Relativistic Mean Field Calculations Research Articles

Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the π-meson and ρ-tensor (ρ-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta (l˜). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-l˜ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the ρ-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.

Prolate-oblate shape transitions and O(6) symmetry in even-even nuclei: A theoretical overview

Abstract Prolate to oblate shape transitions have been predicted in an analytic way in the framework of the Interacting Boson Model (IBM), determining O(6) as the symmetry at the critical point. Parameter-independent predictions for prolate to oblate transitions in various regions on the nuclear chart have been made in the framework of the proxy-SU(3) and pseudo-SU(3) symmetries, corroborated by recent non-relativistic and relativistic mean field calculations along series of nuclear isotopes, with parameters fixed throughout, as well as by shell model calculations taking advantage of the quasi-SU(3) symmetry. Experimental evidence for regions of prolate to oblate shape transitions is in agreement with regions in which nuclei bearing the O(6) dynamical symmetry of the IBM have been identified, lying below major shell closures. In addition, gradual oblate to prolate transitions are seen when crossing major nuclear shell closures, in analogy to experimental observations in alkali clusters.

Pseudospin symmetry in resonant states in deformed nuclei

Pseudospin symmetry (PSS) plays critical roles in the formation of many physical phenomena, and has been studied extensively from spherical nuclei to deformed nuclei. However, there remains an open question about the PSS in resonant states in deformed systems. For the first time, we investigate the PSS in resonant states in deformed nuclei by solving the Dirac equation in the complex-momentum representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field (RMF) calculations. Taking 170Yb as an example, we explore the PSS in the single-particle resonant states by examining the energies, widths and the density distribution. Compared with the bound states, the pseudospin splittings between the resonant pseudospin doublets are found to be small, and the radial density distributions of pseudospin doublets look very similar, which indicates that the PSS of resonant states is well reserved in deformed nuclei. Moreover, we have comprehensively studied the dependencies of the PSS on nuclear deformations and the shape of potential, which are helpful to recognize the evolution of resonant pseudospin doublets in weakly-bound deformed nuclei and understand their exotic properties.

Shape coexistence and possible isomers in 117Sn

Excited states of 117Sn have been populated using the fusion-evaporation reaction 114Cd(7Li, 1p3n) at a beam energy of 48[Formula: see text]MeV. A total of nine new transitions have been identified and added into the level scheme of 117Sn. Based on the systematical comparisons with the neighboring Sn isotopes and the configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations, a collective structure and two isomers are proposed to exist in 117Sn. The phenomenon of shape coexistence has been extended to A = 117 in odd-A Sn isotopes for the first time.

Possible collective band in neutron-rich 119Sn * *Partly supported by the Major Program of Natural Science Foundation of Shandong Province (ZR2020ZD30), the National Natural Science Foundation of China (12075137, 12075138, 11975315, U1867210, U1932209), and the Young Scholars Program of Shandong University

Excited states of 119Sn have been studied using an in-beam γ-ray spectroscopic technique following the incomplete fusion of 7Li on a 116Cd target at a beam energy of 42 MeV. A new bandlike structure is proposed to result from deformed two-particle-two-hole (2p-2h) proton excitations across the Z = 50 closed shell based on the systematics of odd-A Sn isotopes and configuration-fixed constrained triaxial relativistic mean-field calculations. This observation extends the boundaries of the deformed 2p-2h collective band to A = 119 in Sn isotopes.

Investigation of pseudospin and spin symmetries in relativistic mean field theory combined with a similarity renormalization group approach

Similarity renormalization group (SRG) is combined with the relativistic mean-field (RMF) theory, the Schr\"odinger-like Hamiltonian describing the motion of nucleon is obtained. The Hamiltonian with the scalar and vector potential from the self-consistent RMF calculations is used to explore the pseudospin and spin symmetries and their evolution with mass number for Sn isotopes. The contribution of every term to the pseudospin (spin) energy splitting is extracted. The spin energy splitting comes almost entirely from spin-orbit coupling, whereas the pseudospin energy splitting is also dominated by nonrelativistic and dynamical terms. The magnitude of the splitting is related to the radial, angular, and isospin quantum numbers of the doublet. The isospin dependence of pseudospin (spin) symmetry comes from the nonrelativistic term (the spin-orbit coupling). The pseudospin symmetry of neutron is superior to that of proton from the weakening of nonrelativistic and dynamical breaking. These results are helpful to understand the origin and breaking mechanism of pseudospin and spin symmetries.

