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Results: We find that the tensor force affects the height of fission barriers and the double-humped structure of fission path of 240Pu. On the PES, the fission valley becomes larger in the (Q20, Q30) plane, and the triaxial deformation is suppressed around the outer barrier after considering the tensor force. Incorporating the tensor force into the dynamical process enhances the difference in shape evolution between two asymmetric channels. More interestingly, the charge distribution from TDHF with double PNP calculations shows a strong odd-even effect after including the tensor force. In addition, the total mass and charge distributions of fission fragments show a slight shift towards larger asymmetry and are more consistent with the experiments when tensor components are included. We also find that the tensor force enhances energy gaps of the deformed shells for heavy fragments. Moreover, the TKEs of fragments are in accord with the experiments, and after incorporating the tensor force, we observe a higher concentration of the calculated TKEs for heavy fragments at Z = 52 and Z = 56. Conclusions: The tensor force plays a role in both static and dynamical processes in nuclear fission, improving the accuracy of theoretical descriptions within the current framework. Our calculations have shown that the fission-barrier height with SLy5t is closer to the empirical value than that of SLy5. Additionally, the inclusion of the tensor force not only manifests the odd-even effect in charge distribution but also improves the description of total mass and charge distributions., Comment: 16 pages, 13 figures, Submitted to Phys. Rev. C

A notable issue, the proper description of mass and charge distributions of fission fragments within nonadiabatic descriptions of fission dynamics, is investigated by performing double particle number projection on the outcomes of time-dependent Hartree-Fock (TDHF) simulation. The induced fission process of the benchmark nucleus 240Pu is studied. In the three-dimensional Cartesian coordinate without any symmetry restrictions, we get the static fission pathway from the two-dimensional potential energy surface, and then the fission dynamics from saddle to scission point are obtained using TDHF. We show that the charge numbers of primary heavy fragments from TDHF simulation strongly depend on the deformations of initial configurations via the two asymmetric fission channels, which can be distinguished according to the dynamical fission trajectories. The charge distribution of fission fragments is well reproduced using the double particle number projection technique. After applying the Gaussian kernel estimation based on the distribution from the double particle number projection technique, the mass distribution is also consistent with the experimental results. Besides, the results of the total kinetic energy of fission fragments are reasonably consistent with the experiments., Comment: 8 pages, 3 figures

The mass table in the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the PC-PK1 density functional has been established for even-$Z$ nuclei with $8\le Z\le120$, extended from the previous work for even-even nuclei [Zhang $\it{et.~al.}$ (DRHBc Mass Table Collaboration), At. Data Nucl. Data Tables 144, 101488 (2022)]. The calculated binding energies, two-nucleon and one-neutron separation energies, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, quadrupole deformations, and neutron and proton Fermi surfaces are tabulated and compared with available experimental data. A total of 4829 even-$Z$ nuclei are predicted to be bound, with an rms deviation of 1.477 MeV from the 1244 mass data. Good agreement with the available experimental odd-even mass differences, $\alpha$ decay energies, and charge radii is also achieved. The description accuracy for nuclear masses and nucleon separation energies as well as the prediction for drip lines is compared with the results obtained from other relativistic and nonrelativistic density functional. The comparison shows that the DRHBc theory with PC-PK1 provides an excellent microscopic description for the masses of even-$Z$ nuclei. The systematics of the nucleon separation energies, odd-even mass differences, pairing energies, two-nucleon gaps, $\alpha$ decay energies, rms radii, quadrupole deformations, potential energy curves, neutron density distributions, and neutron mean-field potentials are discussed., Comment: 394 pages, 17 figures, 2 tables, published in Atomic Data and Nuclear Data Tables, data file in the TXT form is available for download under "Ancillary files"

