Relativistic Continuum Hartree-Bogoliubov Theory Research Articles

Nuclear mass predictions of the relativistic continuum Hartree-Bogoliubov theory with the kernel ridge regression

Nuclear mass predictions of the relativistic continuum Hartree-Bogoliubov theory with the kernel ridge regression

A unified description of the halo nucleus 37Mg from microscopic structure to reaction observables

Based on the structure input directly from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we fully study reaction observables to search for halo evidence of 37Mg with the Glauber model. In this scheme, we evaluate the reaction cross sections of 20–37Mg bombarding a C target at 240 MeV/nucleon and find that most of the results agree well with the experimental data within 1σ uncertainty, especially good for the case of 37Mg. Our predicted doubling of the cross section change from 36Mg to 37Mg over that from 34Mg to 35Mg is consistent with a halo structure in 37Mg. Additionally, our calculated narrow longitudinal momentum distribution of 36Mg residues from 37Mg + 12C breakup agrees well with data and imply a nuclear size much larger than 35Mg. Furthermore, our study shows a dominant p-wave contribution to the longitudinal momentum distribution, supporting the conclusion that 37Mg is a p-wave halo nucleus. Our study provides the first unified description of the halo characteristics of 37Mg from nuclear structure to reaction dynamics.

Evolution of N = 20, 28, 50 shell closures in the 20 ≤ Z ≤ 30 region in deformed relativistic Hartree-Bogoliubov theory in continuum* *Supported in part by the National Natural Science Foundation of China (NSFC) (11975041, 11961141004). Xiang-Xiang Sun is supported in part by NSFC (12205308), and the Deutsche Forschungsgemeinschaft (DFG) and NSFC through the funds provided to the

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 shell closures in the 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 region, the shell closure disappears or becomes quenched, mainly due to the deformation effects. Similarly, both experimental data and theoretical predictions indicate that the shell closure disappears in the Mn isotopic chain, mainly due to the deformation effects. The DRHBc theory predicts the existence of the 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.

Isospin-dependence of the charge-changing cross-section shaped by the charged-particle evaporation process

We present the charge-changing cross sections (CCCS) of 11−15C, 13−17N, and 15,17−18O at around 300 MeV/nucleon on a carbon target, which extends to p-shell isotopes with N<Z for the first time. The Glauber model, which considers only the proton distribution of projectile nuclei, underestimates the cross sections by more than 10%. We show that this discrepancy can be resolved by considering the contribution from the charged-particle evaporation process (CPEP) following projectile neutron removal. Using nucleon densities from the deformed relativistic Hartree-Bogoliubov theory in continuum, we investigate the isospin-dependent CPEP contribution to the CCCS for a wide range of neutron-to-proton separation energy asymmetry. Our calculations, which include the CPEP contribution, agree well with existing systematic data and reveal an “evaporation peak” at the isospin symmetric region where the neutron-to-proton separation energy is close to zero. These results suggest that analysis beyond the Glauber model is crucial for accurately determining nuclear charge radii from CCCSs.

One-proton emission from 148−151Lu in the DRHBc+WKB approach

One-proton radioactivity in 149Lu, the latest identified proton emitter, is studied in the Wentzel-Kramers-Brillouin (WKB) approach with the proton-nucleus potential extracted from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for the first time. The predicted half-life turns out to be consistent with the experimental measurement within uncertainties and (almost) independent of the density functionals in the DRHBc theory. Such a microscopic self-consistent calculation reveals that 149Lu is oblately deformed with a quadrupole deformation β2≈−0.18, and rules out the possibility of a prolate quadrupole deformation suggested in the nonadiabatic quasiparticle model. We also check the validity of this approach in the description of 150,151Lu and their isomeric states. The deviations of the predicted half-lives from their experimental counterparts are mostly smaller than those of the theoretical studies without considering deformation effects. Furthermore, we predict 148Lu to be a more oblately deformed proton-emitter with a longer half-life than that of 149Lu, which can be checked in the future. Our studies show that the DRHBc + WKB approach provides a new alternative method to evaluate the half-lives of well-deformed proton emitters.

