arXiv subjects

P. W. Zhao

Publications and source records attributed to P. W. Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Mass Probe of Tetrahedral Symmetry in Atomic Nuclei

Tetrahedral symmetry has long been predicted as an exotic shape degree of freedom in atomic nuclei, yet clear experimental manifestations remain elusive. We show that the triple binding energy difference $δV_{pn}^{(3)}$ can isolate a structural effect of tetrahedral symmetry in $^{80}$Zr. Using relativistic density functional theory solved on a three-dimensional lattice without symmetry restrictions, the experimental $δV_{pn}^{(3)}$ values for even-even $^{80\text{-}90}$Zr isotopes are well reproduced without adjustable parameters. While an enhancement of $δV_{pn}^{(3)}$ near $N\simeq Z$ is commonly attributed to proton-neutron correlations beyond the mean field, the pronounced nonmonotonic peak at $N=40$ emerges at the mean-field level only when the tetrahedral degree of freedom is included. Constraining the tetrahedral deformation to zero removes the peak and leads to clear deviations from experiment. The anomaly is traced to a well-localized tetrahedral minimum in $^{80}$Zr, supported by potential energy surfaces and characteristic single-particle level splittings. Calculations restricted to quadrupole and triaxial shapes fail to reproduce the localized enhancement, indicating that the effect is not a generic proton-neutron correlation but a symmetry-selective increase of proton-neutron binding associated with tetrahedral geometry. We therefore identify the $δV_{pn}^{(3)}$ anomaly in $^{80}$Zr as a structural mechanism distinct from the conventional Wigner-type enhancement and show that nuclear masses constitute a sensitive probe of tetrahedral symmetry.

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arXiv2026

Intrinsic generation of angular momenta and entanglement in fission

Nuclear time-dependent density functional theory is used to investigate spin generation and entanglement of fission fragments in spontaneous fission of $^{252}$Cf, incorporating both axial and non-axial deformations. Axially symmetric fission trajectories enforce strict constraints: counter rotation (twisting mode) along the fission axis and equiprobable bending/wriggling modes perpendicular to it. Non-axial modes broaden the distributions of fission fragment spin projection on the fission axis, and allow for axial (tilting) collective rotations, which are forbidden on axially symmetric trajectories. Mutual information analysis reveals that axial-symmetry breaking reduces spin-spin correlations along the fission axis of symmetric cases, while perpendicular correlations remain more resilient. The effect of triaxial degrees of freedom on the opening angle distribution between the spins of the fission fragments is analyzed.

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arXiv2026

Configuration-interaction time-dependent density functional theory for nuclear dynamics

A configuration-interaction time-dependent density functional theory (CI-TDDFT) for nuclear dynamics is developed. In this framework, the correlated nuclear many-body wave function is expanded in terms of time-dependent many-particle configurations built from a common set of orthonormal single-particle states. The equations of motion for both the expansion coefficients and the single-particle states are derived self-consistently using the Dirac-Frenkel time-dependent variational principle. This formulation extends conventional time-dependent density functional theory (TDDFT) by incorporating configuration mixing and beyond-mean-field correlations, while preserving energy and particle-number conservation. As an illustrative application, the method is implemented using the relativistic point-coupling functional PC-PK1 in the particle-hole channel and a monopole pairing interaction in the particle-particle channel, and is applied to the study of isoscalar giant monopole resonance in $^{58}$Ni and $^{60}$Ni. Numerical tests show that both the total energy and particle number are conserved, with relative deviations within $4\times 10^{-4}$ during the time evolution. Compared with conventional TDDFT, CI-TDDFT yields broader strength distributions for giant monopole resonances while keeping the main peak positions close to those from TDDFT. This broadening is associated with configuration mixing in the valence space and suggests a coupling of the monopole oscillation to additional collective degrees of freedom. These results demonstrate the potential of CI-TDDFT as a quantum, microscopic beyond-mean-field framework for nuclear dynamics.

