The shell-model-like approach (SLAP) based on cranking covariant density functional theory (CDFT) with a separable pairing force is developed. The developed cranking CDFT-SLAP with separable pairing force is applied to investigate the rotational spectra in $^{60}$Fe, including the positive-parity yrast band and two negative-parity signature partner bands, in comparison with the cranking CDFT-SLAP with monopole pairing force calculations. Excellent agreement with the available data is achieved.
A separable form of the Gogny pairing force is implemented in tilted axis cranking covariant density functional theory for the description of rotational bands in open shell nuclei. The developed method is used to investigate the yrast sequence of 109Ag for an example. The experimental energy spectrum, angular momenta, and electromagnetic transition probabilities are well reproduced by taking into account pairing correlations with the separable pairing force. An abrupt transition of the rotational axis from the long-intermediate plane to the long-short one is obtained and discussed in detail.
Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectivelyinterpreted in terms of the shears mecha-nism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing series of nuclear ground-states and excited state…
The shell-model-like approach is implemented to treat the cranking many-body Hamiltonian based on the covariant density functional theory including pairing correlations with exact particle number conservation. The self-consistency is achieved by iterating the single-particle occupation probabilities back to the densities and currents. As an example, the rotational structures observed in the neutron-rich nucleus $^{60}$Fe are investigated and analyzed. Without introducing any \emph{ad hoc} parameters, the bandheads, the rotational spectra, and the relations between the angular momentum and rota…
The global dynamical correlation energies for 575 even-even nuclei with proton numbers ranging from Z=8 to Z=108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematicall…
Excitations of chiral rotation observed in triaxial nuclei and magnetic and/or antimagnetic rotations seen in near-spherical nuclei have attracted a lot of attention. Unlike conventional rotation in well-deformed or superdeformed nuclei, here the rotational axis is not necessary coinciding with any principal axis of the nuclear density distribution. Thus, tilted axis cranking is mandatory to describe these excitations self-consistently in the framework of covariant density functional theory (CDFT). We will briefly introduce the formalism of tilted axis cranking CDFT and its application for mag…
Well-known examples of shears bands in the nuclei 198Pb and 199Pb are investigated within tilted axis cranking relativistic mean-field theory. Energy spectra, the relation between spin and rotational frequency, deformation parameters and reduced $M1$ and $E2$ transition probabilities are calculated. The results are in good agreement with available data and with calculations based on the phenomenological pairing plus-quadrupole-quadrupole tilted-axis cranking model. It is shown that covariant density functional theory provides a successful microscopic and fully self-consistent description of ma…
The observed shears bands in 198Pb and 199Pb are investigated within the framework of tilted axis cranking covariant density functional theory, and the separable pairing force is adopted to consider the pairing correlations. The energy spectra, total angular momenta, and transition probabilities agree well with the experimental data. The bandhead energy differences are reproduced satisfactorily without any ad hoc renormalizations when the pairing correlations are taken into account. The angular momentum vectors are discussed in detail to analyze the pairing effects on magnetic rotations.
The paper considers the electrodisintegration of the deuteron for kinematic conditions of the JLab experiment E-94-019. The calculations have been performed within the covariant Bethe-Salpeter approach with a separable kernel of nucleon-nucleon interactions. The results have been obtained using the relativistic plane wave impulse approximation and compared with experimental data and other models. The influence of nucleon electromagnetic form factors has been investigated.
Two different methods of the covariant relativistic separable kernel construction in the Bethe-Salpeter approach are considered. One of them leads in the center-of-mass system of two particles to the quasipotential equation. The constructed 4-dimensional covariant functions are used to reproduce neutron-proton phase shifts for total angular momenta $J=0,1$. Obtained results are compared with other model calculations.
