arXiv subjects

Wen Hui Long

Publications and source records attributed to Wen Hui Long.

At least 19 recordsLinked to original sources

arXiv2026

B(E2) Serves as a Robust Signature of N = 32,34 Shell Evolution

Electric quadrupole transition probabilities $B(E2)$ serve as key probe of nuclear shell evolution, yet anomalous $B(E2)$ values in exotic nuclei complicate the identification of new magic numbers. In this letter, employing the configuration-interaction relativistic Hartree-Fock model, we demonstrate that effective charges are sensitive to orbital radii, and this orbital dependence is significantly amplified by the halo structure of valence nucleons. This mechanism is critical for reliably describing $E2$ transitions and understanding the unusual behavior of $B(E2)$ in exotic nuclei. Our calculations predict reduced $B(E2; 2^+_1 \rightarrow 0^+_1)$ values in $^{52,54}\text{Ca}$, signaling the emergence of subshell closures at $N=32$ and 34. Furthermore, the suppressed $B(E2; 7/2^{-}_{1} \rightarrow 11/2^{-}_{1})$ transition in $^{53}\text{Sc}$ underscores the robustness of the $N=32$ new magic number, whereas the enhanced transition strength in $^{55}\text{Sc}$ indicates the rapid erosion of the $N=34$ shell gap with the occupancy of the proton orbital $\pi1f_{7/2}$.

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arXiv2026

Single-Particle Resonant States in Relativistic Hartree-Fock Theory: A Green's Function Approach

Relativistic Hartree-Fock theory is combined with the Green's function method in coordinate space to study both single-particle bound and resonant states within a unified framework. Within this approach, single-particle resonance energies and widths are unambiguously extracted from the density of states, and the influence of the Coulomb exchange effects on proton resonances in $N=82$ isotones are systematically examined. It is found that the exact treatment of Coulomb exchange terms reduces proton resonance energies of approximate $0.09\sim0.21$ MeV, a significantly smaller effect than that obtained from the phenomenological treatment. Moreover, except for rather narrow resonances, the proton resonance widths are visibly reduced by the Coulomb exchange terms, also being much less pronounced than the phenomenological approach. Notably, clear shell effects are observed in the isotonic evolutions of the resonance energy reductions for specific resonances. All these highlight the necessity of a microscopical and exact treatment of the Coulomb exchange terms.

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arXiv2025

Configuration interaction relativistic Hartree-Fock model

The configuration interaction relativistic Hartree-Fock (CI-RHF) model is developed in this work. Compared to the conventional configuration interaction shell model (CISM), the CI-RHF model can be applied to study the structural properties of a wide range of nuclei without readjusting any parameters, as the effective Hamiltonian for different model space can be deduced consistently from a universal density-dependent Lagrangian based on the Hartree-Fock single-particle basis. The convergence of intermediate-state excitations has been examined in evaluating the effective interactions, and the core-polarization effects are illustrated, by using $^{18}$O as an example. Employing the CI-RHF model, both the bulk properties and low-lying spectra of even-even nuclei $^{18\sim 28}$Ne have been well reproduced with the model space restricted to the $sd$ shell. Studies of the isotopic evolution concerning charge radii and low-lying spectra highlight the shell closure at $N=14$ for neon isotopes. Furthermore, the cross-shell calculations extending from the $sd$ to $pf$ shell successfully reproduced the low-lying spectra of $^{30}$Ne and $^{32}$Ne. Notably, remarkably low excitation energies $E(2^{+}_{1})$ of $^{30}$Ne suggest the disappearance of the conventional magicity $N=20$.

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arXiv2024

Exploration on $1n$ halo nucleus $^{19}$C from D-RHFB structure to reaction observables

We utilize the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model to describe the structure of neutron-rich carbon isotopes, taking into account the continuum, pairing correlations, tensor force and their interplay. In this scheme, one- and two-neutron separation energies of neutron-rich carbon isotopes agree well with measured data, as well as the spin and parity $J^π=1/2^+$ for the ground state of $^{19}$C, which is a long-standing problem for theoretical structure models. With the structure input extracted from the microscopic D-RHFB model, the reaction observables are well described the Glauber model. In particular, this unified approach accurately reproduces the inclusive longitudinal momentum distributions of the breakup reaction $^{19}$C + $^{12}$C at 240 MeV/nucleon, which rule out the possibility of the ground state of $^{19}$C being $J^π=3/2^+$. Moreover, the continuum plays a crucial role in the formation of the halo, which is further confirmed by the reaction cross sections and longitudinal momentum distributions. However, the tensor force components carried by the $π$-coupling are not as significant as anticipated. Consequently, the D-RHFB + Glauber approach turns out to be a promising tool to search for halo candidates from the structure to the reaction.

