functional theory

Predictions for the systematics of low-lying states in neutron-rich $N=50$ isotones from \nuclide[80]{Zn} to \nuclide[70]{Ca}, where experimental information remains scarce, exhibit substantial model dependence. We investigate these nuclei using multi-reference covariant density functional theory based on a relativistic energy density functional, in which nuclear wave functions are constructed as superpositions of symmetry-restored mean-field states with different quadrupole deformations. The low-lying states of \nuclide[78]{Ni} are reasonably reproduced, and a prolate rotational band built on the second $0^+$ state is predicted in addition to a near-spherical ground state. As the proton number decreases toward $Z=20$, the low-energy structure exhibits a nonmonotonic evolution from spherical to strongly deformed and subsequently back to spherical shapes, consistent with valence-space shell-model predictions. In particular, the emergence of deformed ground states in \nuclide[76]{Fe} and \nuclide[74]{Cr} is accompanied by enhanced quadrupole collectivity and stronger shape mixing. The results provide a coherent microscopic description of the structural evolution from the doubly magic \nuclide[78]{Ni} to the neutron-rich $N=50$ isotones.

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arXiv2026

Systematic study of superheavy nuclei within a microscopic collective Hamiltonian: Impact of quantum shape fluctuations

The even-even superheavy nuclei with $104 \leqslant Z \leqslant 126$ and $N\leqslant 258$ have been investigated using a microscopic five-dimensional collective Hamiltonian (5DCH) based on constrained triaxial relativistic Hartree-Bogoliubov calculations with the PC-PK1 density functional. The 5DCH approach effectively captures the characteristic of isospin dependence of nuclear binding energies, two-nucleon separation energies, and $\alpha$-decay energies across isotopic chains and demonstrates consistent accuracy as $Z$ increases, underscoring the model's predictive power. The collective potentials, average quadrupole deformations, and characteristic collective observables: $E(2^+_1)$, $R_{42}$, and $B(E2; 2^+_1\to 0^+_1)$ reveal a shape transition from well-prolate deformation around $N=150$ and $N=210$ to medium-deformed $\gamma$-soft shape around $N=176$ and $N=246$, and finally to a spherical shape near $N=184$ and $N=258$ for the isotopic chains with $104\leqslant Z\leqslant 118$. Oblate deformations are favored for $Z\geqslant 120$ isotopes around $N=178$. Remarkably, for a substantial range of transitional superheavy nuclei with $N\gtrsim184$ and $N\gtrsim240$, no $0^+$ states bounded by the fission saddles are predicted within their very shallow potential wells due to quantum shape fluctuations (QSFs). Additionally, sharp variations predicted for two-neutron separation energies $S_{2n}$ and $\alpha$-decay energies $Q_\alpha$ at $N=184$ and $258$ in mean-field calculations are significantly reduced and shifted to $N=182$ and $256$ in the 5DCH calculations, which is caused by the rapid evolution of the dynamical correlation energies related to QSFs around the nuclear spherical shells.

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arXiv2025

Microscopic triaxial quadrupole-octupole collective Hamiltonian for low-energy nuclear excitations

We present a microscopic triaxial quadrupole-octupole collective Hamiltonian (TQOCH) that unifies collective rotations, quadrupole-octupole vibrations, and their couplings to model low-lying nuclear states of both parities. The TQOCH's dynamics are governed by collective parameters derived from multidimensionally constrained covariant density functional theory. The model's validity is demonstrated through calculations of $^{152}$Sm, including its deformation energy surfaces, excitation spectra, and transition probabilities. As a predictive tool, the TQOCH probes complex nuclear phenomena like shape coexistence and phase transitions, directly connecting their microscopic origins to spectroscopic observables.