Extraction of the second and fourth radial moments of nuclear charge density from the elastic electron-nucleus scattering

The expression for the radial moments of the nuclear charge density has been discussed under the plane wave Born approximation method recently, which is significant to investigate the nuclear surface thickness and neutron distribution radius. In this paper, we extend the studies of extracting second-order moment and fourth-order moment from the Coulomb form factors |F C(q)|2 by the distorted wave Born approximation (DWBA) at the small momentum transfer q region. Based on the relativistic mean-field calculations, the DWBA form factors are expanded into q 4, where the corresponding charge distributions are corrected by the contributions of neutron and spin–orbit densities. In the small q region, it is found that the experimental |F C(q)|2 can be well reproduced by considering the contributions of the at the small q region. Through further analyzing the second-order and fourth-order expansion coefficients of the , the relationship between the expansion coefficients and proton number Z is obtained. By the relationship, we extract the and from the limited experimental data of form factors at the small q region. Within the permissible range of error, the extracted are consistent with the experimental data in this paper.

Role of quadrupole deformation and continuum effects in the “island of inversion” nuclei F28,29,31

Background: The peculiar properties of nuclei in the so-called ``island of inversion'' around $Z=10$ and $N=20$ are the focus of current nuclear physics research. Recent studies showed that $^{28}\mathrm{F}$ has a negative-parity ground state and thus lies within the southern shore of the island of inversion, and $^{29}\mathrm{F}$ presents a halo structure in its ground state, but it is unclear which effects, such as deformation, shell evolution due to tensor forces, or couplings to the continuum, lead to this situation.Purpose: We investigate the role of quadrupole deformation and continuum effects on the single-particle structure of $^{28,29,31}\mathrm{F}$ from a relativistic mean-field approach and show how both phenomena can lead to a negative-parity ground state in $^{28}\mathrm{F}$ and halo structures in $^{29,31}\mathrm{F}$.Methods: We solve the Dirac equation in the complex-momentum (Berggren) representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field calculations using the NL3 interaction and calculate the continuum level densities using the Green's function method.Results: We extract single-particle energies and widths from the continuum level densities to construct the Nilsson diagrams of $^{28,29,31}\mathrm{F}$ in the continuum and analyze the evolution of both the widths and occupation probabilities of relevant Nilsson orbitals in $^{28}\mathrm{F}$ and find that some amount of prolate deformation must be present. In addition, we calculate the density distributions for bound Nilsson orbitals near the Fermi surface in $^{29,31}\mathrm{F}$ and reveal that, for a quadrupole deformation $0.3\ensuremath{\le}{\ensuremath{\beta}}_{2}\ensuremath{\le}0.45$ (prolate), characteristic halo tails appear at large distances.Conclusions: Using the relativistic mean-field approach in the complex-momentum representation with the Green's function method, we demonstrate that in neutron-rich fluorine isotopes, while in the spherical case the $pf$ shells are already inverted and close to the neutron emission threshold, a small amount of quadrupole deformation can dramatically reduce the gap between positive- and negative-parity states and increase the role of continuum states, ultimately leading to the negative parity in the ground state of $^{28}\mathrm{F}$ and the halo structures in $^{29,31}\mathrm{F}$.

