Search

The studies of transuranium nuclei are of vital significance in exploring the existence of the ``island of superheavy nuclei". This work presents the systematic investigations for the ground-state properties and structure evolutions of odd-$A$ transuranium Bk isotopes taking the deformed relativistic Hartree-Bogoliubov theory in continuum~(DRHBc) with PC-PK1 density functional, in comparison with those by spherical relativistic continuum Hartree-Bogoliubov~(RCHB) theory. The DRHBc calculations offer improved descriptions of the binding energies, closely aligning with the experimental data. The incorporation of deformation effects in DRHBc results in enhanced nuclear binding energies and a notable reduction in $\alpha$-decay energies. With the rotational corrections further incorporated, the theoretical deviation by DRHBc from the experimental data is further reduced. Based on the two-neutron gap $\delta_{\rm 2n}$ and the neutron pairing energy $E_{\rm pair}^n$, prominent shell closures at $N=184$ and $258$, as well as potential sub-shell structures at $N=142, 150, 162, 178, 218$, and $230$ are exhibited. A quasi-periodic variation among prolate, oblate, and spherical shapes as well as prolate deformation predominance have been shown in the evolutions of the quadrupole deformation. Possible shape coexistence is predicted in $^{331}$Bk with the oblate and prolate minima in close energies, which is further supported by the triaxial relativistic Hartree-Bogoliubov theory in continuum~(TRHBc) calculations., Comment: 9 pages, 7 figures

We propose a new theoretical framework to investigate the properties of finite nuclei based on an extended Nambu-Jona-Lasinio (eNJL) model, where the Dirac sea, the spontaneous chiral symmetry breaking, and the quark degrees of freedom are considered by extending the SU(3) NJL model and treating baryons as clusters of quarks. The eNJL model can then be readily adopted to examine the matter states ranging from baryonic matter to quark matter in a unified manner. In this work, by assuming spherically symmetric finite nuclei and neglecting the center-of-mass or rotational corrections, we systematically investigate the properties of finite nuclei based on the eNJL model with additional pairing correlations. It is found that our model generally reproduces the binding energies of the 2495 nuclei ($A>2$) from the 2016 Atomic Mass Evaluation (AME2016) with the root-mean-square deviations $5.38$ MeV. The deviations are mainly attributed to the too large shell gaps at magic numbers $N(Z) =28$, 50, and 82 as well as the spurious shell closures at $N(Z)=34$, 58, and 92. Meanwhile, the obtained charge radii of 906 nuclei are systematically smaller than the experimental values with root-mean-square deviations $0.127$ fm. In our future study, we expect to reduce the uncertainties of our predictions by carefully calibrating the density dependence of coupling constants and considering deformations with microscopic collective corrections from the nucleons in the Fermi sea and quarks in the Dirac sea.

We consider the free boundary problem for a layer of compressible viscous barotropic fluid lying above a fixed rigid bottom and below the atmosphere of positive constant pressure. The fluid dynamics is governed by the compressible Navier--Stokes equations with gravity, and the effect of surface tension is neglected on the upper free boundary. We prove the global well-posedness of the reformulated problem in flattening coordinates near the equilibrium in both two and three dimensions without any low frequency assumption of the initial data. The key ingredients here are the new control of the {\it Eulerian spatial derivatives} of the solution, which benefits a crucial nonlinear cancellation of the highest order spatial regularity of the free boundary, and the time weighted energy estimates., Comment: 39 pages; to appear in Mathematische Annalen

Large Language Models (LLMs) have transformed machine learning but raised significant legal concerns due to their potential to produce text that infringes on copyrights, resulting in several high-profile lawsuits. The legal landscape is struggling to keep pace with these rapid advancements, with ongoing debates about whether generated text might plagiarize copyrighted materials. Current LLMs may infringe on copyrights or overly restrict non-copyrighted texts, leading to these challenges: (i) the need for a comprehensive evaluation benchmark to assess copyright compliance from multiple aspects; (ii) evaluating robustness against safeguard bypassing attacks; and (iii) developing effective defense targeted against the generation of copyrighted text. To tackle these challenges, we introduce a curated dataset to evaluate methods, test attack strategies, and propose lightweight, real-time defense to prevent the generation of copyrighted text, ensuring the safe and lawful use of LLMs. Our experiments demonstrate that current LLMs frequently output copyrighted text, and that jailbreaking attacks can significantly increase the volume of copyrighted output. Our proposed defense mechanism significantly reduces the volume of copyrighted text generated by LLMs by effectively refusing malicious requests. Code is publicly available at https://github.com/xz-liu/SHIELD, Comment: Work in progress