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arXiv2025

Multireference covariant density functional theory for shape coexistence and isomerism in $^{43}$S

We extend the multireference covariant density functional theory (MR-CDFT) to describe the low-lying states of the odd-mass nucleus $^{43}$S near the neutron magic number $N=28$ with shape coexistence. The wave functions of the low-lying states are constructed as superpositions of configurations with different intrinsic shapes and $K$ quantum numbers, projected onto good particle numbers and angular momenta. The MR-CDFT successfully reproduces the main features of the low-energy structure in $^{43}$S. Our results indicate that the ground state, $3/2^-_1$, is predominantly composed of the intruder prolate one-quasiparticle (1qp) configuration $\nu1/2^-[321]$. In contrast, the $7/2^-_1$ state is identified as a high-$K$ isomer, primarily built on the prolate 1qp configuration $\nu7/2^-[303]$. Additionally, the $3/2^-_2$ state is found to be an admixture dominated by an oblate configuration with $K^\pi = 1/2^-$, along with a small contribution from a prolate configuration with $K^\pi = 3/2^-$. These results demonstrate the capability of MR-CDFT to capture the intricate interplay among shape coexistence, $K$-mixing, and isomerism in the low-energy structure of odd-mass nuclei around $N = 28$.

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arXiv2023

Coupling shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals (II): low-energy excitation spectra of triaxial nuclei

The triaxial quadrupole collective Hamiltonian, based on relativistic energy density functionals, is extended to include a pairing collective coordinate. In addition to triaxial shape vibrations and rotations, the model describes pairing vibrations and the coupling between triaxial shape and pairing degrees of freedom. The parameters of the collective Hamiltonian are determined by a covariant energy density functional, with constraints on the intrinsic triaxial shape and pairing deformations. The effect of coupling between triaxial shape and pairing degrees of freedom is analyzed in a study of low-lying spectra and transition rates of $^{128}$Xe. When compared to results obtained with the standard triaxial quadrupole collective Hamiltonian, the inclusion of dynamical pairing compresses the low-lying spectra and improves interband transitions, in better agreement with data. The effect of zero-point energy (ZPE) correction on low-lying excited spectra is also discussed.

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arXiv2021

Interplay between pairing and triaxial shape degrees of freedom in Os and Pt nuclei

The effect of coupling between pairing and quadrupole triaxial shape vibrations on the low-energy collective states of $\gamma$-soft nuclei is investigated using a model based on the framework of nuclear energy density functionals (EDFs). Employing a constrained self-consistent mean-field (SCMF) method that uses universal EDFs and pairing interactions, potential energy surfaces of characteristic $\gamma$-soft Os and Pt nuclei with $A\approx190$ are calculated as functions of the pairing and triaxial quadrupole deformations. Collective spectroscopic properties are computed using a number-nonconserving interacting boson model (IBM) Hamiltonian, with parameters determined by mapping the SCMF energy surface onto the expectation value of the Hamiltonian in the boson condensate state. It is shown that, by simultaneously considering both the shape and pairing collective degrees of freedom, the EDF-based IBM successfully reproduces data on collective structures based on low-energy $0^{+}$ states, as well as $\gamma$-vibrational bands.

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arXiv2021

Coupling of pairing and triaxial shape vibrations in collective states of $γ$-soft nuclei

In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in nuclear structure theory. Here we address the problem in terms of self-consistent mean-field calculations of collective deformation energy surfaces, and the framework of the interacting boson approximation. In addition to quadrupole shape vibrations and rotations, the explicit coupling to pairing vibrations is taken into account by a boson-number non-conserving Hamiltonian, specified by a choice of a universal density functional and pairing interaction. An illustrative calculation for $^{128}$Xe and $^{130}$Xe shows the importance of dynamical pairing degrees of freedom, especially for structures built on low-energy $0^+$ excited states, in $γ$-soft and triaxial nuclei.

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arXiv2020

Pairing vibrations in the interacting boson model based on density functional theory

We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number non-conserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially-symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for $^{122}$Xe, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^+$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.