The stability of the linear chain structure of three $α$ clusters for $^{12}$C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods. Starting from a twisted three $α$ initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of $\sim$2.0 MeV to $\sim$2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributi…
Within a covariant Bethe-Salpeter approach a rank-six separable neutron-proton interaction kernel for the triplet coupled $^3S_1$-$^3D_1$ partial-wave state is constructed. Two different methods of a relativistic generalization of initially nonrelativistic form factors parametrizing the kernel are considered. The model parameters are determined by fitting the elastic $^3S_1$ and $^3D_1$ phase shifts and the triplet scattering length as well as the asymptotic $D/S$ ratio of the deuteron wave functions and the deuteron binding energy. The $D$-state probability constraints 4-7\% are taken into ac…
High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by t…
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significa…
The three-dimensional tilted axis cranking covariant density functional theory (3D-TAC CDFT) is used to study the chiral modes in $^{135}$Nd. By modeling the motion of the nucleus in rotating mean field as the interplay between the single-particle motions of several valence particle(s) and hole(s) and the collective motion of a core-like part, a classical Routhian is extracted. This classical Routhian gives qualitative agreement with the 3D-TAC CDFT result for the critical frequency corresponding to the transition from planar to aplanar rotation. Based on this investigation a possible understa…
In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe-Salpeter equation for the T matrix is considered in the rank- one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables { low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels forthe partial-wave channels with total angular momentum J = 0 (1S0, 3P0) and J = 1 (3S1 -3D1, 1P1, 3P1) are constructed.
The toroidal states in $^{28}$Si with spin extending to extremely high are investigated with the cranking covariant density functional theory on a 3D lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are obtained, and their stabilities against particle emissions are studied by analyzing the density distributions and potentials. The excitation energies of the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed three resonances extracted from the 7-$α$ de-excitation of $^{28}$Si. The $α$ clustering of these toroidal states is supported by the $α$-…
A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref. [1]. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in neutron subsystem. However, the situation is less certain in proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent …
The solution for the nucleon-nucleon T matrix in the framework of the covariant Bethe-Salpeter approach for a two spin-one-half particle system with a separable kernel of interaction is analyzed. The explicit analytical connection between parameters of the separable kernel and low energy scattering parameters, deuteron binding energy and phase shifts is established.Covariant separable kernels for positive-energy partial channels with total angular momentum J=0 (1S0+, 3P0+) and J=1 (3S1+-3D1+, 1P1+, 3P1+) are constructed by using obtained relations.
Recent developments of the covariant Bethe-Salpeter (BS) approach with the use of the separable interaction for the deuteron are reviewed. It is shown that the BS formalism allows a covariant description of various electromagnetic reactions like the lepton-deuteron scattering, deuteron electro-disintegration, deep inelastic scattering (DIS) of leptons on light nuclei. The procedure of the construction of the separable nucleon-nucleon (NN) interaction is discussed. The BS formalism facilitates analysis of the role of the P-waves (negative energy components) in the electromagnetic properties of …
We investigate the relation between the rank I separable potential for the covariant Bethe-Salpeter equation and the one-boson-exchange potential. After several trials of the parameter choices, it turns out that it is not always possible to reproduce the phase-shifts calculated from a single term of the one-boson-exchange potential especially of the $σ$-exchange term, separately by the rank I separable potential. Instead, it is shown that the separable potential is useful to parameterize the total nucleon-nucleon interaction.
A study of 4$α$ linear-chain structure in high-lying collective excitation states of $^{16}$O with a covariant density functional theory is presented. The low-spin states are obtained by configuration mixing of particle-number and angular-momentum projected quadrupole deformed mean-field states with generator coordinate method. The high-spin states are determined by cranking calculations. These two calculations are based on the same energy density functional PC-PK1. We have found a rotational band at low-spin with the dominated intrinsic configuration considered to be the one that 4$α$ cluster…
Covariant density functional theory and the tilted axis cranking method are used to investigate antimagnetic rotation (AMR) in nuclei for the first time in a fully self-consistent and microscopic way. The experimental spectrum as well as the B(E2) values of the recently observed AMR band in 105Cd are reproduced very well. This gives a further strong hint that AMR is realized in specific bands in nuclei.
