Triaxial Relativistic Mean Field Research Articles

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. A periodic evolution for the ground state shapes is shown with the neutron number, i.e., spherical shapes at shell closures N=126, 184, 258, and prolate dominated shapes between them. In analogy to the shape evolution, the inner fission barriers also exhibit a periodic behavior: peaks at the shell closures and valleys in the mid-shells. The triaxial effect to the inner fission barrier is evaluated using the triaxial relativistic mean field calculations plus a simple BCS method for pairing. With the triaxial correction included, good consistency in the inner barrier heights is found with the available empirical data.
Besides, the evolution from the proton to the neutron drip line is in accord with the results by the multi-dimensionally constrained relativistic mean field theory. A flat valley in the fission barrier height is predicted around the neutron-rich nucleus 318U which may play a role of fission recycling in the astrophysical r-process nucleosynthesis.

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 existence of chiral and multiple chiral nuclei in thallium isotopes * *This work is partly support by the Major Program of Natural Science Foundation of Shandong Province (ZR2020ZD30), the Outstanding Youth Fund of Natural Science Foundation of Shandong Province (ZR2020YQ07), the National Natural Science Foundation of China (11675094, 12075138), and the Young Scholars Program of Shandong University, Weihai. The

The chirality in thallium isotopes is investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field theory. Several minima with prominent triaxial deformation and proper configuration, where the chiral doublet bands may appear, are obtained in odd-odd nuclei Tl and odd-mass nuclei Tl. Furthermore, the possible existence of multiple chiral doublet bands (MχD) is demonstrated in Tl. As the chiral doublet bands in Tl and MχD in 195Tl have been observed experimentally, further experimental exploration for the chirality in Tl and MχD in thallium isotopes is expected to verify the predictions.

Possible Candidates for Chirality in the Odd-Odd As IsotopesSupported by the National Natural Science Foundation of China (Grant Nos. 11705102 and 11675094), the Shandong Natural Science Foundation (Grant No. JQ201701), and the Young Scholars Program of Shandong University, Weihai.

The deformations and the corresponding configurations of the odd-odd As isotopes are investigated using the adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) theory. Energy minima with triaxial deformations and high-j particle-hole configurations are obtained in 72,74,76,78,80As, where the chiral doublet bands are possible to appear. The existence of multiple chiral doublet (MχD) is demonstrated in 74,76,78As. Based on the calculated single-particle levels, we also find possible coexistence of chiral and pseudospin symmetries in the odd-odd As isotopes.

Extension of the nuclear landscape to hyperheavy nuclei

The properties of hyperheavy nuclei and the extension of nuclear landscape to hyperheavy nuclei are extensively studied within covariant density functional theory. Axial reflection symmetric and reflection asymmetric relativistic Hartree-Bogoliubov (RHB) calculations are carried out. The role of triaxiality is studied within triaxial RHB and triaxial relativistic mean field + BCS frameworks. With increasing proton number beyond Z~130 the transition from ellipsoidal-like nuclear shapes to toroidal ones takes place. The description of latter shapes requires the basis which is typically significantly larger than the one employed for the description of ellipsoidal-like shapes. Many hyperheavy nuclei with toroidal shapes are expected to be unstable towards multifragmentation. However, three islands of stability of spherical hyperheavy nuclei have been predicted for the first time in Ref. [1]. Proton and neutron densities, charge radii, neutron skins and underlying shell structure of the nuclei located in the centers of these islands have been investigated in detail. Large neutron shell gaps at N=228, 308 and 406 define approximate centers of these islands in neutron number. On the contrary, large proton gap appear only at Z=154 in the (Z~156, N~310) island. As a result, this is the largest island of stability of spherical hyperheavy nuclei found in the calculations. The calculations indicate the stability of the nuclei in these islands with respect of octupole and triaxial distortions. Fission barriers in neutron-rich superheavy nuclei are studied in triaxial RHB framework; the impact of triaxiality on the heights of fission barriers is substantial in some parts of this region. Based on the results obtained in the present work, the extension of nuclear landscape to hyperheavy nuclei is provided.