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arXiv2026

De-excitation effects on entanglement in multi-nucleon transfer reactions

This study quantifies the impact of nuclear de-excitation on correlations in multi-nucleon transfer (MNT) reactions. To bridge the gap between initial collision dynamics and final experimental observables, we introduce a hybrid TDCDFT+GEMINI approach, integrating time-dependent covariant density functional theory (TDCDFT) with the statistical de-excitation model GEMINI++. Applied to the $^{40}$Ca + $^{208}$Pb reaction, our method demonstrates that the de-excitation is essential for reconciling theoretical cross sections with experimental data. Analysis of the cross-section Shannon entropy reveals that new reaction channels open abruptly at a specific energy threshold. By employing mutual information, we show that the de-excitation process significantly degrades the initial quantum entanglement between the projectile-like and the target-like fragments, revealing a key mechanism through which fundamental quantum correlations are lost.

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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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arXiv2025

The charge radii of calcium isotopes within relativistic density functional theory: nucleon's finite-size and quadrupole shape fluctuation effects

The anomaly in the charge radii of Ca isotopes has been puzzling for nuclear theory for decades. We present the first self-consistent solution to this puzzle within the density functional theory without resorting to local parameter adjustment. By taking into account both the intrinsic electromagnetic structure of nucleons and the zero-point motions of nuclear shape, which have been often neglected in previous studies, the similar charge radii of $^{40}$Ca and $^{48}$Ca as well as an inverted parabolic behavior between them are reproduced. It is found that these effects also play crucial roles in the description of the isotonic shift between the charge radii of Sn and Cd isotopes.

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arXiv2025

Next-to-leading-order prediction for the neutrinoless double-beta decay

The neutrinoless double-beta decay ($0νββ$) of two neutrons$nn \rightarrow ppee$ is the elementary subprocess of $0νββ$ decay in nuclei. Accurate knowledge of the $nn \rightarrow ppee$ amplitude is required to pin down the short-range contributions in the nuclear matrix elements of the candidate nuclei for large-scale $0νββ$ searches. In this Letter, we report the first next-to-leading-order prediction of the nn \rightarrow ppee amplitude, with Bayesian uncertainty quantification. This is made possible by the development of the relativistic chiral effective field theory, in which no unknown contact term is required up to next-to-leading order. The theory is validated by reproducing in a parameter-free way the available data on the charge independence and charge symmetry breaking contributions in the two-nucleon scattering. The present work makes an essential step towards addressing the uncertainty in the theoretical calculations of the nuclear matrix elements relevant for $0νββ$ searches.

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arXiv2025

Tilted-axis-cranking covariant density functional theory for the high-spin spectroscopy in $^{69}$Ga

The tilted-axis-cranking covariant density functional theory is applied to investigate the three newly-observed positive-parity bands SI, SII, and SIII in $^{69}$Ga. The energy spectra and angular momenta are calculated and compared with the experimental data. For the yrast band SI, pairing correlations play a crucial role for the states with spin $I\leq 23/2\hbar$. The bands SII and SIII are suggested to be signature partner bands with positive and negative signatures, respectively. The transition probabilities $B(E2)$ for these bands are predicted, and await further experimental verification. By analyzing the angular momentum alignments microscopicly, it is revealed that the $g_{9/2}$ protons and neutrons play an important role in the description of the collective structure of $^{69}$Ga.

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arXiv2025

Microscopic model for yields and total kinetic energy in nuclear fission

An extension of time-dependent density functional theory (TDDFT), the generalized time-dependent generator coordinate method (TDGCM), is applied to a study of induced nuclear fission dynamics. In the generalized TDGCM, the correlated nuclear wave function is represented as a coherent superposition of time-dependent DFT trajectories. In the first realistic application, a large basis of 25 TDDFT trajectories is employed to calculate the charge yields and total kinetic energy distribution for the fission of $^{240}$Pu. The results are compared with available data, and with those obtained using a standard TDDFT, that does not consider quantum fluctuations, and the adiabatic TDGCM+GOA (Gaussian overlap approximation). It is shown that fragment yields and kinetic energies can simultaneously be described in a consistent microscopic framework that includes fluctuations in the collective degrees of freedom and the one-body dissipation mechanism.