Following the previous letter on the first microscopic description of the antimagnetic rotation (AMR) in 105Cd, a systematic investigation and detailed analysis for the AMR band in the frame-work of tilted axis cranking (TAC) model based on covariant density functional theory are carried out. After performing the microscopic and self-consistentTAC calculations with an given density functional, the configuration for the observed AMR band in 105Cd is obtained from the single-particle Routhians. With the configuration thus obtained, the tilt angle for a given rotational frequency is determined se…
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in the two fermions in an external potential and in the three-fermion problems. The covariance of the two-fermion propagators insures the covariance of the two-body equations obtained by switching off the external potential, or by switching off all interactions between any pair of two fermions and the third one, even if the series giving the 3D potential is limi…
Covariant density functional theory and three-dimensional tilted axis cranking are used to investigate multiple chirality in nuclear rotation for the first time in a fully self-consistent and microscopic way. Two distinct sets of chiral solutions with negative and positive parities, respectively, are found in the nucleus 106Rh. The negative-parity solutions reproduce well the corresponding experimental spectrum as well as the B(M1)/B(E2) ratios of the transition strengths. This indicates that a predicted positive-parity chiral band should also exist. Therefore, it provides a further strong hin…
The structure of low-lying excitation states of even-even $N=40$ isotones is studied using a five-dimensional collective Hamiltonian with the collective parameters determined from the relativistic mean-field plus BCS method with the PC-PK1 functional in the particle-hole channel and a separable paring force in the particle-particle channel. The theoretical calculations can reproduce not only the systematics of the low-lying states along the isotonic chain but also the detailed structure of the spectroscopy in a single nucleus. We find a picture of spherical-oblate-prolate shape transition alon…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties sensitively depend on time-odd mean fields and currents in density functional theories. Moreover, they show a considerable interplay of collective and single-particle degrees of freedom. In this chapter, I discuss the basic features of the description of rotating nuclei in one-dimensional cranking approximation of covariant density functional theory. The succ…
The dynamics of chiral nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. The experimental energies of the two pairs of the chiral doublet bands in $^{135}$Nd are well reproduced without any adjustable parameters beyond the well-defined density functional. A novel mechanism, i.e., chiral precession, is revealed from the microscopic dynamics of the total angular momentum in the body-fixed frame, whose harmonicity is associated with a transi…
Recent microscopic studies, based on the theoretical framework of nuclear energy density functionals, have analyzed dynamic (least action) and static (minimum energy) fission paths, and it has been shown that in addition to the important role played by nonaxial and/or octupole collective degrees of freedom, fission paths crucially depend on the approximations adopted in calculating the collective inertia. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm is explored. The fission paths, action integrals and the corresponding half-lives predicted by the functionals PC-PK1 and DD-P…
A systematic investigation of even-even superheavy elements in the region of proton numbers $100 \leq Z \leq 130$ and in the region of neutron numbers from the proton-drip line up to neutron number $N=196$ is presented. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of fini…
A systematic investigation of octupole deformed nuclei is presented for even-even systems with $Z\leq 106$ located between the two-proton and two-neutron drip lines. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range. This allows us to assess theoretical uncerta…
The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $N\approx60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calcula…
Recently, a relativistic chiral nucleon-nucleon interaction is formulated up to leading order which provides a good description of the phase shifts of $J\leq1$ partial waves [Chin. Phys. C 42 (2018) 014103]. Nevertheless, a separable regulator function that is not manifestily covariant was used in solving the relativistic scattering equation. In the present work, we first propose a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging $^1S_0$ channel which features several low-energy scales. In addition to being self…
A systematic global investigation of differential charge radii has been performed within the CDFT framework for the first time. Theoretical results obtained with conventional covariant energy density functionals and separable pairing interaction are compared with experimental differential charge radii in the regions of the nuclear chart in which available experimental data crosses neutron shell closures at N = 28, 50, 82 and 126. The analysis of absolute differential radii of different isotopic chains and their relative properties indicate clearly that such properties are reasonably well descr…
