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The empirical coupled-channel (ECC) model and the universal fusion function (UFF) prescription are used to analyse the data of capture cross sections for reactions ${}^{39}$K$+{}^{181}$Ta and ${}^{46}$K$+{}^{181}$Ta reported recently by A. Wakhle {\it et al.} [Phys. Rev. C 97, 021602(R) (2018)]. The results of the ECC model are in good agreement with the data of ${}^{39}$K$+{}^{181}$Ta while, for ${}^{46}$K$+{}^{181}$Ta, the predictions of the ECC model overestimate the above-barrier capture cross sections. Comparing the reduced data of these two reactions, it is found that the above-barrier cross sections of ${}^{39}$K$+{}^{181}$Ta are consistent with the UFF and are larger than those of ${}^{46}$K$+{}^{181}$Ta. This implies that the capture cross sections of ${}^{46}$K$+{}^{181}$Ta are suppressed at energies above the Coulomb barrier. Furthermore, at sub-barrier energies, the reduced calculated capture cross sections of ${}^{39}$K$+{}^{181}$Ta are a little larger than those of ${}^{46}$K$+{}^{181}$Ta, which is owing to the coupling to the positive $Q$-value two-neutron transfer channel., Comment: 6 pages, 3 figures. Accepted for publication in PRC

We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of $x$ and $y$ axes; i.e., the intrinsic symmetry group is $V_4$ and all shape degrees of freedom $\beta_{\lambda\mu}$ with even $\mu$ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of $^{110}$Zr is predicted to be tetrahedral with both functionals and so is that of $^{112}$Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around $Z=40$ and $N=70$ when $\beta_{32}$ deformation is included. Although the inclusion of the $\beta_{30}$ deformation can also reduce the energy around $\beta_{20}=0$ and lead to minima with pear-like shapes for nuclei around $^{110}$Zr, these minima are unstable due to their shallowness., Comment: 16 pages, 6 figures, 4 tables, accepted for publication in Phys. Rev. C

Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results show that the suppression of complete fusion are roughly independent of the target for the reactions involving the same projectile., Comment: 9 pages, 6 figures, 3 tables

The dynamic coupling effects on fusion cross sections for reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universal fusion function formalism and an empirical coupled channel (ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in $^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in $^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with $^{94}$Zr as target should be similar as that in the reactions with $^{96}$Zr as target. This implies that the quadrupole deformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similar to each other. However, $\beta_2$'s predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on $^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve the puzzling issue concerning $\beta_2$ for $^{94}$Zr., Comment: 8 pages, 5 figures. arXiv admin note: text overlap with arXiv:1504.00756

The conventionally separated treatments for strangelets and strange stars are now unified with a more comprehensive theoretical description for objects ranging from strangelets to strange stars. After constraining the model parameter according to the Witten-Bodmer hypothesis and observational mass-radius probability distribution of pulsars, we investigate the properties of this kind of objects. It is found that the energy per baryon decreases monotonously for increasing baryon number and reaches its minimum at the maximum baryon number, corresponding to the most massive strange star. Due to the quark depletion, an electric potential well for negatively charged particles is formed on the surface of the quark part, which may provide some unique observables. For a rotational bare strange star, a magnetic field with the typical strength of pulsars is generated.

We perform a systematic study of capture excitation functions by using an empirical coupled-channel model. In this model, a barrier distribution is used to take effectively into account the effects of couplings between the relative motion and intrinsic degrees of freedom. The shape of the barrier distribution is of an asymmetric Gaussian form. The effect of neutron transfer channels is also included in the barrier distribution. Based on the interaction potential between the projectile and the target, empirical formulas are proposed to determine the parameters of the barrier distribution. Theoretical estimates for barrier distributions and calculated capture cross sections together with experimental cross sections of 220 reaction systems with $182 \leqslant Z_{\rm P}Z_{\rm T} \leqslant 1640$ are tabulated. The results show that our empirical formulas work quite well in the energy region around the Coulomb barrier. This model can provide prediction of capture cross sections for the synthesis of superheavy nuclei as well as valuable information on capture and fusion dynamics., Comment: 120 pages, 32 figures, 3 tables, accepted for publication in Atomic Data and Nuclear Data Tables