Nuclear charge radii and shape evolution of Kr and Sr isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

Nuclear charge radii and shape evolution of Kr and Sr isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

Missed prediction of the neutron halo in 37Mg

Halo phenomena have long been an important frontier in both experimental and theoretical nuclear physics. 37Mg was identified as a halo nucleus in 2014 and remains the heaviest nuclear halo system to date. While the halo phenomenon in 37Mg was not predicted before the discovery, its description has been still challenging afterwards. In this Letter, we report a microscopic and self-consistent description of the neutron halo in 37Mg using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) that was developed in 2010. The experimental neutron separation energies and empirical matter radii of neutron-rich magnesium isotopes as well as the deformed p-wave halo characteristics of 37Mg are well reproduced without any free parameters. In particular, the orbital occupied by the halo neutron in 37Mg, exhibiting p-wave components comparable to those suggested in experiments, remains consistent across various employed density functionals including PC-F1, PC-PK1, NL3*, and PK1. The DRHBc theory investigated only even-even magnesium isotopes in previous works and for that reason missed predicting 37Mg as a halo nucleus before 2014. Although the core and the halo of 37Mg are both prolate, higher-order shape decoupling on the hexadecapole and hexacontatetrapole levels is predicted.

Prolate-shape dominance in atomic nuclei within the deformed relativistic Hartree-Bogoliubov theory in continuum

Prolate-shape dominance in atomic nuclei within the deformed relativistic Hartree-Bogoliubov theory in continuum

Spherical, Axial, and Triaxial Symmetries in the Study of Halo Nuclei with Covariant Density Functional Theory

The halo phenomenon in exotic nuclei has long been an important frontier in nuclear physics research since its discovery in 1985. In parallel with the experimental progress in exploring halo nuclei, the covariant density functional theory has become one of the most successful tools for the microscopic study of halo nuclei. Based on spherical symmetry, the relativistic continuum Hartree–Bogoliubov theory describes the first halo nucleus 11Li self-consistently and predicts the giant halo phenomenon. Based on axial symmetry, the deformed relativistic Hartree–Bogoliubov theory in continuum has predicted axially deformed halo nuclei 42,44Mg and the shape decoupling effects therein. Based on triaxial symmetry, recently the triaxial relativistic Hartree–Bogoliubov theory in continuum has been developed and applied to explore halos in triaxially deformed nuclei. The theoretical frameworks of these models are presented, with the efficacy of exploiting symmetries highlighted. Selected applications to spherical, axially deformed, and triaxially deformed halo nuclei are introduced.

Collapse of the N=28 shell closure in the newly discovered Na39 nucleus and the development of deformed halos towards the neutron dripline

Halos and changes of nuclear magicities have been extensively investigated in exotic nuclei during past decades. The newly discovered $^{39}\mathrm{Na}$ with the neutron number $N=28$ provides a new platform to explore such novel phenomena near the neutron dripline of the sodium isotopic chain. We study the shell property and the possible halo structure in $^{39}\mathrm{Na}$ within the deformed relativistic Hartree-Bogoliubov theory in continuum. It is found that the lowering of $2p$ orbitals in the spherical limit results in the collapse of the $N=28$ shell closure in $^{39}\mathrm{Na}$, and a well-deformed ground state is established. The pairing correlations and the mixing of $pf$ components driven by deformation lead to the occupation of weakly bound or continuum $p$-wave neutron orbitals. An oblate halo is therefore formed around the prolate core in $^{39,41}\mathrm{Na}$, making $^{39}\mathrm{Na}$ a single nucleus with the coexistence of several exotic structures, including the quenched $N=28$ shell closure, Borromean structure, deformed halo, and shape decoupling. The microscopic mechanisms behind the shape decoupling phenomenon and the development of halos towards dripline are revealed.

Finite-nuclear-size effect in hydrogenlike ions with relativistic nuclear structure

The finite-nuclear-size (FNS) effect has a large contribution to atomic spectral properties, especially for heavy nuclei. By adopting the microscopic nuclear charge-density distributions obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, we systematically investigate the FNS corrections to atomic energy levels and bound-electron $g$ factors of hydrogenlike ions with nuclear charge up to 118. The comparison of the present numerical calculations with the predictions from empirical nuclear charge models, the nonrelativistic Skyrme-Hartree-Fock calculations, and the results based on experimental charge densities indicate that both the nuclear charge radius and the detailed shape of the charge-density distribution play important roles in determining the FNS corrections. The variation of FNS corrections to energy levels and $g$ factors with respect to the nuclear charge are investigated for the several lowest bound states of hydrogenlike ions. It is shown that they both increase by orders of magnitude with increasing nuclear charge, while the ratio between them has a relatively weak dependence on the nuclear charge. The FNS corrections to the ${s}_{1/2}$ and ${p}_{1/2}$ bound-state energies from the RCHB calculations are generally in good agreement with the analytical estimations by Shabaev [V. M. Shabaev, J. Phys. B 26, 1103 (1993)] based on the homogeneously charged sphere nuclear model, with the discrepancy indicating the distinct contribution of microscopic nuclear structure to the FNS effects.