Magicity, or shell closure, plays an important role in our understanding of complex nuclear phenomena. In this work, we employ one of the state-of-the-art density functional theories, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1, to investigate the evolution of the $N=20,28,50$ shell closures in the $ 20 \leqslant Z \leqslant 30$ region. We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii, two-neutron separation energies, two-neutron gaps, quadrupole deformations, and single-particle levels. In particular, we find that in the $ 21 \leqslant Z \leqslant 27$ region, the $N=50$ shell closure disappears or becomes quenched, mainly due to the deformation effects. Similarly, both experimental data and theoretical predictions indicate that the $N=28$ shell closure disappears in the Mn isotopic chain, also predominantly due to the deformation effects. The DRHBc theory predicts the existence of the $N=20$ shell closure in the Ca, Sc, and Ti isotopic chains, but the existing data for the Ti isotopes suggests the contrary, and therefore more investigations are needed., Comment: 9 pages, 9 figures

One-proton radioactivity in 149Lu, the latest identified proton emitter, is studied in the Wentzel-Kramers-Brillouin (WKB) approach with the proton-nucleus potential extracted from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for the first time. The predicted half-life turns out to be consistent with the experimental measurement within uncertainties and (almost) independent of the density functionals in the DRHBc theory. Such a microscopic self-consistent calculation reveals that 149Lu is oblately deformed with a quadrupole deformation -0.18, and rules out the possibility of a prolate quadrupole deformation suggested in the nonadiabatic quasiparticle model. We also check the validity of this approach in the description of 150,151Lu and their isomeric states. The deviations of the predicted half-lives from their experimental counterparts are mostly smaller than those of the theoretical studies without considering deformation effects. Furthermore, we predict 148Lu to be a more oblately deformed proton-emitter with a longer half-life than that of 149Lu, which can be checked in the future. Our studies show that the DRHBc plus WKB approach provides a new alternative method to evaluate the half-lives of well-deformed proton emitters.

Pairing effects manifests themselves in many aspects in nuclear systems ranging from finite nuclei to nuclear matter and compact stars. Although with some specific features for nuclear systems, the mechanism of pairing between nucleons in these systems resembles that of electrons in superconductors. The Bardeen-Cooper-Schrieffer (BCS) theory, the first successful and microscopic theory for superconductivity, and the Bogoliubov transformation, the generalization of the BCS theory, have been widely used to describe pairing correlations in nuclear systems. To deal with the problem of particle number non-conservation in the BCS method and generalized Bogoliubov transformation, particle number projection techniques as well as several approaches which keep the particle number conserved, have been proposed. In the study of exotic nuclei, which are quantum open systems, the continuum contributions have to be taken into account. In this chapter, a thorough but brief discussion of pairing effects in nuclear systems will be introduced. Then nuclear models dealing with pairing correlations in nuclear structure properties will be presented to different extent of details. Although formulas are given, the emphasis is mainly put on the basic ideas concerning these models., Comment: Contribution to the "Handbook of Nuclear Physics", Springer, 2022, edited by I. Tanihata, H. Toki, and T. Kajino. 32 pages, 5 figures, and 1 table

We provide a microscopic description of the fusion reactions between $^{40,48}$Ca and $^{78}$Ni. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ is more obvious than those of $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$. By comparing the calculated fusion cross sections between $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ and $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$, an interesting enhancement of sub-barrier fusion cross sections for the former system is found, which can be explained by the narrow width of internuclear potential for $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ while the barrier heights and positions are very close to each other. The tensor force suppresses the sub-barrier fusion cross sections of both two systems., Comment: 8 pages, 6 figures

The understanding of the fusion probability is of particular importance to reveal the mechanism of producing superheavy elements. We present a microscopic study of the compound nucleus formation by combining time-dependent density functional theory, coupled-channels approach, and dynamical diffusion models. The fusion probability and compound nucleus formation cross sections for cold-fusion reactions $^{48}$Ca+$^{208}$Pb, $^{50}$Ti+$^{208}$Pb, and $^{54}$Cr+$^{208}$Pb are investigated and it is found that the deduced capture barriers, capture cross sections for these reactions are consistent with experimental data. Above the capture barrier, our calculations reproduce the measured fusion probability reasonably well. Our studies demonstrate that the restrictions from the microscopic dynamic theory improve the predictive power of the coupled-channels and diffusion calculations., Comment: 9 pages, 4 figures