We investigate the one-body dissipation dynamics in heavy-ion collisions of $^{16}{\rm O}$+$^{16}{\rm O}$ using a fully three-dimensional time-dependent Hartree-Fock (TDHF) theory with the modern Skyrme energy functional and without any symmetry restrictions. The energy dissipation is revealed to decrease in deep-inelastic collisions of the light systems as the bombarding energy increases owing to the competition between collective motion and single-particle degrees of freedom. The role of spin-orbit force is given particular emphasis in deep-inelastic collisions. The spin-orbit force causes a significant enhancement of the dissipation. The time-even coupling of spin-orbit force plays a dominant role at low energies, while the influence of time-odd terms is notable at high energies. About 40-65\% of the total dissipation depending on the different parameter sets is predicted to arise from the spin-orbit force. The theoretical fusion cross section has a reasonably good agreement with the experimental data, considering that no free parameters are adjusted to reaction dynamics in the TDHF approach., Comment: accepted for publication in Phys. Rev. C

The role of tensor force on the collision dynamics of $^{16}$O+$^{16}$O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25\%, while the calculation with tensor force T11 has good agreement with experimental cross section.

A large number of complete fusion excitation functions of reactions including the breakup channel were measured in recent decades, especially in the last few years. It allows us to investigate the systematic behavior of the breakup effects on the complete fusion cross sections. To this end, we perform a systematic study of the breakup effects on the complete fusion cross sections at energies above the Coulomb barrier. The reduced fusion functions F(x) are compared with the universal fusion functions which are used as a uniform standard reference. The complete fusion cross sections at energies above the Coulomb barrier are suppressed by the breakup of projectiles. This suppression effect for reactions induced by the same projectile is independent of the target and mainly determined by the lowest energy breakup channel of the projectile. There holds a good exponential relation between the suppression factor and the energy corresponding to the lowest breakup threshold., Comment: 10 pages, 9 figures; Fig. 9 and related discussions modified

Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier the occurrence of a third one was predicted by Mic-Mac model calculations in the 1970s, but contradictory results were later reported. In this paper, triple-humped barriers in actinide nuclei are investigated with covariant density functional theory (CDFT). Calculations are performed using the multidimensionally-constrained relativistic mean field (MDC-RMF) model, with functionals PC-PK1 and DD-ME2. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Two-dimensional PES's of $^{226,228,230,232}$Th and $^{232,234,236,238}$U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and $^{238}$U. The third minima in $^{230,232}$Th are very shallow, whereas those in $^{226,228}$Th and $^{238}$U are quite prominent. With PC-PK1 a third barrier is found only in $^{226,228,230}$Th. Single-nucleon levels around the Fermi surface are analyzed in $^{226}$Th, and it is found that the formation of the third minimum is mainly due to the $Z=90$ proton energy gap at $\beta_{20} \approx 1.5$ and $\beta_{30} \approx 0.7$. The possible occurrence of a third barrier in actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases with increasing neutron number. The origin of the third minimum is due to the proton $Z=90$ shell gap at relevant deformations., Comment: 10 pages, 7 figures; Phys. Rev. C, in press; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file

In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\beta_{\lambda\mu}$ with even $\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied., Comment: 5 pages, 5 figures; to be published in Proceedings of the 20th Nuclear Physics Workshop "Marie & Pierre Curie", Kazimierz, Poland, Sep. 25-29, 2013; references updated

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry directly connected with the small component of the nucleon Dirac wave function. Much effort has been made to study this symmetry in bound states. Recently, a rigorous justification of the PSS in single particle resonant states was achieved by examining the asymptotic behaviors of the radial Dirac wave functions: The PSS in single particle resonant states in nuclei is conserved exactly when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances were investigated by employing spherical square well potentials in which the PSS breaking part can be well isolated in the Jost function. A threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners were found when the depth of the square well potential varies from zero to a finite value., Comment: 4 pages, 2 figures; invited talk at the International School on Nuclear Physics, Neutron Physics and Applications, Sep 16-22, 2013, Varna, Bulgaria

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin $ST$ channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the isospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below the normal nuclear matter density, the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T=1 component is almost independent of isospin-asymmetry. As the density increases, the T=1 channel contribution becomes sensitive to the isospin-asymmetry and at high enough densities its isospin-dependence may even become more pronounced than that of the T=0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories., Comment: 5 pages, 3 figures