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.

Candidate chiral nuclei in bromine isotopes based on triaxial relativistic mean field theory

Following the observation of candidate chiral doublet bands in $^{78,80}$Br, triaxial deformations with corresponding configurations in odd-odd bromine isotopes have been investigated using adiabatic and configuration-fixed constrained triaxial relativistic-mean-field calculations with an aim of finding the boundary of chirality in the chain of Br isotopes. Several minima with triaxial deformation and the proper particle-hole configuration were obtained in $^{74,76,78,80,82}$Br, where the chiral doublet bands have the possibility of occurrence. Furthermore, the possible existence of multiple chiral doublet (M$\chi$D) bands is demonstrated in $^{74,76,78,80,82}$Br. Experiments to explore the chirality and M$\chi$D properties of Br isotopes are conducted to verify the predictions.

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.

The Role of One Single Lambda Hyperon on Binding Energy Difference of Hypernuclear Mirror Pair

Investigation on isospin symmetry in light Lambda hypernuclei is one of the most important issues in hypernuclear physics. In order to know the influences introduced by a single Lambda hyperon, we study the binding energy difference of mirror hypernuclear pair with mass A = 16, 18, 28, 40, and 42 using a time-odd triaxial relativistic mean field theory. Effects as the spin-orbit interaction, the time-odd component of vector fields, the core polarization, the proton-neutron mass difference, and the center-of-mass energy correction are self-consistently considered. Compared to the reported results of ordinary nuclei, the binding energy difference of mirror hypernuclei shows trivial change. With core polarization modified by an impurity hyperon, the isospin nonconserving effect between proton and neutron is hardly reduced for nuclei in study.

Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method

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 significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), $\mathrm{DD}\text{\ensuremath{-}}\mathrm{ME}\ensuremath{\delta}$ (2.29 MeV), and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\ensuremath{\sim}34%$ in comparison with the cranking prescription.

Possible multiple chiral doublet bands in107Ag

Two pairs of nearly degenerate doublet bands in ${}^{107}$Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (PRM), which suggests these bands as two distinct sets of chiral doublet bands. For the suggested $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{2}$ and $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}{d}_{5/2}$ configurations, the favorable triaxial deformation $\ensuremath{\gamma}$ for nuclear chirality can be obtained from the configuration-fixed constrained triaxial RMF calculations. Adopting the PRM, the data available are reproduced very well for the two pairs of doublet bands. Chiral geometry is further conformed by analyzing the angular momentum components. We suggest that two pairs of doublet bands in ${}^{107}$Ag would be another example of multiple chiral doublet bands.

Evidence for Multiple Chiral Doublet Bands inCe133

Two distinct sets of chiral-partner bands have been identified in the nucleus 133Ce. They constitute a multiple chiral doublet, a phenomenon predicted by relativistic mean field (RMF) calculations and observed experimentally here for the first time. The properties of these chiral bands are in good agreement with results of calculations based on a combination of the constrained triaxial RMF theory and the particle-rotor model.

Multiple chiral doublet candidate nucleusRh105in a relativistic mean-field approach

Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\chi$D) phenomenon. The existence of M$\chi$D phenomenon in $^{105}$Rh is highly expected.

Triaxial deformation in 104Rh of the chiral doublet bands

Triaxial relativistic mean field (RMF) approaches are used to study the properties of 104Rh. The existence of multiple chiral doublets is suggested for 104Rh based on the triaxial deformations and their corresponding proton and neutron configurations.

