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H. Z. Liang

Publications and source records attributed to H. Z. Liang.

At least 19 recordsLinked to original sources
arXiv2026

Construction of Nuclear Covariant Energy Density Functional from A Physics-Guaranteed Neural Network Approach

Density functional theory is a practical approach for solving quantum many-body problems with available computational resources. The complexity of the nuclear force makes constructing an accurate nuclear energy density functional much more challenging. The feasibility of constructing a nuclear covariant energy density functional with deep neural networks is demonstrated. This physics-guaranteed neural network approach achieves high accuracy in predicting nuclear energy density and exhibits significantly better extrapolation abilities than traditional machine learning methods for binding energies. When combined with the existing covariant density functional, the neural network approach improves the binding energy accuracy from $644$ keV to $86$ keV in the known region and also effectively captures the microscopic shell effect. Furthermore, its extrapolation performance is also significantly enhanced, achieving an accuracy of approximately $5$ MeV even when extrapolating up to $30$ steps. This work paves the way for the construction of accurate nuclear energy density functionals through machine learning.

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arXiv2026

From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure

Magic numbers lie at the heart of nuclear structure, reflecting enhanced stability in nuclei with closed shells. While the emergence of magic numbers beyond 20 is commonly attributed to strong spin-orbit coupling, the microscopic origin of the spin-orbit potential remains elusive, owing to its dependence on the resolution scale and renormalization scheme of nuclear forces. Here, we investigate the evolution of shell structure with varying momentum resolution in nuclear interactions derived from chiral effective field theory, using the similarity renormalization group to link different scales. We uncover a novel transition from spin symmetry to pseudospin symmetry as the resolution scale decreases, during which magic numbers emerge naturally. A similar pattern is found in calculations using relativistic one-boson-exchange potentials, underscoring the robustness of the phenomenon. This establishes a direct connection between realistic nuclear forces with a high resolution scale and effective nuclear forces at coarse-grained scales, offering a first-principles explanation for the origin of magic numbers and pseudospin symmetry in nuclear shell structure, and new insights into the structure of exotic nuclei far from stability.

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arXiv2025

Relativistic orbital-free kinetic energy density functional for one-particle nuclear systems

This letter aims to derive the exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one-dimensional case. The kinetic energy is expressed as a functional of both vector and scalar densities. The functional derivatives of the kinetic energy density functional are also derived. Both the kinetic energy density functional and its functional derivatives are validated to be correct. This serves as a foundation for further exploration of more general relativistic orbital-free kinetic energy density functionals.

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arXiv2022

Nuclear mass predictions with machine learning reaching the accuracy required by $r$-process studies

Nuclear masses are predicted with the Bayesian neural networks by learning the mass surface of even-even nuclei and the correlation energies to their neighbouring nuclei. By keeping the known physics in various sophisticated mass models and performing the delicate design of neural networks, the proposed Bayesian machine learning (BML) mass model achieves an accuracy of $84$~keV, which crosses the accuracy threshold of the $100$~keV in the experimentally known region. It is also demonstrated the corresponding uncertainties of mass predictions are properly evaluated, while the uncertainties increase by about $50$~keV each step along the isotopic chains towards the unknown region. The shell structures in the known region are well described and several important features in the unknown region are predicted, such as the new magic numbers around $N = 40$, the robustness of $N = 82$ shell, the quenching of $N = 126$ shell, and the smooth separation energies around $N = 104$.

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arXiv2018

Predictions of nuclear $β$-decay half-lives with machine learning and their impacts on $r$ process

Nuclear $β$ decay is a key process to understand the origin of heavy elements in the universe, while the accuracy is far from satisfactory for the predictions of $β$-decay half-lives by nuclear models up to date. In this letter, we pave a novel way to accurately predict $β$-decay half-lives with the machine-learning based on the Bayesian neural network, in which the known physics has been explicitly embedded, including the ones described by the Fermi theory of $β$ decay, and the dependence of half-lives on pairing correlations and decay energies. The other potential physics, which is not clear or even missing in nuclear models nowadays, will be learned by the Bayesian neural network. The results well reproduce the experimental data with a very high accuracy and further provide reasonable uncertainty evaluations in half-life predictions. These accurate predictions for half-lives with uncertainties are essential for the $r$-process simulations.

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arXiv2018

Gamow-Teller transitions from high-spin isomers in $N=Z$ nuclei

Gamow-Teller (GT) transitions from high-spin isomers are studied using the sum-rule approach and the shell model. The GT transition strengths from the high-spin isomeric states show a stronger collectivity than those from the ground states in two $N=Z$ nuclei, $^{52}$Fe and $^{94}$Ag. It is argued that the spin-up and spin-down Fermi spheres involved in the GT transitions from the high-spin isomeric states play important roles. These Fermi spheres are analogous to the isospin-up and isospin-down Fermi spheres for the GT transitions from the ground states in $N>Z$ nuclei and create a strong collectivity.

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arXiv2018

Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for single-nucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic mean-field model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach.

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arXiv2017

The limits of the nuclear landscape explored by the relativistic continuum Hatree-Bogoliubov theory

The ground-state properties of nuclei with 8 $\le$ Z $\le$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. It is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the alpha-decay energies and proton emitters based on the RCHB calculations are investigated.