A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the study of neutron halos in deformed nuclei and the halo phenomenon in deformed weakly bound nuclei is investigated. Magnesium and neon isotopes are studied and some results are presented for the deformed neutron-rich and weakly bound nuclei 44Mg and 36Ne. The core of the former nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurrence of this decoupling effect are discussed., Comment: 7 pages, 2 figures; invited talk at the XXXV Brazilian Workshop on Nuclear Physics, Sep 2-6, 2012, Maresias, Brazil

The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [PRL 109, 072501 (2012)]. To understand more deeply the PSS, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated., Comment: 12 pages, 9 figures; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file; Phys. Rev. C, in press

We have developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) for finite nuclei in which the shape degrees of freedom \beta_{\lambda\mu} with even \mu, e.g., \beta_{20}, \beta_{22}, \beta_{30}, \beta_{32}, \beta_{40}, etc., can be described simultaneously. The functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. For the pp channel, either the BCS approach or the Bogoliubov transformation is implemented. The MDC-CDFTs with the BCS approach for the pairing (in the following labelled as MDC-RMF models with RMF standing for "relativistic mean field") have been applied to investigate multi-dimensional potential energy surfaces and the non-axial octupole $Y_{32}$-correlations in N=150 isotones. In this contribution we present briefly the formalism of MDC-RMF models and some results from these models. The potential energy surfaces with and without triaxial deformations are compared and it is found that the triaxiality plays an important role upon the second fission barriers of actinide nuclei. In the study of Y_{32}-correlations in N=150 isotones, it is found that, for 248Cf and 250Fm, \beta_{32} > 0.03 and the energy is lowered by the \beta_{32} distortion by more than 300 keV; while for 246Cm and 252No, the pocket with respect to \beta_{32} is quite shallow., Comment: 8 pages, 5 figures; invited talk at the XXXVI Mexican Symposium on Nuclear Physics, Hacienda Cocoyoc (Cocoyoc, Morelos, Mexico), Jan 7-10, 2013

By breaking both the axial and the spatial reflection symmetries, we develop multidimensionally constrained relativistic mean field (MDC-RMF) models. The nuclear shape is assumed to be invariant under the reversion of $x$ and $y$ axes, i.e., the intrinsic symmetry group is $V_{4}$ and all shape degrees of freedom $\beta_{\lambda\mu}$ with even $\mu$, such as $\beta_{20}$, $\beta_{22}$, $\beta_{30}$, $\beta_{32}$, $\beta_{40}$, $\dots$, are included self-consistently. The Dirac wave functions are expanded in an axially deformed harmonic oscillator basis. The RMF functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the nonlinear or density-dependent couplings. The pairing effects are taken into account with the BCS approach. The 1-, 2-, and 3-D potential energy surfaces (PES's) of $^{240}$Pu are illustrated for numerical checks and for the study of the effect of the triaxiality on the fission barriers. Potential energy curves of even-even actinide nuclei around the first and second fission barriers are studied systematically. Besides the first ones, the second fission barriers in these nuclei are also lowered considerably by the triaxial deformation. This lowering effect is independent of the effective interactions used in the RMF functionals. Further discussions are made about different predictions on the effect of the triaxiality between the macroscopic-microscopic and MDC-RMF models, possible discontinuities on PES's from self-consistent approaches, and the restoration of broken symmetries. MDC-RMF models give reasonably good description of fission barriers of even-even actinide nuclei. It is important to include both the nonaxial and the reflection asymmetric shapes simultaneously for the study of PES's and fission barriers of actinide nuclei and of those in unknown mass regions such as, e.g., superheavy nuclei., Comment: 16 pages, 8 figures, 2 tables; version published in Phys. Rec. C; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file

The effect of nuclear superfluidity on antimagnetic rotation bands in $^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed., Comment: 14 pages, 4 figures

In this contribution we present some results on the study of pseudospin symmetry (PSS) in single particle resonant states. The PSS is a relativistic dynamical symmetry connected with the small component of the nucleon Dirac wave function. Many efforts have been made to study this symmetry in bound states. We recently gave a rigorous justification of the PSS in single particle resonant states by examining the zeros of Jost functions corresponding to the small components of the radial Dirac wave functions and phase shifts of continuum states [1, Phys. Rev. Lett. 109 (2012) 072501]. We have shown that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Examples of exact conservation and breaking of this symmetry in single particle resonances are given for spherical square-well and Woods-Saxon potentials., Comment: 5 pages, 1 figures; invited talk at the 8th China-Japan Joint Nuclear Physics Symposium (CJJNPS 2012), Beijing, China, 15-19 October 2012