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arXiv2020

Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals

The quadrupole collective Hamiltonian, based on relativistic energy density functionals, is extended to include a pairing collective coordinate. In addition to quadrupole shape vibrations and rotations, the model describes pairing vibrations and the coupling between shape and pairing degrees of freedom. The parameters of the collective Hamiltonian are determined by constrained self-consistent relativistic mean-field plus Bardeen-Cooper-Schrieffer (RMF+BCS) calculations in the space of intrinsic shape and pairing deformations. The effect of coupling between shape and pairing degrees of freedom is analyzed in a study of low-energy spectra and transition rates of four axially symmetric $N=92$ rare-earth isotones. When compared to results obtained with the standard quadrupole collective Hamiltonian, the inclusion of dynamical pairing increases the moment of inertia, lowers the energies of excited $0^+$ states and reduces the E0-transition strengths, in better agreement with data.

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arXiv2018

Shape evolution and coexistence in neutron-deficient Nd and Sm nuclei

The evolution of shapes and low-energy shape coexistence is analyzed in neutron-deficient Nd and Sm nuclei, using a five-dimensional quadrupole collective Hamiltonian (5DCH). Deformation energy surfaces, calculated with the relativistic energy density functional PC-PK1 and a separable finite-range pairing interaction, exhibit a transition from spherical shapes near $N=80$, to $γ-$soft shapes, and to prolate deformed minima in lighter isotopes. The corresponding 5DCH model calculation, based on the self-consistent mean-field potentials, reproduces the empirical isotopic trend of characteristic collective observables, and predicts significantly different deformations for the first two $0^+$ states in the $N=74$ isotones $^{134}$Nd and $^{136}$Sm. In addition to bands based on the triaxial $γ-$soft ground state, in excellent agreement with data, the occurrence of a low-energy rotational band is predicted, built on the prolate deformed ($β\sim0.4$) excited state $0^+_2$.

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arXiv2018

Quantum and Coulomb repulsion effects on the bubble structures in $^{204, 206}$Hg

The decreasing proton and charge densities from around 5.0 fm towards the center of $^{204, 206}$Hg are investigated by a covariant density functional theory at the beyond mean-field level.The charge-density difference between $^{208}$Pb and $^{204}$Hg is improved significantly and a central depression is still visible in the ground-state density of $^{204, 206}$Hg when the dynamic correlations associated with symmetry restoration and shape mixing are taken into account. For the $0_2^+$ and $2_1^+$ excited states of $^{204, 206}$Hg, their densities remain decreasing from 5.0 fm to around 2.0 fm, but become flat in the interior region. The results show that the bubble structure in $^{204, 206}$Hg within 2.0 fm is mainly attributed to the quantum effect, while that beyond 2.0 fm is formed by the Coulomb repulsion.

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arXiv2014

Covariant density functional analysis of shape evolution in $N =40$ isotones

The structure of low-lying excitation states of even-even $N=40$ isotones is studied using a five-dimensional collective Hamiltonian with the collective parameters determined from the relativistic mean-field plus BCS method with the PC-PK1 functional in the particle-hole channel and a separable paring force in the particle-particle channel. The theoretical calculations can reproduce not only the systematics of the low-lying states along the isotonic chain but also the detailed structure of the spectroscopy in a single nucleus. We find a picture of spherical-oblate-prolate shape transition along the isotonic chain of $N=40$ by analyzing the potential energy surfaces. The coexistence of low-lying excited $0^+$ states has also been shown to be a common feature in neutron-deficient $N=40$ isotones.

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arXiv2013

Effect of pairing correlations on nuclear low-energy structure: BCS and general Bogoliubov transformation

Low-lying nuclear states of Sm isotopes are studied in the framework of a collective Hamiltonian based on covariant energy density functional theory. Pairing correlation are treated by both BCS and Bogoliubov methods. It is found that the pairing correlations deduced from relativistic Hartree-Bogoliubov (RHB) calculations are generally stronger than those by relativistic mean-field plus BCS (RMF+BCS) with same pairing force. By simply renormalizing the pairing strength, the diagonal part of the pairing field is changed in such a way that the essential effects of the off-diagonal parts of the pairing field neglected in the RMF+BCS calculations can be recovered, and consequently the low-energy structure is in a good agreement with the predictions of the RHB model.