Novel relativistic mean field Lagrangian guided by pseudo-spin symmetry restoration * * Supported by National Natural Science Foundation of China (11675065, 11875152, 11905088), Fundamental Research Funds for the central universities (lzujbky-2019-11), and the Supercompuer Center of HIRFL

The relativistic mean field (RMF) model has achieved great success in describing various nuclear phenomena. However, several serious defects are common. For instance, the pseudo-spin symmetry of high-l orbits is distinctly violated in general, leading to spurious shell closures and . This leads to problems in describing structure properties, including shell structures, nuclear masses, etc. Guided by the pseudo-spin symmetry restoration [Geng et al., Phys. Rev. C, 100: 051301 (2019)], a new RMF Lagrangian DD-LZ1 is developed by considering the density-dependent meson-nucleon coupling strengths. With the newly obtained RMF Lagrangian DD-LZ1, satisfactory descriptions can be obtained for the bulk properties of nuclear matter and finite nuclei. In particular, significant improvements on describing the single-particle spectra are achieved by DD-LZ1. In particular, the spurious shell closures and , commonly found in previous RMF calculations, are eliminated by the new effective interaction DD-LZ1, and consistently the pseudo-spin symmetry (PSS) around the Fermi levels is reasonably restored for both low-l and high-l orbits. Moreover, the description of nuclear masses is also notably improved by DD-LZ1, as compared to the other RMF Lagrangians.

Doublet bands at borders of A ≈ 130 island of chiral candidates: Case study of 120I * * Supported by the National Natural Science Foundation of China (11675063, 11205068, 11475072, 11847310)

Positive-parity doublet bands were reported in 120I. Based on these, we discuss the corresponding experimental characteristics, including rotational alignment, and re-examine the corresponding configuration assignment. The self-consistent tilted axis cranking relativistic mean-field calculations indicate that the doublet bands are built on the configuration . By adopting the two quasiparticles coupled with a triaxial rotor model, the excitation energies, energy staggering parameter S(I), , effective angles, and K plots are discussed and compared with available data. The obtained results support the interpretation of chiral doublet bands for the positive-parity doublet bands in 120I, and hence identify this nucleus as the border of the A ≈ 130 island of chiral candidates.

Spin-orbit interaction near the neutron drip line and shell effects at N = 82 near the r-process path

We have studied the behavior of charge and neutron radii across the shell-closure at N = 82 near the neutron dripline in a comparative approach which includes Relativistic Mean Field (RMF) Theory and the nonrelativistic Skyrme-Hartree-Fock (SHF) Theory. We have investigated the extent and the effects of the spin-orbit interaction on the ground state properties of neutron-rich nuclei in the extreme region. RMF and SHF calculations have been performed for nuclei in the isotopic chains from Kr (Z = 36) to Sn (Z = 50) near the neutron dripline across the magic number N = 82. We present the results of shell-effects on charge radii, neutron radii, and the neutron skin thickness. We have examined the single particle energies (SPE) in the context of the kinks in the radii. It is shown that RMF theory produces a kink in charge radii, similar to what was seen experimentally for Pb (Z = 82) isotopic chains. This is in contrast to the Skyrme forces, which do not produce such a kink.

Possibility of C14 cluster as a building block of medium-mass nuclei

The possibility of the $^{14}\mathrm{C}$ cluster being a basic building block of medium-mass nuclei is discussed. Although $\ensuremath{\alpha}$ cluster structures have been widely discussed in the light $N\ensuremath{\approx}Z$ mass region, the neutron-to-proton ratio deviates from unity in the nuclei near $\ensuremath{\beta}$-stability line and in neutron-rich nuclei. Thus, more neutron-rich objects with $N>Z$ could become the building blocks of cluster structures in such nuclei. The $^{14}\mathrm{C}$ nucleus is strongly bound and can be regarded as such a candidate. In addition, the path to the lowest shell-model configuration at short relative distances is closed for the $^{14}\mathrm{C}+^{14}\mathrm{C}$ structure, contrary to the case of the $^{12}\mathrm{C}+^{12}\mathrm{C}$ structure; this allows an appreciable separation distance between the $^{14}\mathrm{C}$ clusters. The recent development of the antisymmetrized quasicluster model (AQCM) allows us to utilize a $jj$-coupling shell-model wave function for each cluster in a simplified way. The AQCM results for the $^{14}\mathrm{C}+^{14}\mathrm{C}$ structure in $^{28}\mathrm{Mg}$ are compared with the ones of cranked relativistic mean field (CRMF) calculations. Although theoretical frameworks of these two models are quite different, they give similar results for the nucleonic densities and rotational properties of the structure under investigation. The existence of a linear chain three-$^{14}\mathrm{C}$ cluster structure in $^{42}\mathrm{Ar}$ has also been predicted in AQCM. These results confirm the role of the $^{14}\mathrm{C}$ cluster as a possible building block of cluster structures in medium-mass nuclei.