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arXiv2024

Time-dependent Relativistic Hartree-Fock model with spherical symmetry

This work establishes the time-dependent relativistic Hartree-Fock (TD-RHF) model with spherical symmetry for the first time. The time-dependent integro-differential Dirac equations are solved by expanding Dirac spinors on the spherical Dirac Woods-Saxon (DWS) basis. The numerical verification demonstrates the high conservation qualities for both the total binding energy and the particle number, as well as the time-reversal invariance of the system, which ensures the precision and reliability of the newly developed TD-RHF model. Subsequently, the isoscalar giant monopole resonance (ISGMR) mode of $^{208}$Pb is investigated using the RHF Lagrangian PKO1. The constrained energy of the ISGMR calculated by PKO1 is found to be in close agreement with the experimental data, and the strength function is similar to the results given by the relativistic Hartree-Fock plus random phase approximation. Based on the advantage of the TD-RHF model in avoiding complicated calculations of the residual interactions, the ISGMR mode of $^{208}$Pb is calculated by twelve relativistic effective Lagrangians. The results indicate that the value of the incompressibility of nuclear matter $K_\infty$ constrained by relativistic effective Lagrangians is in the range of $237\sim246$ MeV, which is lower than the previous investigations based on the relativistic models.

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arXiv2024

Relativistic Hartree-Fock model for axial-symmetric nuclei with quadruple and octupole deformations

\textbf{Background:} The initial observation of a negative-parity state in proximity to the ground state in the 1950s marked the advent of extensive research into octupole deformed nuclei. Since then, the physics of octupole deformed nuclei has consistently held a special interest within the field of nuclear physics. In the present era, with the advent of sophisticated radioactive ion beam (RIB) facilities and advanced detectors, coupled with the remarkable capabilities of high-performance computing, extensive and intensive explorations are being conducted from both experimental and theoretical perspectives to elucidate the physics of octupole deformed nuclei. \textbf{Results:} This work establishes the OD-RHF model, which provides a reliable tool for studying octupole nuclei over a fairly wide range. The reliability of the newly developed OD-RHF model is illustrated by taking the octupole nucleus $^{144}$Ba as an example. Furthermore, the octupole deformation effects in $^{144}$Ba is verified by using the RHF Lagrangians PKO$i$ ($i=1,2,3$) and the RMF one DD-ME2. The intrusion of the neutron $1i_{13/2}$ and proton $1h_{11/2}$ components is demonstrated to play an essential role in determining the notable octupole deformation of $^{144}$Ba using PKO$i$ ($i=1,2,3$) and DD-ME2. It is indicated that the Fock terms play an important role in stabilizing the octupole deformation. More specifically, due to the repulsive tensor coupling between the intrude components and the core of $^{144}$Ba, the tensor force component carried by the $π$-PV coupling, that contributes only via the Fock terms, plays an opposing role in the formation of the octupole deformation of $^{144}$Ba.

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arXiv2023

Deformed ground state of $^{32}$Mg and breaking of pseudo-spin symmetry

Deformed ground state of $^{32}$Mg is investigated using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model with the effective Lagrangian PKA1, which provides coincident description with the experimental measurements. It is illustrated that obvious breaking of the pseudo-spin symmetry (PSS) given by PKA1, being consistent with the experimental observation in nearby isotone $^{40}$Ca, is crucial for describing correctly the deformed ground state by producing unique shape evolution of neutron orbit $1/2_4^+$ in $^{32}$Mg. The PSS breaking is essentially determined by characteristic in-medium balance between nuclear attractions and repulsions that is manifested as unparalleled density dependent behaviors for coupling strengths $g_σ$ and $g_ω$ in dominant $σ$-scalar and $ω$-vector channels.

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arXiv2023

Unified mechanism behind the even-parity ground state and neutron halo of $^{11}$Be

Using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model, we explore the mechanism behind the parity inversion and halo occurrence in $^{11}$Be, which are well reproduced by the RHF Lagrangian PKA1. It is illustrated that evidently enhanced deformation effects by the $π$-pseudo-vector and $ρ$-tensor couplings in PKA1 are crucial for correctly describing both even-parity ground state (GS) and neutron halo of $^{11}$Be. Coupling with the deformation, the intrude $1d_{5/2}$ component largely enhances the couplings between the even-parity orbit $1/2_2^+$ and the nuclear core to promise the even-parity GS, whereas the $2s_{1/2}$ component therein dominates the halo formation in $^{11}$Be. Moreover, the deformed halo in $^{11}$Be is found to be stabilized by the attractive inherent correlations between the $1d_{5/2}$ and $2s_{1/2}$ components of the halo orbit $1/2_2^+$, instead of pairing correlations, which paves a new way to understand the halo pictures in deformed unstable nuclei.