In this contribution we present some recent results about neutron halos in deformed nuclei. A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed and the halo phenomenon in deformed weakly bound nuclei is investigated. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Magnesium and neon isotopes are studied and detailed results are presented for the deformed neutron-rich and weakly bound nuclei 42Mg. The core of this nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurrence of this decoupling effect are discussed., Comment: 6 pages, 2 figures; invited talk at the 2nd Int. Conf. on Nuclear Structure & Dynamics (NSD12), Opatija, Croatia, 9-13 July 2012

The non-axial reflection-asymmetric $\beta_{32}$ shape in some transfermium nuclei with N=150, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No are investigated with multidimensional constrained covariant density functional theories. By using the density-dependent point coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that, for the ground states of $^{248}$Cf and $^{250}$Fm, the non-axial octupole deformation parameter $\beta_{32} > 0.03$ and the energy gain due to the $\beta_{32}$ distortion is larger than 300 keV. In $^{246}$Cm and $^{252}$No, shallow $\beta_{32}$ minima are found. The occurrence of the non-axial octupole $\beta_{32}$ correlations is mainly from a pair of neutron orbitals $[734]9/2$ ($\nu j_{15/2}$) and $[622]5/2$ ($\nu g_{9/2}$) which are close to the neutron Fermi surface and a pair of proton orbitals $[521]3/2$ ($\pi f_{7/2}$) and $[633]7/2$ ($\pi i_{13/2}$) which are close to the proton Fermi surface. The dependence of the non-axial octupole effects on the form of energy density functional and on the parameter set is also studied., Comment: 5 pages, 2 figures

The ground state band was recently observed in the superheavy nucleus 256Rf. We study the rotational properties of 256Rf and its neighboring even-even nuclei by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The kinematic and dynamic moments of inertia of the ground state bands in these nuclei are well reproduced by the theory. The spin of the lowest observed state in 256Rf is determined by comparing the experimental kinematic moments of inertia with the PNC-CSM calculations and agrees with previous spin assignment. The effects of the high order deformation varepsilon6 on the angular momentum alignments and dynamic moments of inertia in these nuclei are discussed., Comment: 7 pages, 6 figures; References and discussion about the cranking Nilsson model added, Fig. 3 modified and Figs. 5 and 6 added; Phys. Rev. C, in press

The pseudospin symmetry is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of pseudospin symmetry in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the pseudospin symmetry in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of pseudospin symmetry are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials., Comment: 5 pages, 2 figures; Figure 2 and discussion modified; Phys. Rev. Lett., in press

By using a newly developed di-nuclear system model with a dynamical potential energy surface---the DNS-DyPES model, hot fusion reactions for synthesizing superheavy nuclei (SHN) with the charge number Z = 112-120 are studied. The calculated evaporation residue cross sections are in good agreement with available data. In the reaction 50Ti+249Bk -> (299-x)119 + xn, the maximal evaporation residue (ER) cross section is found to be about 0.11 pb for the 4n-emission channel. For projectile-target combinations producing SHN with Z=120, the ER cross section increases with the mass asymmetry in the incident channel increasing. The maximal ER cross sections for 58Fe+244Pu and 54Cr + 248Cm are relatively small (less than 0.01 pb) and those for 50Ti+249Cf and 50Ti+251Cf are about 0.05 and 0.25 pb, respectively., Comment: 6 pages, 5 figures; Phys. Rev. C, in press

In order to describe the exotic nuclear structure in unstable odd-$A$ or odd-odd nuclei, the deformed relativistic Hartree Bogoliubov theory in continuum has been extended to incorporate the blocking effect due to the odd nucleon. For a microscopic and self-consistent description of pairing correlations, continuum, deformation, blocking effects, and the extended spatial density distribution in exotic nuclei, the deformed relativistic Hartree Bogoliubov equations are solved in a Woods-Saxon basis in which the radial wave functions have a proper asymptotic behavior at large $r$. The formalism and numerical details are provided. The code is checked by comparing the results with those of spherical relativistic continuum Hartree Bogoliubov theory in the nucleus $^{19}$O. The prolate deformed nucleus $^{15}$C is studied by examining the neutron levels and density distributions., Comment: 4 pages, 3 figures; Chin. Phys. Lett., in press