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arXiv2013

Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes

Neutron-deficient krypton isotopes are of particular interest due to the coexistence of oblate and prolate shapes in low-lying states and the transition of ground-state from one dominate shape to another as a function of neutron number. A detailed interpretation of these phenomena in neutron-deficient Kr isotopes requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. The aim of this work is to provide a systematic calculation of low-lying state in the even-even 68-86Kr isotopes and to understand the shape coexistence phenomenon and the onset of large collectivity around N=40 from beyond relativistic mean-field studies. The starting point of our method is a set of relativistic mean-field+BCS wave functions generated with a constraint on triaxial deformations (beta, gamma). The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions. To examine the role of triaxiality, a configuration mixing of both particle number (PN) and angular momentum (AM) projected axially deformed states is also carried out within the exact generator coordinate method (GCM) based on the same energy density functional. The energy surfaces, the excitation energies of 0^+_2, 2^+_1, 2^+_2 states, as well as the E0 and E2 transition strengths are compared with the results of similar 5DCH calculations but with parameters determined by the non-relativistic mean-field wave functions, as well as with the available data...

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arXiv2012

Enhanced collectivity in neutron-deficient Sn isotopes in energy functional based collective Hamiltonian

The low-lying collective states in Sn isotopes are studied by a five-dimensional collective Hamiltonian with parameters determined from the triaxial relativistic mean-field calculations using the PC-PK1 energy density functional. The systematics for both the excitation energies of $2^+_1$ states and $B(E2;0^+_1\to 2^+_1)$ values are reproduced rather well, in particular, the enhanced E2 transitions in the neutron-deficient Sn isotopes with N<66. We show that the gradual degeneracy of neutron levels 1g7/2 and 2d5/2 around the Fermi surface leads to the increase of level density and consequently the enhanced paring correlations from N=66 to 58. It provokes a large quadrupole shape fluctuation around the spherical shape, and leads to an enhanced collectivity in the isotopes around N=58.

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arXiv2012

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

The rapid structural change in low-lying collective excitation states of neutron-rich Sr and Zr isotopes is tudied by solving a five-dimensional collective Hamiltonian with parameters determined by both relativistic mean-field and non-relativistic Skyrme-Hartree-Fock calculations using the PC-PK1 and SLy4 forces respectively. Pair correlations are treated in BCS method with either a separable pairing force or a density-dependent zero-range force. The isotope shifts, excitation energies, electric monopole and quadrupole transition strengths are calculated and compared with corresponding experimental data. The calculated results with both the PC-PK1 and SLy4 forces exhibit a picture of spherical-oblate-prolate shape transition in neutron-rich Sr and Zr isotopes. Compared with the experimental data, the PC-PK1 (or SLy4) force predicts a more moderate (or dramatic) change in most of the collective properties around N=60. The underlying microscopic mechanism responsible for the rapid transition is discussed.

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arXiv2011

Covariant description of shape evolution and shape coexistence in neutron-rich nuclei at N\approx60

The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $N\approx60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both $^{98}$Sr and $^{100}$Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for $^{98}$Sr and $^{100}$Zr. The resultant excitation energy of $0^+_2$ state and E0 transition strength $ρ^2(E0;0^+_2\rightarrow0^+_1)$ are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the $γ$ deformation in $^{100}$Zr gives rise to the larger $ρ^2(E0;0^+_2\rightarrow0^+_1)$ than that in $^{98}$Sr.

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arXiv2010

Low-lying states in $^{30}$Mg: a beyond relativistic mean-field investigation

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of $^{30}$Mg. The effects of triaxiality on the low-energy spectra and E0 and E2 transitions are examined.

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