Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

Tilted Axis Rotation of ^(57)Mn in Covariant Density Functional Theory

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.

Robustness of the octupole collectivity in 144Ba within the cranking covariant density functional theory in 3D lattice

The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).

Three-dimensional potential energy surface for fission of^(236)U within covariant density functional theory

We calculate the three-dimensional potential energy surface(PES)for the fission of the compound nucleus^(236)U using covariant density functional theory with constraints on the axial quadrupole and octupole deformations(β_(2),β_(3))coexistence of the elongated and compact fission modes is predicted for comes shallow across a large range of quadrupole and octupole deformations for small scission line in the(β_(2),β_(3))plane extends to a shallow band,leading to fluctuations of several to ten MeV in the estimated total kinetic energies and of several to approximately ten nucleons in the fragment masses.

Level density of odd-A nuclei at saddle point

Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated via the convolution of the intrinsic level density and the collective level density.The intrinsic level densities are obtained in the finite-temperature covariant density functional theory,which takes into account the nuclear deformation and pairing self-consistently.For saddle points on the free energy surface in the(β_(2),γ)plane,the entropy and the associated intrinsic level density are compared with those of the global minima.By introducing a quasiparticle to the two neighboring even–even core nuclei,whose properties are determined by the five-dimensional collective Hamiltonian model,the collective levels of the odd-A nuclei are obtained via the CQC model.The total level densities of the^(234-240)U agree well with the available experimental data and Hilaire’s result.Furthermore,the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.

Strangeness S=-2 baryon-baryon interactions and femtoscopic correlation functions in covariant chiral effective field theory

We study the baryon-baryon interactions with strangeness S=-2 and corresponding momentum correlation functions in leading order covariant chiral effective field theory.The relevant low energy constants are determined by fitting to the latest HAL QCD simulations,taking into account all the coupled channels.Extrapolating the so-obtained strong interactions to the physical point and considering both quantum statistical effects and the Coulomb interaction,we calculate the ΛΛ and Ξ^(-)p correlation functions with a spherical Gaussian source and compare them with recent experimental data.We find a good agreement between our predictions and the experimental measurements by using the source radius determined in proton-proton correlations,which demonstrates the consistency between theory,experiment,and lattice QCD simulations.Moreover,we predict the Σ^(+)Σ^(+),Σ^(+)Λ,and Σ^(+)Σ^(-) interactions and corresponding momentum correlation functions.We further investigate the influence of the source shape and size of the hadron pair on the correlation functions studied and show that the current data are not very sensitive to the source shape.Future experimental measurements of the predicted momentum correlation functions will provide a non-trivial test of not only SU(3) flavor symmetry and its breaking but also the baryon-baryon interactions derived in covariant chiral effective field theory.

Evolution of N=20,28,50 shell closures in the 20≤Z≤30 region in deformed relativistic Hartree-Bogoliubov theory in continuum

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≤Z≤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≤Z≤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,mainly 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 suggest the contrary,and therefore further research is needed.

α-cluster structure of ^(12)C and ^(16)O in the covariant density functional theory with a shell-model-like approach

The α-cluster structures for 12^C and 16^O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like approach. The ground states of 12^C and 160 have been calculated and the density distributions demonstrate an equilateral triangle 3α clustering for 12^C and a regular tetrahedron 4α clustering for 16^O The existence of linear nα chain structure of both 12^C and 16^O is revealed at high quadrupole deformation.

Nuclear magnetic moments in covariant density functional theory

Nuclear magnetic moment is an important physical variable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be successful in describing the nuclear ground-states and excited states properties. However, a long-standing problem is its failure to predict magnetic moments. This article reviews the recent progress in the description of the nuclear magnetic moments within the covariant density functional theory. In particular, the magnetic moments of spherical odd-A nuclei with doubly closed shell core plus or minus one nucleon and deformed odd-A nuclei.

Exact treatment of pairing correlations in Yb isotopes with covariant density functional theory

The effects of pairing correlation in Yb isotopes are investigated by covariant density functional theory with pairing correlations and blocking effects treated exactly by a shell model like approach （SLAP）. Experimental one- and two-neutron separation energies are reproduced quite well. The traditional BCS calculations always give larger pairing energies than those given by SLAP calculations, particularly for the nuclei near the proton and neutron drip lines. This may be caused because many of the single particle orbits above the Fermi surface are involved in the BCS calculations, but many of them are excluded in the SLAP calculations.

Magnetic moments of odd-A aluminum isotopes in covariant density functional theory

The ground-state properties,especially the magnetic moments,of odd-A aluminum isotopes have been studied and well reproduced in covariant density functional theory after considering the rotational coupling.The present calculations support the rotational structure in the ground state of odd-A aluminum isotopes,i.e.the ground state 5/2^+is built on the intrinsic state 5/2[202].In addition,the contribution from the time-odd fields is also discussed.

Covariant open string field theory on multiple Dp-branes

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind （BFSS） matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya （IKKT） matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in （p＋1）-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.