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arXiv2022

Quenched Λ spin-orbit splitting by relativistic Fock diagram in single-Λ hypernuclei

We extend the relativistic Hartree-Fock (RHF) theory to study the structure of single-$Λ$ hypernuclei. The density dependence is taken in both meson-nucleon and meson-hyperon coupling strengths, and the induced $Λ$-nucleon ($ΛN$) effective interactions are determined by fitting $Λ$ separation energies to the experimental data for several single-$Λ$ hypernuclei. The equilibrium of nuclear dynamics described by the RHF model in normal atomic nuclei, namely, the balance between nuclear attractive and repulsive interactions, is then found to be drastically changed in single-$Λ$ hypernuclei, revealing a different role of Fock terms via $Λ$ hyperon from the nucleon exchange. Since only one hyperon exists in a single-$Λ$ hypernucleus, the overwhelmed $ΛN$ and $ΛΛ$ attractions via the Hartree than the $ΛΛ$ repulsion from the Fock terms require an alternation of meson-hyperon coupling strengths in RHF to rebalance the effective nuclear force with the strangeness degree of freedom, leading to an improved description of $Λ$ Dirac mass and correspondingly a systematically reduced $σ$-$Λ$ coupling strength $g_{σΛ}$ in current models as compared to those relativistic mean-field (RMF) approaches without Fock terms. As a result, the effective $Λ$ spin-orbit coupling potential in the ground state of hypernuclei is suppressed, and these RHF models predict correspondingly a quenching effect in $Λ$ spin-orbit splitting in comparison with the RMF cases. Furthermore, the $Λ$ spin-orbit splitting could decrease efficiently by evolving the hyperon-relevant couplings $g_{σΛ}$ and $g_{ωΛ}$ simultaneously, where to reconcile with the empirical value the RHF models address a larger parameter space of meson-hyperon couplings.

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arXiv2022

Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei

Staring from the Lagrangian density that foots on the meson-propagated picture of nuclear force, the full Hamiltonian, that contains both mean field and pairing contributions, is derived by quantizing the Dirac spinor field in the Bogoliubov quasi-particle space, and the expectation with respect to the Bogoliubov ground state gives the full energy functional. As an extension of the D-RHF model, the degree of freedom associated with the $ρ$-tensor ($ρ$-T) coupling is implemented, and incorporating with the Bogoliubov scheme the finite-range Gogny force D1S is utilized as the pairing force. Moreover, qualitative analysis on the nature of the $π$-PV and $ρ$-T couplings are presented for better understanding their enhancements on the deformation effects. Space convergence related to the spherical DWS base is confirmed for the D-RHFB model by taking light nucleus $^{24}$Mg and mid-heavy one $^{156}$Sm as candidates. Compared to light nuclei, extraordinary more negative energy states are necessitated to keep the expansion completeness on the spherical DWS base for mid-heavy and heavy nuclei, due to the enhanced correlations between the expansion components with large $κ$-quantity as indicated by the nature of the $π$-PV and $ρ$-T couplings. Furthermore, because of the enhanced deformation effects by the $π$-PV and $ρ$-T couplings, the RHF Lagrangian PKA1 presents deeper bound ground state for $^{24}$Mg than the other selected Lagrangians, in addition to predicting a fairly deep bound local minimum with large oblate deformation.

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arXiv2021

Exploring effects of tensor force and its strength via neutron drops

The tensor-force effects on the evolution of the spin-orbit splittings in the neutron drops are investigated within the framework of the relativistic Hartree-Fock theory. For fair comparisons on the pure mean-field level, the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data. Through a quantitative analysis, we certify that the $π$-pseudovector ($π$-PV) coupling affects the evolutionary trend through the tensor force embedded. The strength of the tensor force is explored by enlarging the strength $f_π$ of the $π$-PV coupling. It is found that weakening the density dependence of $f_π$ is slightly better than enlarging it with a factor. We thus provide a semiquantitative support for the \textit{renormalization persistency} of the tensor force within the framework of density functional theory. This will serve as an important guidance for the further development of the relativistic effective interactions with particular focus on the tensor force.

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arXiv2019

New magicity $N=32$ and $34$ triggered by strong couplings between Dirac inversion partners

Inspired by recent experiments, the successive new magicity $N = 32$ and $34$ in Ca isotopes are studied within the relativistic density functional theory. It is illustrated that the strong couplings between the $s_{1/2}$ and neutron ($ν$) $\nu2p_{1/2}$ orbits, here referred as "Dirac inversion partners" (DIPs), play a key role in opening both subshells $N = 32$ and $34$. Such strong couplings originate from the inversion similarity between the DIPs, that the upper component of the Dirac spinor of one partner shares the same orbital angular momentum as the lower component of the other, and vice versa. Following the revealed mechanism, it is predicted that the magicity $N = 32$ is reserved until $^{48}$S, but vanishes in $^{46}$Si.