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arXiv2016

Improved radial basis function approach with the odd-even corrections

The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities of ($Z$, $N$), i.e., the (even $Z$, even $N$), (even $Z$, odd $N$), (odd $Z$, even $N$), and (odd $Z$, odd $N$). By separately training the RBF for these four different groups, it is found that the systematic odd-even deviations can be cured in a large extend and the predictive power of nuclear mass models can thus be further improved. Moreover, this new approach can better reproduce the single-nucleon separation energies. Based on the latest version of Weizsäcker-Skyrme model WS4, the root-mean-square deviation of the improved masses with respect to known data falls to $135$ keV, approaching the chaos-related unpredictability limit ($\sim 100$ keV).

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arXiv2016

Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations and $β$-decay half-lives

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $β$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $β$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.

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arXiv2014

Three-dimensional mesh calculations for covariant density functional theory

In contrast to the non-relativistic approaches, three-dimensional (3D) mesh calculations for the {\it relativistic} density functional theory have not been realized because of the challenges of variational collapse and fermion doubling. We overcome these difficulties by developing a novel method based on the ideas of Wilson fermion as well as the variational principle for the inverse Hamiltonian. We demonstrate the applicability of this method by applying it to $^{16}$O, $^{24}$Mg, and $^{28}$Si nuclei, providing detailed explanation on the formalism and verification of numerical implementation.

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arXiv2013

Nuclear charge-exchange excitations in localized covariant density functional theory

The recent progress in the studies of nuclear charge-exchange excitations with localized covariant density functional theory is briefly presented, by taking the fine structure of spin-dipole excitations in 16O as an example. It is shown that the constraints introduced by the Fock terms of the relativistic Hartree-Fock scheme into the particle-hole residual interactions are straightforward and robust.

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arXiv2013

$β$-decay half-lives of neutron-rich nuclei and matter flow in the $r$-process

The $β$-decay half-lives of neutron-rich nuclei with $20 \leqslant Z \leqslant 50$ are systematically investigated using the newly developed fully self-consistent proton-neutron quasiparticle random phase approximation (QRPA), based on the spherical relativistic Hartree-Fock-Bogoliubov (RHFB) framework. Available data are reproduced by including an isospin-dependent proton-neutron pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the calculated $β$-decay half-lives of neutron-rich nuclei a remarkable speeding up of $r$-matter flow is predicted. This leads to enhanced $r$-process abundances of elements with $A \gtrsim 140$, an important result for the understanding of the origin of heavy elements in the universe.

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arXiv2013

Nuclear $β^+$/EC decays in covariant density functional theory and the impact of isoscalar proton-neutron pairing

Self-consistent proton-neutron quasiparticle random phase approximation based on the spherical nonlinear point-coupling relativistic Hartree-Bogoliubov theory is established and used to investigate the $β^+$/EC-decay half-lives of neutron-deficient Ar, Ca, Ti, Fe, Ni, Zn, Cd, and Sn isotopes. The isoscalar proton-neutron pairing is found to play an important role in reducing the decay half-lives, which is consistent with the same mechanism in the $β$ decays of neutron-rich nuclei. The experimental $β^+$/EC-decay half-lives can be well reproduced by a universal isoscalar proton-neutron pairing strength.

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arXiv2012

Covariant density functional theory for antimagnetic rotation

Following the previous letter on the first microscopic description of the antimagnetic rotation (AMR) in 105Cd, a systematic investigation and detailed analysis for the AMR band in the frame-work of tilted axis cranking (TAC) model based on covariant density functional theory are carried out. After performing the microscopic and self-consistentTAC calculations with an given density functional, the configuration for the observed AMR band in 105Cd is obtained from the single-particle Routhians. With the configuration thus obtained, the tilt angle for a given rotational frequency is determined self-consistently by minimizing the total Routhian with respect to the tilt angle. In such a way, the energy spectrum, total angular momenta, kinetic and dynamic moments of inertia, and the B(E2) values for the AMR band in 105Cd are calculated. Good agreement with the data is found. By investigating microscopically the contributions from neutrons and protons to the total angular momentum, the "two-shears-like" mechanism in the AMR band is clearly illus-trated. Finally, the currents leading to time-odd mean fields in the Dirac equation are presented and discussed in detail. It is found that they are essentially determined by the valence particles and/or holes. Their spatial distribution and size depend onthe specific single-particle orbitals and the rotational frequency.

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arXiv2011

Antimagnetic Rotation Band in Nuclei: A Microscopic Description

Covariant density functional theory and the tilted axis cranking method are used to investigate antimagnetic rotation (AMR) in nuclei for the first time in a fully self-consistent and microscopic way. The experimental spectrum as well as the B(E2) values of the recently observed AMR band in 105Cd are reproduced very well. This gives a further strong hint that AMR is realized in specific bands in nuclei.

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arXiv2011

Novel structure for magnetic rotation bands in 60Ni

The self-consistent tilted axis cranking relativistic mean-field theory based on a point-coupling interaction has been established and applied to investigate systematically the newly observed shears bands in 60Ni. The tilted angles, deformation parameters, energy spectra, and reduced M1 and $E2$ transition probabilities have been studied in a fully microscopic and self-consistent way for various configurations and rotational frequencies. It is found the competition between the configurations and the transitions from the magnetic to the electric rotations have to be considered in order to reproduce the energy spectra as well as the band crossing phenomena. The tendency of the experimental electromagnetic transition ratios B(M1)/B(E2) is in a good agreement with the data, in particular, the B(M1) values decrease with increasing spin as expected for the shears mechanism, whose characteristics are discussed in detail by investigating the various contributions to the total angular momentum as well.

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