A deformed relativistic Hartree Bogoliubov (RHB) theory in continuum is developed aiming at a proper description of exotic nuclei, particularly those with a large spatial extension. In order to give an adequate consideration of both the contribution of the continuum and the large spatial distribution in exotic nuclei, the deformed RHB equations are solved in a Woods-Saxon (WS) basis in which the radial wave functions have a proper asymptotic behavior at large distance from the nuclear center. This is crucial for the proper description of a possible halo. The formalism of deformed RHB theory in continuum is presented. A stable nucleus, 20Mg and a weakly-bound nucleus, 42Mg, are taken as examples to present numerical details and to carry out necessary numerical checks. In addition, the ground state properties of even-even magnesium isotopes are investigated. The generic conditions of the formation of a halo in weakly bound deformed systems and the shape of the halo in deformed nuclei are discussed. We show that the existence and the deformation of a possible neutron halo depend essentially on the quantum numbers of the main components of the single particle orbitals in the vicinity of the Fermi surface., Comment: 19 pages, 12 figures; Expanded article of arXiv: 0909.1600 (Phys. Rev. C82, 011301R); Phys. Rev. C, in press

For the first time the potential energy surfaces of actinide nuclei in the $(\beta_{20}, \beta_{22}, \beta_{30})$ deformation space are obtained from a multi-dimensional constrained covariant density functional theory. With this newly developed theory we are able to explore the importance of the triaxial and octupole shapes simultaneously along the whole fission path. It is found that besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The outer barrier as well as the inner barrier are lowered by the triaxial deformation compared with axially symmetric results. This lowering effect for the reflection asymmetric outer barrier is 0.5 $\sim$ 1 MeV, accounting for $10 \sim 20%$ of the barrier height. With the inclusion of the triaxial deformation, a good agreement with the data for the outer barriers of actinide nuclei is achieved., Comment: 6 pages, 5 figures; corrected typos in Fig. 4, added refs. & discussions on numerical accuracy; Phys. Rev. C, in press

The rotational bands in nuclei with $Z \approx 100$ are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) and deformation parameters ($\varepsilon_2$ and $\varepsilon_4$) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-$A$ and odd-odd nuclei, and the bandhead energies of the 1-quasiparticle bands in odd-$A$ nuclei, are reproduced quite well by the PNC-CSM calculations. By analyzing the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the angular momentum alignment, the upbending mechanism in this region is understood clearly., Comment: 21 pages, 24 figures, extended version of arXiv: 1101.3607 (Phys. Rev. C83, 011304R); added refs.; added Fig. 4 and discussions; Phys. Rev. C, in press

With the relativistic Coulomb wave function boundary condition, the energies, widths and wave functions of the single proton resonant orbitals for $^{17}$Ne are studied by the analytical continuation of the coupling constant (ACCC) approach within the framework of the relativistic mean field (RMF) theory. Pairing correlations and contributions from the single-particle resonant orbitals in the continuum are taken into consideration by the resonant Bardeen-Cooper-Schrieffer (BCS) approach, in which constant pairing strength is used. It can be seen that the fully self-consistent calculations with NL3 and NLSH effective interactions mostly agree with the latest experimental measurements, such as binding energies, matter radii, charge radii and densities. The energy of $\pi$2s$_{1/2}$ orbital is slightly higher than that of $\pi1d_{5/2}$ orbital, and the occupation probability of the $(\pi$2s$_{1/2})^2$ orbital is about 20%, which are in accordance with the shell model calculation and three-body model estimation.

The shapes of light normal nuclei and $\Lambda$ hypernuclei are investigated in the $(\beta, \gamma)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $\gamma$ direction, differ a lot for several nuclei. For $\Lambda$ hypernuclei, in most cases, the addition of a $\Lambda$ hyperon alters slightly the location of the ground state minimum towards the direction of smaller $\beta$ and softer $\gamma$ in the potential energy surface $E \sim (\beta, \gamma)$. There are three exceptions, namely, $^{13}_\Lambda$C, $^{23}_\Lambda$C, and $^{31}_\Lambda$Si in which the polarization effect of the additional $\Lambda$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei., Comment: 11 pages, 3 figures; added references and arguments in Sections III and IV; to be published in Phys. Rev. C