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arXiv2019

Towards an ab initio covariant density functional for nuclear structure

Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided.

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arXiv2019

Pseudo-spin symmetry restoration and the in-medium balance between nuclear attractive and repulsive interactions

The mechanism that restores the pseudo-spin symmetry (PSS) are investigated under the relativistic Hartree-Fock (RHF) approach, by focusing on the in-medium balance between nuclear attractive and repulsive interactions. It is illustrated that the modelings of both the equilibrium of nuclear dynamics and the in-medium effects can be essentially changed by the $ρ$-tensor coupling that play the role almost fully via the Fock terms, from which the model discrepancy on the PSS restoration is verified. Specifically, the largely different density-dependent behaviors of the isoscalar coupling strengths $g_σ$ and $g_ω$, deduced from the parametrization of the RHF Lagrangian PKA1, play an essential role in restoring the PSS of the high-$l'$ pseudo-spin doublets around the Fermi levels. Qualitatively, a guidance is provided for the modelings of both the equilibrium of nuclear dynamics and the in-medium effects via the PSS restoration.

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arXiv2019

Restoration of pseudo-spin symmetry in $N=32$ and $34$ isotones described by relativistic Hartree-Fock theory

Restoration of pseudo-spin symmetry (PSS) along the $N=32$ and $34$ isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with effective Lagrangian PKA1. Taking the proton pseudo-spin partners $(\pi2s_{1/2},\pi1d_{3/2})$ as candidates, systematic restoration of PSS along both isotonic chains is found from sulphur (S) to nickel (Ni), while distinct violation from silicon (Si) to sulphur is discovered near the drip lines. The effects of the tensor-force components introduced naturally by the Fock terms are investigated, which can only partly interpret the systematics from calcium to nickel, but fail for the overall trends. Further analysis following the Schrödinger-like equation of the lower component of Dirac spinor shows that the contributions from the Hartree terms dominate the overall systematics of the PSS restoration, and such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. Specifically the distinct PSS violation is found to tightly relate with the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.

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arXiv2018

Quantitative analysis of tensor effects in the relativistic Hartree-Fock theory

Tensor force is identified in each meson-nucleon coupling in the relativistic Hartree-Fock theory. It is found that all the meson-nucleon couplings, except the $σ$-scalar one, give rise to the tensor force. The effects of tensor force on various nuclear properties can now be investigated quantitatively, which allows fair and direct comparisons with the corresponding results in the non-relativistic framework. The tensor effects on nuclear binding energies and the evolutions of the $Z,\,N = 8,\,20$, and $28$ magic gaps are studied. The tensor contributions to the binding energies are shown to be tiny in general. The $Z,\,N = 8$ and $20$ gaps are sensitive to the tensor force, but the $Z,\,N = 28$ gaps are not.

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arXiv2018

Hypernuclear stars from relativistic Hartree-Fock density functional theory

The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of $Λ$ and $Ξ$ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced.

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arXiv2018

Si-48: An atypical nucleus?

Based on the relativistic Hartree-Fock formalism and one of the most advanced Lagrangian PKA1, we investigate the properties of the exotic nucleus 48Si. We found that 48Si may be an atypical nucleus characterized by i) the onset of doubly magicity, ii) its location at the drip line, iii) the presence of a doubly semibubble (central depletion of the neutron and proton density profiles) in the ground state, and iv) the occurrence of pairing reentrance at finite temperature. These phenomenons are not independent from each others. We illustrate for instance that the doubly semibubble reduces the spin-orbit splitting of low-l orbitals and modifies the splitting of relevant pseudospin partners, favoring N = 34 as a new magic number for neutron rich nuclei. Since 48Si is predicted doubly magic, it could have an extra stability which puts it at the drip line. Moreover, 48Si may have interesting excited states which may induce pairing reentrance at finite temperature. While not being new, these phenomenons are found to serendipitously occur together in 48Si, from our theoretical calculation. Theoretical nuclear modelings are known to be poorly predictive in general, and we asset our confidence in the prediction of our modeling on the fact that the predictions of PKA1 in various regions of the nuclear chart have systematically been found correct and more specifically in the region around 48Si, our approach correctly reproduce the known features of neighboring nuclei. Whether our predictions are confirmed or not, 48Si provides a concrete benchmark for the understanding of the nature of nuclear forces.

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