Systematic investigations of positive-parity doublet bands with three-quasiparticle configurations in Cs125,127,129,131

The experimental features of positive-parity doublet bands in the odd-\emph{A} cesium isotopes $^{125,127,129,131}$Cs, including angular momentum alignment, energy staggering, $B(M1)/B(E2)$ etc. are studied systematically and compared to those of the candidate chiral bands in the adjacent odd-odd Cs isotopes. The configuration assignments and the dynamics of these bands are discussed. The self-consistent tilted axis cranking relativistic mean-field calculations are performed with configuration reassigned to these bands. The experimental level schemes of four nuclei are well reproduced, and the calculations also show four nuclei have obvious triaxial deformations and thus support the candidate chiral doublet bands in $^{125,127,129,131}$Cs.

Possible antimagnetic rotational band and neutron alignment in In113

High-spin states of $^{113}\mathrm{In}$ have been populated using the $^{110}\mathrm{Pd}(^{7}\mathrm{Li},4n)^{113}\mathrm{In}$ reaction at beam energies of 38 and 50 MeV. More than 50 new $\ensuremath{\gamma}$ transitions are observed in $^{113}\mathrm{In}$. Three previously observed magnetic dipole bands are extended to higher spin states, and several new $E2$ crossover transitions within the bands are observed in two of the dipole bands. A new positive-parity $▵I=2$ band built on the $\ensuremath{\pi}{d}_{5/2}$ configuration is established. The known $▵I=2$ band is extended to $51/{2}^{+}$ state, and a gentle up-bend associated to the alignment of neutrons in the normal-parity $\ensuremath{\nu}{g}_{7/2}/{d}_{5/2}$ orbitals is found. The properties of this band are discussed based on the self-consistent tilted axis cranking relativistic mean-field model calculations. The predicted $B(E2)$, deformation parameters ${\ensuremath{\beta}}_{2}$ and $\ensuremath{\gamma}$, and ${J}^{(2)}/B(E2)$ ratios indicate that the $▵I=2$ band based on the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{g}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{({h}_{11/2})}^{2}$ and $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{g}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{({h}_{11/2})}^{2}{({g}_{7/2}/{d}_{5/2})}^{2}$ configurations, has the characteristics of antimagnetic rotation. Furthermore, the two-shears-like mechanism for the possible antimagnetic rotational bands is examined by investigating the orientation of the angular momenta.

The effect of the delta-rich hadronic stellar matter in the maximum neutron star mass using the nonlinear Walecka and Zimanyi-Moszkowski models

In this work, the delta-rich hadronic stellar matter condensate is studied in the context of a relativistic mean field calculation for hadrons and mesons using the nonlinear Walecka (NLW) and Zimanyi-Moszkowski (ZM) models. Considering different values of delta-mesons coupling constants we present the delta matter effect in the equation of state in each of these models. Solving numerically the Tolman-Oppenheimer-Volkoff (TOV) equation, we obtain the maximum neutron star mass. We note that the NLW model provides a stiffer equation of state when compared to the ZM model for the same values of delta-mesons coupling constants, and as a consequence gives more massive neutron stars.