The recently observed high-spin rotational bands in odd-$A$ nuclei $^{247, 249}$Cm and $^{249}$Cf [Tandel \textit{et al.}, Phys. Rev. C 82 (2010) 041301R] are investigated by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency $\omega$ are reproduced very well by the PNC-CSM calculations. By examining the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals to the angular momentum alignment in each major shell, the level crossing and upbending mechanism in each nucleus is understood clearly., Comment: 6 pages, 5 figures, to be published in Phys. Rev. C

Halo phenomenon in deformed nuclei is studied by using a fully self-consistent deformed relativistic Hartree-Bogoliubov model in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Taking a deformed neutron-rich and weakly bound nucleus $^{44}$Mg as an example and by examining contributions of the halo, deformation effects, and large spatial extensions, we show a decoupling of the halo orbitals from the deformation of the core., Comment: 6 pages, 2 figures, to appear in the proceedings of the International Nuclear Physics Conference (INPC 2010), July 4-9 2010, Vancouver

The stability of excited superheavy nuclei (SHN) with $100 \leq Z \leq 134$ against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. In present calculations the neutron separation energies and shell correction energies are consistently taken from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z=115 and N=179. It turns out that this island of stability persists for excited SHN in the sense that the calculated survival probabilities in the 1n-channel of excited SHN at the optimal excitation energy are maximized around Z=115 and N=179. This indicates that the survival probability in the 1n-channel is mainly determined by the nuclear shell effects., Comment: 5 pages, 3 EPS figures, to be published in "Science China Physics, Mechanics and Astronomy"

The spherical-box approach is extended to calculate the resonance parameters and the real part of the wave function for single particle resonances in a potential containing the long-range Coulomb interaction. A model potential is taken to demonstrate the ability and accuracy of this approach. The calculated resonance parameters are compared with available results from other methods. It is shown that in the presence of the Coulomb interaction, the spherical-box approach works well for not so broad resonances. In particular, for very narrow resonances, the present method gives resonance parameters in a very high precision., Comment: 10 pages, 5 EPS figures; to be published in J. Phys. B

Halo phenomena in deformed nuclei are investigated within a deformed relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Contributions of the halo, deformation effects, and large spatial extensions of these systems are described in a fully self-consistent way by the DRHB equations in a spherical Woods-Saxon basis with the proper asymptotic behavior at large distance from the nuclear center. Magnesium and neon isotopes are studied and detailed results are presented for the deformed neutron-rich and weakly bound nucleus $^{44}$Mg. The core of this nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the occurence of this decoupling effects are discussed., Comment: 5 pages, 6 EPS figures; to be published in Phys. Rev. C

Starting from the WKB approximation, a new barrier penetration formula is proposed for potential barriers containing a long-range Coulomb interaction. This formula is especially proper for the barrier penetration with penetration energy much lower than the Coulomb barrier. The penetrabilities calculated from the new formula agree well with the results from the WKB method. As a first attempt, this new formula is used to evaluate alpha decay half-lives of atomic nuclei and a good agreement with the experiment is obtained., Comment: RevTeX4, 7 pages, 3 figures; to be published in Int. J. Mod. Phys. E

We develop the real stabilization method within the framework of the relativistic mean field (RMF) model. With the self-consistent nuclear potentials from the RMF model, the real stabilization method is used to study single-particle resonant states in spherical nuclei. As examples, the energies, widths and wave functions of low-lying neutron resonant states in $^{120}$Sn are obtained. These results are compared with those from the scattering phase shift method and the analytic continuation in the coupling constant approach and satisfactory agreements are found., Comment: 9 pages, 7 figures, Phys. Rev. C, in press

A non-convergent difficulty near level-repulsive region is discussed within the self-consistent mean-field theory. It is shown by numerical and analytic studies that the mean-field is not realized in the many-fermion system when quantum fluctuations coming from two-body residual interaction and quadrupole deformation are larger than an energy difference between two avoided crossing orbits. An analytic condition indicating a limitation of the mean-field concept is derived for the first time.