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arXiv2025

Relativistic configuration-interaction density functional theory: Nonaxial effects on nuclear $ββ$ decay

The relativistic configuration-interaction density functional theory is developed for even-even and odd-odd nuclei and is used to predict the nuclear matrix element of the neutrinoless $ββ$ ($0νββ$) decay in nucleus $^{76}$Ge, amongst the most promising $ββ$-decay candidates. The nonaxial deformation, i.e., triaxiality, which poses severe challenges in evaluating the nuclear matrix element of $^{76}$Ge, is incorporated within a full model space for the first time. The spectroscopic properties of the $ββ$-decay partners $^{76}$Ge and $^{76}$Se, and the nuclear matrix element governing the two-neutrino $ββ$ ($2νββ$) decay in $^{76}$Ge are well reproduced, providing solid examinations for the validity of theoretical calculations. The inclusion of the triaxial degree of freedom enhances the nuclear matrix element of the $0νββ$ decay significantly by a factor around two. The present results indicate that the goals of next-generation experiments searching for the $0νββ$ decay in $^{76}$Ge can be achieved using only a quarter amount of the experimental materials.

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arXiv2024

Machine learning orbital-free density functional theory: taming quantum shell effects in deformed nuclei

Accurate description of deformed atomic nuclei by the orbital-free density functional theory has been a longstanding textbook challenge, due to the difficulty in accounting for the intricate quantum shell effects that are present in such systems. Orbital-free density functional theory is, in principle, capable of describing all effects of nuclear systems, as guaranteed by the Hohenberg-Kohn theorem. However, from a microscopic perspective, shell and deformation effects are believed to be intrinsically connected to single-orbital structures, posing a significant challenge for orbital-free approaches. Here, we develop a machine learning approach to the orbital-free density functional theory, which is capable of achieving a high level of accuracy in describing the ground-state properties and potential energy curves for both spherical $^{16}$O and deformed $^{20}$Ne nuclei. This is the inaugural instance where a fully orbital-free energy density functional has succeeded in taming the complex shell effects in deformed nuclei. It demonstrates that the orbital-free energy density functional, which is directly based on the Hohenberg-Kohn theorem, is not only a theoretical concept but also a practical one for nuclear systems.

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arXiv2024

Neutrinoless double-beta decay in a finite volume from relativistic effective field theory

The neutrinoless double-beta decay process $nn\rightarrow ppee$ within the light Majorana-exchange scenario is studied using the relativistic pionless effective field theory (EFT) in finite-volume cubic boxes with the periodic boundary conditions. Using the low-energy two-nucleon scattering observables from lattice QCD available at $m_π=300$, 450, 510, and 806 MeV, the leading-order $nn\rightarrow ppee$ transition matrix elements are predicted and their volume dependence is investigated. The predictions for the $nn\rightarrow ppee$ transition matrix elements can be directly compared to the lattice QCD calculations of the $nn\rightarrow ppee$ process at the same pion masses. In particular for the matrix element at $m_π=806$ MeV, the predictions with relativistic pionless EFT are confronted to the recent first lattice QCD evaluation. Therefore, the present results are expected to play a crucial role in the benchmark between the nuclear EFTs and the upcoming lattice QCD calculations of the $nn\rightarrow pp ee$ process, which would provide a nontrivial test on the predictive power of nuclear EFTs on neutrinoless double-beta decay.

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arXiv2024

Entanglement in multinucleon transfer reactions

Nuclear reactions present an interesting case for studies of the time-evolution of entanglement between complex quantum systems. In this work, the time-dependent nuclear density functional theory is employed to explore entanglement in multinucleon transfer reactions. As an illustrative example, for the reaction $^{40}$Ca $+$ $^{208}$Pb at $E_{\rm lab} = 249$ MeV, in the interval of impact parameters $4.65-7.40$ fm, and the relativistic density functional PC-PK1, we compute the von Neumann entropies, entanglement between fragments, nucleon-number fluctuations, and Shannon entropy for the nucleon-number observable. A simple linear correlation is established between the entanglement and nucleon-number fluctuation of the final fragments. The entanglement between the fragments can be related to the corresponding excitation energies and angular momenta. The relationship between the von Neumann entropy and the Shannon entropy for the nucleon-number observable is analyzed, as well as the time-evolution of the entanglement (nucleon-number fluctuation). The entanglement is also calculated for a range of incident energies and it is shown how, depending on the impact parameter, the entanglement increases with the collision energy.

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arXiv2024

Time-dependent density functional theory study of induced-fission dynamics of $^{226}$Th

A microscopic finite-temperature model based on time-dependent nuclear density functional theory (TDDFT), is employed to study the induced-fission process of $^{226}$Th. The saddle-to-scission dynamics of this process is explored, starting from various points on the deformation surface of Helmholtz free energy at a temperature that corresponds to the experimental excitation energy, and following self-consistent isentropic fission trajectories as they evolve toward scission. Dissipation effects and the formation of excited fragments are investigated and, in particular, the difference in the evolution of the local temperature along asymmetric and symmetric fission trajectories. The relative entropies and entanglement between fission fragments emerging at scission are analyzed.