Coexistence of chiral symmetry and pseudospin symmetry in one nucleus: triplet bands in 105Ag

The nearly degenerate triplet bands with the configuration in 105Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM). The configuration-fixed constrained triaxial RMF calculations exhibit pseudospin symmetry in single-particle spectra and triaxial shape coexistence. The experimental excitation energies and electromagnetic transition probabilities for the triplet bands are well reproduced by the MPRM calculations. The first and second lowest energy bands of the triplet bands are interpreted as pseudospin doublet bands, and the second and third bands are interpreted as chiral doublet bands. The chiral doublet bands show the same phase in the B(M1)/B(E2) staggering, while the pseudospin doublet bands hold the opposite phase. Such triplet bands in 105Ag provide the first example for the coexistence of chiral symmetry and pseudospin symmetry in one single nucleus.

Description of nuclei with magic number Z (N) = 6

Encouraged by the evidence for Z = 6 magic number in neutron-rich carbon isotopes, we have performed relativistic mean-field plus BCS calculations to investigate ground state properties of entire chains of isotopes (isotones) with Z (N) = 6 including even and odd mass nuclei. Our calculations include deformation, binding energy, separation energy, single particle energy, root mean squared radii, along with charge and neutron density profile, etc., and are found to be an excellent match with latest experimental results demonstrating Z = 6 as a strong magic number. N = 6 is also found to have a similar kind of strong magic character.

Investigation of nonlinear isoscalar–isovector coupling in a relativistic mean-field model by elastic magnetic electron scattering

In this paper, we study the sensitivity of single valence neutron properties and elastic magnetic form factors to three different relativistic mean-field (RMF) parameter sets: NL3, FSUGold, and IU-FSU. To perform our calculation, seven odd-A nuclei having single valence neutron on top of a magic neutron core: Be7, O17, Ca41, Ni57, Zr91, Ba139, and Pb209 are considered as model nuclei. The wave-function of the outer most neutron orbit, matter density, valence neutron density, and magnetic form factors are numerically calculated. It is shown that there are significant differences between the magnetic form factors in the mediate- and high-momentum transfer regions when calculate with different parameter sets. Such separation is more evident with larger nuclear mass and isospin asymmetry. By fitting to the experimental data, the spectroscopic factors for O17 and Ca41 are obtained. From the fitting, we infer that including the isoscalar–isovector meson self-coupling can give a better performance of the RMF calculation.

Possible candidates for multiple chiral doublet bands in cesium isotopes

Following the reports of candidate chiral doublet bands observed in odd-$A$ cesium isotopes, the triaxial deformations with corresponding configuration and the possible multiple chiral doublet ($\mathrm{M}\ensuremath{\chi}\mathrm{D}$) phenomenon in $^{125,127,129,131}\mathrm{Cs}$ are investigated within the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations. The existence of the $\mathrm{M}\ensuremath{\chi}\mathrm{D}$ phenomenon in $^{125,129,131}\mathrm{Cs}$ is demonstrated and expected based on different high-$j$ particle-hole configurations and triaxial deformations.

Microscopic analysis of shape transition in neutron-deficient Yb isotopes

The development of nuclear collectivity in even-even $^{152\text{--}170}\mathrm{Yb}$ is studied with three types of mean-field calculations: the nonrelativistic Hartree-Fock plus BCS calculation using the Skyrme SLy4 force plus a density-dependent $\ensuremath{\delta}$ pairing force and the relativistic mean-field calculation using a point-coupling energy functional supplemented with either a density-independent $\ensuremath{\delta}$ pairing force or a separable pairing force. The low-lying states are obtained by solving a five-dimensional collective Hamiltonian with parameters determined from the three mean-field solutions. The energy surfaces, excitation energies, electric multiple transition strengths, and differential isotope shifts are presented in comparison with available data. Our results show that different treatments of pairing correlations have a significant influence on the speed of developing collectivity as the increase of neutron number. All the calculations demonstrate the important role of dynamic shape-mixing effects in resolving the puzzle in the dramatic increase of charge radius from $^{152}\mathrm{Yb}$ to $^{154}\mathrm{Yb}$ and the role of triaxiality in $^{160,162,164}\mathrm{Yb}$.