The projected shell model is used to study the multi-quasiparticle and collective excitations of 178Hf. With an axially symmetric basis, the spin-16 isomer at 2.4 MeV appears to be well separated in energy/spin space from other configurations. However, projected energy surface calculations suggest that 178Hf has significant softness to axially asymmetric shapes, which can strongly modify the level distribution. The implications for photodeexitation of the isomer are discussed., Comment: 8 pages, 4 figures

A shape change of the self-consistent mean-field induced by a configuration change is discussed within the conventional constrained Hartree-Fock (CHF) theory. It is stressed that a single-particle level crossing dynamics should be treated carefully, because the shape of the mean-field in such a finite many-body system as the nucleus strongly changes depending on its configuration. This situation is clearly shown by applying an adiabatic assumption, where the most energetically favorable single-particle states are assumed to be occupied. The excited HF states and the continuously-connected potential energy curves are given by applying the configuration dictated CHF method. The effect of pairing correlation is discussed in the level crossing region. Triaxial deformed results in our Hartree-Fock-Bogoliubov (HFB) calculation with Gogny force nicely reproduce the available experimental data of Ge isotopes. From our numerical calculation, it is concluded that the CHFB state is more fragile than the CHF state in the level crossing region., Comment: 25 pages, 6 figures and 2 tables

This paper was withdrawn by arXiv admins because of inappropriate and unverifiable claims of appropriation., Comment: This paper has been withdrawn

A modified method for calculating the pion vacuum susceptibility from an effective quark-quark interaction model is derived. Within this approach it is shown that the pion vacuum susceptibility is free of ultraviolet divergence and is much smaller than the previous estimations., Comment: 13 pages, 2 figures

A method for obtaining the small current quark mass effect on the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach both explicit and dynamical chiral symmetry breaking has been analyzed. a comparision with previous results is given., Comment: 10 pages, 2 figures

According to Wick's theorem, the second order self-energy corrections of hadrons in the hot and dense nuclear matter are calculated. Furthermore, the Feynman rules are summarized, and an effective formulation on quantum hadrodynamics at finite temperatures and densities is evaluated. As the strong couplings between nucleons are considered, the self-consistency of this method is discussed in the framework of relativistic mean-field approximation. Debye screening masses of the scalar and vector mesons in the hot and dense nuclear matter are calculated with this method in the relativistic mean-field approximation. The results are different from those of thermofield dynamics and Brown-Rho conjecture. Moreover, the effective masses of the photon and the nucleon in the hot and dense nuclear matter are discussed., Comment: Final version, Changed title, 15 pages, 2 tables, 2 figures, Published on Communications in Theoretical Physics

The development on relativistic nuclear many-body theories is reviewed. The second order self-energies of hadrons are calculated from $\hat{S}_2$ matrix, and then an effective method to solve nuclear many-body problems, sum rules on quantum hadrodynamics, is summarized. The differences between this method and quantum hadrodynamics are discussed. The effective nucleon mass in the nuclear matter is redefined in the relativistic Hartree approximation, and a self-consistent relativistic mean-field model based on quantum hadrodynamics 2 is proposed. It is pointed out that the original definition on effective nucleon mass in quantum hadrodynamics 2 is not self-consistent, and all the parameters in the relativistic mean-field approximation should be fixed again according to the new definition., Comment: 16 pages, 4 figures, REVTEX4. Submitted to Phys. Rev. C

The Debye screening masses of the $\sigma$, $\omega$ and neutral $\rho$ mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. It shows a different result with Brown-Rho scaling, which implies a reduction in the mass of all the mesons in the nuclear matter except the pion. Replacing the masses of the mesons with their corresponding screening masses in Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the non-linear self-coupling terms of mesons., Comment: 14 pages, 3 figures, REVTEX4, Accepted for publication in Int. J. Mod. Phys. E

Electromagnetic field in nuclear matter and nuclei are studied. In the nuclear matter, because the expectation value of the electric charge density operator is not zero, different in vacuum, the U(1) local gauge symmetry of electric charge is spontaneously broken, and consequently, the photon gains an effective mass through the Higgs mechanism. An alternative way to study the effective mass of photon is to calculate the self-energy of photon perturbatively. It shows that the effective mass of photon is about $5.42MeV$ in the symmetric nuclear matter at the saturation density $\rho_0 = 0.16fm^{-3}$ and about $2.0MeV$ at the surface of ${}^{238}U$. It seems that the two-body decay of a massive photon causes the sharp lines of electron-positron pairs in the low energy heavy ion collision experiments of ${}^{238}U+{}^{232}Th$ ., Comment: 10 pages, 2 figures, 1 table, REVTEX4, submitted to Int. J. Mod. Phys. E