In recent several years, the tensor force, one of the most important components of the nucleon-nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion cross sections systematically. In this work we present a mini review on the recent progresses on this topic. Considering the recent progress of low-energy reaction theories, we will also mention more possible effects of the tensor force on reaction dynamics., Comment: 30 pages, 4 figures, Accepted Manuscript in Commun. Theor. Phys

The aim of this work is to extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) based on the point-coupling density functionals to odd-$A$ and odd-odd nuclei and examine its applicability by taking odd-$A$ Nd isotopes as examples. In the DRHBc theory, the densities and potentials with axial deformation are expanded in terms of Legendre polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a Dirac Woods-Saxon basis to include the continuum effects. For an odd-$A$ or odd-odd nucleus, the blocking effect of unpaired nucleon(s) is taken into account with the equal filling approximation. To determine its ground state, an automatic blocking procedure is adopted, in which the orbital with the lowest quasiparticle energy is blocked during the iteration. This procedure is justified by comparing with the results from the orbital-fixed blocking calculations, in which the blocked orbital near the Fermi surface is fixed during the iteration. The ground states for both light and heavy nuclei can be provided by the automatic blocking procedure as the orbital-fixed blocking procedure, but with considerably reduced computational cost. The numerical details for even-even nuclei are found to be valid for odd-$A$ and odd-odd nuclei as well. Taking Nd isotopes including both even-even and odd-$A$ ones as examples, the calculated ground-state properties with PC-PK1 are in good agreement with the available experimental data. This work paves the way to construct the DRHBc mass table including all even-even, odd-$A$ and odd-odd nuclei in the nuclear chart., Comment: 39 pages, 13 figures, and 1 table

Ground-state properties of even-even nuclei with $8\le Z\le120$ from the proton drip line to the neutron drip line have been investigated using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1. With the effects of deformation and continuum included simultaneously, 2583 even-even nuclei are predicted to be bound. The calculated binding energies, two-nucleon separation energies, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, quadrupole deformations, and neutron and proton Fermi surfaces are tabulated and compared with available experimental data. The rms deviation from the 637 mass data is 1.518 MeV, providing one of the best microscopic descriptions for nuclear masses. The drip lines obtained from DRHBc calculations are compared with other calculations, including the spherical relativistic continuum Hartree-Bogoliubov (RCHB) and triaxial relativistic Hartree-Bogoliubov (TRHB) calculations with PC-PK1. The deformation and continuum effects on the limits of the nuclear landscape are discussed. Possible peninsulas consisting of bound nuclei beyond the two-neutron drip line are predicted. The systematics of the two-nucleon separation energies, two-nucleon gaps, rms radii, quadrupole deformations, potential energy curves, neutron densities, neutron mean-field potentials, and pairing energies in the DRHBc calculations are also discussed. In addition, the $\alpha$ decay energies extracted are in good agreement with available data., Comment: 217 pages, 15 figures, 2 tables, accepted for publication in Atomic Data and Nuclear Data Tables, data file in the TXT form is available for download under "Ancillary files"

We study the effects of higher-order deformations $\beta_\lambda$ ($\lambda=4,6,8,$ and $10$) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus $^{270}$Hs by using the multidimensionally-constrained (MDC) relativistic mean-field (RMF) model with five effective interactions PC-PK1, PK1, NL3$^{*}$, DD-ME2, and PKDD. The doubly magic properties of $^{270}$Hs are featured by the large energy gaps at $N=162$ and $Z=108$ in the single-particle spectra. By investigating the binding energies and single-particle levels of $^{270}$Hs in multidimensional deformation space, we find that the deformation $\beta_6$ has the greatest impact on the binding energy among these higher-order deformations and influences the shell gaps considerably. Similar conclusions hold for other SHN near $^{270}$Hs. Our calculations demonstrate that the deformation $\beta_6$ must be considered when studying SHN by using MDC-RMF., Comment: accepted for publication in Chin. Phys. C