In hypernuclear systems, interactions involving nucleons and hyperons are intricately influenced by the surrounding particles, particularly by the density and the isospin feature of the nuclear medium. In this work, the relativistic mean-field (RMF) theory is adopted to describe the structure of several typical $\Xi^{-}$ hypernuclei. New sets of $\Xi N$ effective interactions, by taking a density-dependent meson-nucleon/hyperon coupling perspective, are developed by fitting experimental data on the $\Xi^{-}$ hyperon $1s$ and $1p$ state separation energy of $^{15}_{\Xi^{-}}$C as well as the $1p$ state separation energy of $^{13}_{\Xi^{-}}$B. The density-dependent behavior of meson-hyperon coupling strengths sensitively affects the description of hyperon single-particle levels. In fact, the density-dependent meson-baryon coupling strengths introduce additional rearrangement contributions to the hyperon self-energy. Correspondingly, detailed forms of density dependence in these coupling strengths and different considerations of meson-baryon coupling channels will impact the hyperon single-particle properties within hypernuclei. Especially with the additional inclusion of the isovector scalar $ \delta $ meson, the significant enhancement of rearrangement terms in the effective interaction DD-ME$\delta$ impacts the shape of the hyperon potential and alters the characteristics of the isovector channel dynamics balance in the effective nuclear force. Relevant research underscores the importance of precisely accounting for in-medium effects in hyperon-nucleon interactions and incorporating a more comprehensive set of meson-exchange degrees of freedom in effective nuclear forces, offering a potential solution for more self-consistently describing the featured hyperon single-particle behavior of various hypernuclei and for reducing uncertainties in theoretical descriptions., Comment: 13 pages, 4 figures, 4 tables

Spin rotation is central for the spin-manipulation of lepton beams which, in turn, plays an important role in investigation of the properties of spin-polarized lepton beams and the examination of spin-dependent interactions. However, realization of compact and ultrafast spin rotation of lepton beams, between longitudinal and transverse polarizations, still faces significant challenges. Here, we put forward a novel method for ultrafast (picosecond-timescale) spin rotation of a relativistic lepton beam via employing a moderate-intensity terahertz (THz) wave in a dielectric-lined waveguide (DLW). The lepton beam undergoes spin precession induced by the THz magnetic field. We find that optimizing the lepton velocity and THz phase velocity in the DLW can mitigate the impact of transverse Lorentz forces on the lepton beam and increase the precession frequency, thereby maintaining the beam quality and enhancing the efficiency of transverse-to-longitudinal spin rotation. The final polarization degree of the lepton beam exceeds $98\%$, and the energy spread can be improved significantly. Flexibility in adjusting the electromagnetic modes within the DLW adds further potential for spin-manipulation, and holds promise for advancing the development of spin-polarized particle beams, which have broad applications in materials science and atomic, nuclear, and high-energy physics.

The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground state shapes is shown with the neutron number, i.e., spherical shapes at shell closures $N=$126, 184, 258, and prolate dominated shapes between them. In analogy to the shape evolution, the inner fission barriers also exhibit a periodic behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect to the inner fission barrier is evaluated using the triaxial relativistic mean field calculations plus a simple BCS method for pairing. With the triaxial correction included, good consistency in the inner barrier heights is found with the available empirical data. Besides, the evolution from the proton to the neutron drip line is in accord with the results by the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus $^{318}$U which may play a role of fission recycling in the astrophysical $r$-process nucleosynthesis., Comment: 7 pages, 6 figures

In this paper, we reanalyze the top-quark pair production at the next-to-next-to-leading order (NNLO) in QCD at future $e^+e^-$ colliders by using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in $\alpha_s$ are determined by absorbing the non-conformal $\beta$ terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy $\mu_r=\sqrt{s}$, the determined PMC scale $Q_\star$ is far smaller than the $\sqrt{s}$ and increases with the $\sqrt{s}$, yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved due to the elimination of the renormalon divergence. For a typical collision energy of $\sqrt{s}=500$ GeV, the PMC scale is $Q_\star=107$ GeV; the QCD correction factor $K$ for conventional results is $K\sim1+0.1244^{+0.0102+0.0012}_{-0.0087-0.0011}+0.0184^{-0.0086+0.0002}_{+0.0061-0.0003}$, where the first error is caused by varying the scale $\mu_r\in[\sqrt{s}/2, 2\sqrt{s}]$ and the second error is from the top-quark mass $\Delta{m_t}=\pm0.7$ GeV. After applying the PMC, the renormalization scale uncertainty is eliminated and the QCD correction factor $K$ is improved to $K\sim 1+0.1507^{+0.0015}_{-0.0015}-0.0057^{+0.0001}_{-0.0000}$, where the error is from the top-quark mass $\Delta{m_t}=\pm0.7$ GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of properties of the top-quark at future $e^+e^-$ colliders., Comment: 8 pages, 3 figures. Accepted by Chinese Physics C

Detecting and analyzing the local environment is crucial for investigating the dynamical processes of crystal nucleation and shape colloidal particle self-assembly. Recent developments in machine learning provide a promising avenue for better order parameters in complex systems that are challenging to study using traditional approaches. However, the application of machine learning to self-assembly on systems of particle shapes is still underexplored. To address this gap, we propose a simple, physics-agnostic, yet powerful approach that involves training a multilayer perceptron (MLP) as a local environment classifier for systems of particle shapes, using input features such as particle distances and orientations. Our MLP classifier is trained in a supervised manner with a shape symmetry-encoded data augmentation technique without the need for any conventional roto-translations invariant symmetry functions. We evaluate the performance of our classifiers on four different scenarios involving self-assembly of cubic structures, 2-dimensional and 3-dimensional patchy particle shape systems, hexagonal bipyramids with varying aspect ratios, and truncated shapes with different degrees of truncation. The proposed training process and data augmentation technique are both straightforward and flexible, enabling easy application of the classifier to other processes involving particle orientations. Our work thus presents a valuable tool for investigating self-assembly processes on systems of particle shapes, with potential applications in structure identification of any particle-based or molecular system where orientations can be defined., Comment: 14 pages, 9 figures