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arXiv2024

Emergence of High-Order Deformation in Rotating Transfermium Nuclei: A Microscopic Understanding

The rotational properties of the transfermium nuclei are investigated in the full deformation space by implementing a shell-model-like approach in the cranking covariant density functional theory on a three-dimensional lattice, where the pairing correlations, deformations, and moments of inertia are treated in a microscopic and self-consistent way. The kinematic and dynamic moments of inertia of the rotational bands observed in the transfermium nuclei $^{252}$No, $^{254}$No, $^{254}$Rf, and $^{256}$Rf are well reproduced without any adjustable parameters using a well-determined universal density functional. It is found for the first time that the emergence of the octupole deformation should be responsible for the significantly different rotational behavior observed in $^{252}$No and $^{254}$No. The present results provide a microscopic solution to the long-standing puzzle on the rotational behavior in No isotopes, and highlight the risk of investigating only the hexacontetrapole ($β_{60}$) deformation effects in rotating transfermium nuclei without considering the octupole deformation.

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arXiv2024

Relativistic model-free prediction for neutrinoless double beta decay at leading order

Starting from a manifestly Lorentz-invariant chiral Lagrangian, we present a model-free prediction for the transition amplitude of the process $nn\rightarrow pp e^-e^-$ induced by light Majorana neutrinos, which is a key process of the neutrinoless double beta decay ($0νββ$) in heavy nuclei employed in large-scale searches. Contrary to the nonrelativistic case, we show that the transition amplitude can be renormalized at leading order without any uncertain contact operators. The predicted amplitude defines a stringent benchmark for the previous estimation with model-dependent inputs, and greatly reduces the uncertainty of $0νββ$ transition operator in the calculations of nuclear matrix elements. Generalizations of the present framework could also help to address the uncertainties in $0νββ$ decay induced by other mechanisms. In addition, the present work motivates a relativistic {\it ab initio} calculation of $0νββ$ decay in light and medium-mass nuclei.

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arXiv2024

Abnormal Bifurcation of the Double Binding Energy Differences and Proton-Neutron Pairing: Nuclei Close to $N=Z$ Line from Ni to Rb

The recently observed abnormal bifurcation of the double binding energy differences $δV_{pn}$ between the odd-odd and even-even nuclei along the $N=Z$ line from Ni to Rb has challenged the nuclear theories. To solve this problem, a shell-model-like approach based on the relativistic density functional theory is established, by treating simultaneously the neutron-neutron, proton-neutron, and proton-proton pairing correlations both microscopically and self-consistently. Without any \textit{ad hoc} parameters, the calculated results well reproduce the observations, and the mechanism for this abnormal bifurcation is found to be due to the enhanced proton-neutron pairing correlations in the odd-odd $N=Z$ nuclei, compared with the even-even ones. The present results provide an excellent interpretation for the abnormal $δV_{pn}$ bifurcation, and provide a clear signal for the existence of the proton-neutron pairing correlations for nuclei close to the $N=Z$ line.

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arXiv2024

Reconciling light nuclei and nuclear matter: relativistic $ab\ initio$ calculations

It has been a long-standing challenge to accurately predict the properties of light nuclei and nuclear matter simultaneously in nuclear $ab\ initio$ calculations. In this Letter, we develop the relativistic quantum Monte Carlo methods for the nuclear $ab\ initio$ problem, and calculate the ground-state energies of $A\leq4$ nuclei using the two-nucleon Bonn force with an unprecedented high accuracy. For $A=3,4$ nuclei, the present relativistic results significantly outperforms the nonrelativistic results with only two-nucleon forces. Combining the present results for light nuclei and the previous results for nuclear matter with the same Bonn force, a correlation between the properties of light $A\leq4$ nuclei and the nuclear saturation is revealed, and both systems are well described simultaneously, even without introducing three-nucleon forces. This provides a quantitative understanding of the connection between the light nuclei and nuclear matter saturation properties, which has been an outstanding problem in nuclear $ab\ initio$ calculations for decades.

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