We study the exotic deformed nucleus $^{31}$Ne using an approach that combines self-consistent structure and reaction theory. We utilize the fully-relativistic, microscopic deformed Hartree-Bogoliubov theory in continuum (DRHBc) to demonstrate that deformation and pairing correlations give rise to a halo structure with large-amplitude $p$-wave configuration in $^{31}$Ne. We then use the valence nucleon wave functions and angle-averaged density distributions of $^{30}$Ne from this model as input for a Glauber reaction model to study the observables of neutron-rich Neon isotopes and search for halo signatures. Our predictions of the reaction cross sections of these exotic Neon isotopes on a Carbon target can better reproduce the experimental data than those from relativistic mean field model for a spherical shape with resonances and pairing correlations contributions, as well as those from a Skyrme-Hartree-Fock model. The one-neutron removal cross section at 240 MeV/nucleon, the inclusive longitudinal momentum distribution of the $^{30}$Ne, and the valence neutron residues from the $^{31}$Ne breakup reaction are largely improved over previous theoretical predictions and agree well with data. These reaction data indicate a dilute density distribution in coordinate space and are a canonical signature of a halo structure.

The angular momentum projection (AMP) method is implemented in the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the point-coupling density functional. The wave functions of angular momentum projected states are expanded in terms of the Dirac Woods-Saxon (WS) basis, providing a proper description of the asymptotic behavior of the wave functions for weakly bound nuclei. The contribution of continuum induced by the pairing is considered by treating the pairing correlation with the Bogoliubov transformation. We present the formulae and numerical checks for the DRHBc+AMP approach and use it to study low-lying excited states of weakly bound deformed nuclei. Our calculations show that neutron-rich magnesium isotopes $^{36,38,40}$Mg are all well deformed nuclei. The low-lying excited states of these three nuclei are obtained by performing the AMP on the mean-field ground-states. The ground-state rotational bands of $^{36,38,40}$Mg are reproduced reasonably well by using this new DRHBc+AMP approach with the density functional PC-F1., Comment: 18 pages, 11 figures, 3 tables

We explore the rotational feature of deformed halos by performing the angular momentum projection (AMP) on the ground state wave functions obtained from the deformed relativistic Hartree-Bogoliubov theory (DRHBc) in continuum. The DRHBc+AMP approach self-consistently describes the coupling between single particle bound states and the continuum not only in the ground state but also in rotational states. The rotational modes of deformed halos in $^{42}$Mg and $^{44}$Mg are investigated by studying properties of rotational states such as excitation energy, configuration, and density distribution. Our study demonstrates that the deformed halo structure persists from the ground state in the intrinsic frame to collective states. Especially, the typical behavior of shape decoupling effects in rotating deformed halo nuclei is revealed., Comment: 7 pages, 5 figure, and 1 table

Ground state properties of carbon isotopes, including root-mean-square radii, neutron separation energies, single particle spectra, and shapes are systematically studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. The calculations with the effective interaction PK1 reproduce the available data reasonably well. The shell evolution in this isotopic chain is investigated by examining the single particle spectra. The inversion of neutron orbitals $\nu 2s_{1/2}$ and $\nu 1d_{5/2}$ compared with the order of neutron orbitals in stable nuclei is revealed in $^{15-20,22}\mathrm{C}$ when these nuclei are constrained to spherical shape. Neutron halos in $^{15,19,22}$C are studied in detail and their halo structures are mainly caused by the inversion of ($\nu 2s_{1/2},\nu 1d_{5/2}$) and deformation effects. In particular, $^{15}$C and $^{22}$C are deformed halo nuclei with shape decoupling effects in ground states., Comment: 46 pages, 15 figures, and 2 tables; Nucl. Phys. A, in press