Description ofπg9/2⊗νh11/2doublet bands inRh106

Using the particle-rotor model (PRM), in which two quasiparticles are coupled to a triaxial core, the negative-parity doublet bands in $^{106}\mathrm{Rh}$ are studied. The quadrupole deformations \ensuremath{\beta} and \ensuremath{\gamma} for the $\ensuremath{\pi}{g}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration are calculated by configuration-fixed constrained triaxial relativistic mean-field (RMF) approaches, and these self-consistent deformation parameters are used as inputs for the PRM. The present calculated results well reproduce the observed energy spectra, energy staggering parameter, and electromagnetic transition ratios of the doublet bands, thus supporting the chiral interpretation of these doublet bands in $^{106}\mathrm{Rh}$. The effective angles between the angular momenta in the body-fixed frame are calculated for the first time. We demonstrate that rigid triaxial deformation can give rise to the experimentally observed constant energy separation between the yrast and side bands built on the asymmetrical $\ensuremath{\pi}{g}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration in the $A~100$ mass region.

Effects of triaxial deformation and pairing correlation on the proton emitterTm145

The ground-state properties of the recent reported proton emitter $^{145}\mathrm{Tm}$ have been studied within the axially or triaxially deformed relativistic mean field (RMF) approaches, in which the pairing correlation is taken into account by the BCS-method with a constant pairing gap. It is found that triaxiality and pairing correlations play important roles in reproducing the experimental one proton separation energy. The single-particle level, the proton emission orbit, the deformation parameters $\ensuremath{\beta}=0.22$ and $\ensuremath{\gamma}=28.{98}^{\ifmmode^\circ\else\textdegree\fi{}}$ and the corresponding spectroscopic factor for $^{145}\mathrm{Tm}$ in the triaxial RMF calculation are given as well.

Search for multiple chiral doublets in rhodium isotopes

The deformation in rhodium isotopes is investigated using adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) approaches. The triaxial deformations are found in the ground states of (102,104,106,108,110)Rh, which is consistent with triaxial Skyrme Hartree-Fock calculations. Several minima with triaxial deformation in (104,106,108,110)Rh are obtained by the configuration-fixed constrained calculations. The corresponding configurations are characterized by the quantum numbers vertical bar nljm > obtained by transforming wave functions from a Cartesian basis to a spherical basis. The possible existence of multiple chiral doublets (M chi D) is demonstrated in (104,106,108,110)Rh isotopes, based on different particle-hole configurations and triaxial deformations.

Binding energy differences of mirror nuclei in a time-odd triaxial relativistic mean field approach

The binding energy differences of mirror nuclei with $A=15,17,27,39$, and 41 are calculated using a time-odd triaxial relativistic mean field approach with PK1. Compared with the axially deformed RMF calculations with PK1, NL3, and NLSH, the discrepancy between the calculated and experimental values, i.e., Okamoto-Nolen-Schiffer (ONS) anomaly, is systematically reduced by the appropriate treatment of the \ensuremath{\gamma} deformation degree of freedom, center-of-mass motion, and core polarization effect.

Nuclear “pasta” phase in a triaxial relativistic mean field approach

The crust of a neutron star is of special interest because of the phase transition from a gas of nuclei to homogeneous asymmetric nuclear matter. Several efforts have been made to explore the nuclear matter in this region of the neutron star. These calculations have been done mostly in spherical Wigner–Seitz-cells using Skyrme Hartree–Fock (HF) or relativistic mean field (RMF) calculations. We apply both approaches in a Cartesian Wigner–Seitz-cell and get a smooth transition from nuclei to homogeneous matter showing various shapes. In this article we pay special attention to the relativistic mean field. Pairing is included in the BCS approximation.

MIRROR NUCLEI 12B AND 12N IN TIME-ODD TRIAXIAL RELATIVISTIC MEAN FIELD THEORY

Properties of the odd-odd mirror nuclei 12 B and 12 N have been investigated in the time-odd triaxial relativistic mean field approach. Influences of the nuclear magnetism, the mass difference between neutron and proton, the isovector meson field ρ and the Coulomb field on the properties of mirror nuclei have been discussed in detail.