Center-of-mass correction and rotational correction in covariant density functional theory

Center-of-mass（c.m.） correction and rotational correction in even-even Ge isotopes are systematically investigated within the triaxially deformed relativistic Hartree-Bogoliubov model using the PC-PK1 force. The shell effect and deformation effect on the microscopic c.m. correction and rotational correction are discussed, and the importance of both corrections on reproducing the binding energy is demonstrated.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation,pairing correlations and continuum in a unified way.In order to consider the triaxial deformation,the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space.In order to take the pairing correlations into account and treat the continuum properly,by using the Dirac Woods–Saxon basis,which has correct asymptotic behavior,the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved.The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented.Taking an axially deformed nucleus24Ne and a triaxially deformed nucleus76Ge as examples,the numerical checks are performed.A weakly bound nucleus112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters.In addition,the ground-state properties of even–even germanium isotopes are investigated.The evolutions of two-neutron separation energy,deformation,root-mean-square radii and density distribution with mass number are analyzed.The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed.It is found that the neutron drip line is extended from114Ge to118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum

We extend the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)to go beyondmean-field framework by performing a two-dimensional collective Hamiltonian.The influences of dynamical correlations on the ground-state properties are examined in different mass regions,picking Se,Nd,and Th isotopic chains as representatives.It is found that the dynamical correlation energies(DCEs)and the rotational correction energies E_(rot) in the cranking approximation have an almost equivalent effect on the description of binding energies for most deformed nuclei,and the DCEs can provide a significant improvement for the(near)spherical nuclei close to the neutron shells and thus reduce the rms deviations of S_(2n) by≈17%.Furthermore,it is found that the DCEs are quite sensitive to the pairing correlations;taking ^(148)Nd as an example,a 10%enhancement of pairing strength can raise the DCE by≈37%.

Leading order relativistic hyperon-nucleon interactions in chiral effective field theory

We apply a recently proposed covariant power counting in nucleon-nucleon interactions to study strangeness S =-1 ΛN-Σ N interactions in chiral effective field theory. At leading order, Lorentz invariance introduces 12 low energy constants, in contrast to the heavy baryon approach, where only five appear. The Kadyshevsky equation is adopted to resum the potential in order to account for the non-perturbative nature of hyperon-nucleon interactions.A fit to the 36 hyperon-nucleon scattering data points yields χ2 16, which is comparable with the sophisticated phenomenological models and the next-to-leading order heavy baryon approach. However, one cannot achieve a simultaneous description of the nucleon-nucleon phase shifts and strangeness S =-1 hyperon-nucleon scattering data at leading order.

The interplay of single-particle and collective motions in the low-lying states of ^(21)_(A)Ne with quadrupole-octupole correlations

The beyond mean-field approach for low-lying hypernuclear states is extended by mixing the configurations associated with both single-particle and quadrupole-octupole collective excitations within the generator coordinate method based on a covariant den-sity functional theory.The method is demonstrated in the application to the low-lying states of 21ΛNe,where the configurations with theΛhyperon occupying the first(Λ_(s))and second(Λ_(p))lowest-energy states are considered.The results indicate that the positive-parity states are dominated by theα+^(12)C+α+Λ_(s) structure.In contrast,the low-lying negative-parity states are domi-nated by a strong admixture ofα+16O+Λ_(s) structure andα+12C+α+Λ_(p) structure due to the inclusion of octupole correlations.As a result,the low-lying negative-parity states become much lower than what is expected from the previous studies without the mixing,and the electric multipole transition strengths are significantly quenched.

Low-lying state investigations of odd-A Mn isotopes around N=28

Based on the systematic studies for low-lying states of the odd-A^(49-57)Mn isotopes,the groundstates inversion and the rotational properties of a ground-state-based sequence are revealed and discussed.The energy levels of low-lying states and electromagnetic moments in odd-A^(49-57)Mn isotopes have been well reproduced in shell-model calculations,and the above phenomena could be understood with obviously different occupation numbers in proton orbitals such asπf_(7/2)andπp_(3/2),which changes similarly with the obtained quadrupole deformation in covariant density functional theory(CDFT).After considering the coupling of collective rotation and intrinsic single-particle motion,the available experimental magnetic moments in53Mn and adjacent nuclei can be well explained with CDFT.The present calculations suggest that the 5/2^(-)and 7/2^(-)states in53Mn are formed byπ5/2^(-)[312]andπ7/2^(-)[303]respectively.Together with the behavior of levels,this provides proofs for the level sequences of low-lying states in53Mn distinct from the K^(π)=5/2^(-)rotational band in^(49)Cr and other odd-A Mn isotopes.

Density-dependent relativistic mean field approach and its application to single-Λhypernuclei in oxygen hyperisotopes

The in-medium feature of nuclear force, which includes both nucleon-nucleon( NN) and hyperon-nucleon( ΛN) interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new ΛN effective interaction in the covariant density functional(CDF) theory, namely, DD-LZ1-Λ1, is obtained by fitting the experimental data ofΛ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of Λ1p spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of theΛ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei,and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium NN interactions and core polarization effects.

Leading order relativistic chiral nucleon-nucleon interaction

Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian.We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the;S——0 and;P;phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J≥1, the relativistic results are almost the same as their leading order non-relativistic counterparts.