The aim of this work is to develop the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) theory based on the point-coupling density functionals and extend it to provide a unified description for all even-even nuclei in the nuclear chart by overcoming all possible challenges. The nuclear superfluidity is considered via Bogoliubov transformation. Densities and potentials are expanded in terms of Legendre polynomials to include the axial deformation degrees of freedom. Sophisticated relativistic Hartree-Bogoliubov equations in coordinate space are solved in the DiracWoods-Saxon basis to consider the continuum effects. Numerical checks are performed from light nuclei to heavy nuclei. The techniques to construct the DRHBc mass table for even-even nuclei are explored. The DRHBc theory is extended to study heavier nuclei beyond magnesium isotopes. Taking Nd isotopes as examples, the experimental binding energies, two-neutron separation energies, quadrupole deformations, and charge radii are reproduced rather well. The deformation and continuum play essential roles in the description of nuclear masses and prediction of drip-line nuclei. By examining the single-particle levels in the canonical basis and their contributions to the total density, the thickness of the neutron skin, the particles number in continuum, and the Coulomb barrier, the exotic structures including the neutron skin and the proton radioactivity are predicted., Comment: 45 pages, 17 figures, and 1 table, accepted version for Physical Review C

We investigate the ground state properties of $^{22}$C by using a deformed relativistic Hartree-Bogoliubov model in continuum and explore the interplays among the formation of a halo, deformation effects, the inversion of $sd$ states, the shell evolution, and changes of nuclear magicities. It is revealed that there is an inversion between the two spherical orbitals $2s_{1/2}$ and $1d_{5/2}$ in $^{22}$C compared with the conventional single particle shell structure in stable nuclei. This inversion, together with deformation effects, results in a shrunk halo and a quenched shell gap at $N=16$. It is predicted that the core of $^{22}$C is oblate but the halo is prolate. Therefore several exotic nuclear phenomena, including the halo, the shape decoupling effects, the inversion of $sd$ states, and the evolution of shell structure which results in (dis)appearance of magic numbers, coexist in one single nucleus $^{22}\mathrm{C}$., Comment: Phys. Lett. B, in press

Quantum digital signatures (QDS) provide a means for signing electronic communications with informationtheoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders them vulnerable against detector side-channel attacks, just like quantum key distribution. Here, we exploit a measurement-device-independent (MDI) quantum network, over a 200-square-kilometer metropolitan area, to perform a field test of a three-party measurement-device-independent quantum digital signature (MDI-QDS) scheme that is secure against any detector side-channel attack. In so doing, we are able to successfully sign a binary message with a security level of about 1E-7. Remarkably, our work demonstrates the feasibility of MDI-QDS for practical applications., Comment: 5 pages, 1 figure, 2 tables, supplemental materials included as ancillary file

Classical optical communications may be still the main communications technology for the foreseeable future, so integration of the quantum communication network with existing classical optical communication network is necessary because existing telecommunications infrastructure will be shared. This means multiplexing of quantum key distribution (QKD) and strong classical data signals, delivering quantum signals and classic signals in one fiber. Optical splitters are employed to access each user in a gigabit-capable passive optical network (GPON). In a 4-user network the splitter adds at least 6 dB of optical loss to the quantum channel, a 64-user network the splitter adds 18 dB of optical loss to the quantum channel. The optical splitters restrict the transmission distance and performance of QKD. We propose a new integration program of QKD and GPON based on wavelength-division multiplexing (WDM). At the optical splitting point, we use filters to separate the quantum signals and bypass the optical splitter, avoiding losses produced by the optical splitters. This increases the counting rate of the quantum signals states and the signal to noise ratio (SNR) improves, so a higher key generation rate and a longer transmission distance can be obtained with QKD., Comment: 9 Pages, 3 Figures

Quantum cryptography holds the promise to establish an information-theoretically secure global network. All field tests of metropolitan-scale quantum networks to date are based on trusted relays. The security critically relies on the accountability of the trusted relays, which will break down if the relay is dishonest or compromised. Here, we construct a measurement-device-independent quantum key distribution (MDIQKD) network in a star topology over a 200 square kilometers metropolitan area, which is secure against untrustful relays and against all detection attacks. In the field test, our system continuously runs through one week with a secure key rate ten times larger than previous result. Our results demonstrate that the MDIQKD network, combining the best of both worlds --- security and practicality, constitutes an appealing solution to secure metropolitan communications., Comment: 17 pages, 4 figures