Examination of machine learning for assessing physical effects: Learning the relativistic continuum mass table with kernel ridge regression* *Supported by the National Natural Science Foundation of China (11875075, 11935003, 11975031, 12141501, 12070131001), the China Postdoctoral Science Foundation under (2021M700256), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2023ZX01, NPT2023KFY02), and the President's Undergraduate Research Fellowship (PURF) of

The kernel ridge regression (KRR) method and its extension with odd-even effects (KRRoe) are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory. With respect to the binding energies of 9035 nuclei, the KRR method achieves a root-mean-square deviation of 0.96 MeV, and the KRRoe method remarkably reduces the deviation to 0.17 MeV. By investigating the shell effects, one-nucleon and two-nucleon separation energies, odd-even mass differences, and empirical proton-neutron interactions extracted from the learned binding energies, the ability of the machine learning tool to grasp the known physics is discussed. It is found that the shell effects, evolutions of nucleon separation energies, and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods, although the odd-even mass differences can only be reproduced by the KRRoe method.

Nuclear Bubble Configuration in Heavy-Ion Collisions

We study the effects of a bubble configuration in a nucleus on heavy-ion collisions at a few tens and hundreds A MeV. We first investigate the bubble structure of 206Hg using the relativistic continuum Hartree–Bogoliubov theory and then study the 206Hg + 208Pb and 206Hg+206Hg reactions using the DaeJeon–Boltzmann–Uehling–Uhlenbeck (DJBUU) transport model. To see the role of the bubble structure, we consider the maximum density of the produced nuclear matter, directed flow of neutrons and protons, and π−/π+ ratio. We observe that the maximum density is smaller with a bubble nucleus, and the directed flow of nucleons and π−/π+ ratio may depend on the bubble structure.

Microscopic analysis of the ground state properties of the even-even Dy isotopes in the reflection-asymmetric relativistic mean-field theory

Reflection-asymmetric relativistic mean-field theory is used to explore the ground state properties for the even-even Dy isotopes. The results are compared with those from the finite-range droplet model (FRDM), the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), and the available data. The calculated binding energies and quadrupole deformations agree with the experimental data as well as the FRDM and DRHBc calculations. The obtained matter density distributions and potential energy surfaces clearly exhibit the ground state shapes and the presence of deformation in these nuclei. The experimental fingerprints of octupolarity in $^{148,154,156,160}\mathrm{Dy}$ around $N=88$ are convincing in the present calculations. The predictions on the octupole deformation in $^{190\text{--}194,200,202}\mathrm{Dy}$ around $N=134$ agree with the results from the FRDM calculations. In addition, we obtain more knowledge about the shape evolution and phase transition from oblate to pear shape and then to prolate shapes in the Dy isotopes.

Optimized Dirac Woods-Saxon basis for covariant density functional theory

The Woods-Saxon basis has achieved great success in both nonrelativistic and covariant density functional theories in recent years. Due to its nonanalytical nature, however, applications of the Woods-Saxon basis are numerically complicated and computationally time consuming. In this paper, based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we check in detail the convergence with respect to the basis space in the Dirac sea. An optimized Dirac Woods-Saxon basis is proposed, whose corresponding potential is close to the nuclear mean field. It is shown that the basis space of the optimized Dirac Woods-Saxon basis required for convergence is substantially reduced compared with the original one. In particular, it does not need to contain the bases from continuum in the Dirac sea. The application of the optimized Woods-Saxon basis would greatly reduce computing resource for large-scale density functional calculations.

Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional. II. Examples of odd Nd isotopes

Background: One fascinating frontier in nuclear physics is the study of exotic nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which simultaneously includes the nuclear superfluidity, deformation, and continuum effects, can provide proper descriptions for both stable and exotic nuclei. In a previous work [Zhang et al., Phys. Rev. C 102, 024314 (2020)], the DRHBc theory based on the point-coupling density functionals was developed and the DRHBc calculation, previously accessible only for light nuclei, was extended for all even-even nuclei in the nuclear chart. The ground-state properties for the even-even nuclei with 8≤Z≤120 from the DRHBc calculations have been summarized [Zhang et al., At. Data Nucl. Data Tables 144, 101488 (2022)]. Purpose: The aim of this paper is to extend the point-coupling DRHBc theory to odd-A and odd-odd nuclei and examine its applicability by taking odd-A Nd isotopes as examples. Method: In the DRHBc theory, the densities and potentials with axial deformation are expanded in terms of Legendre polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a Dirac Woods-Saxon basis to include the continuum effects. For an odd-A or odd-odd nucleus, the blocking effect of the unpaired nucleon(s) is taken into account with the equal filling approximation. To determine its ground state, an automatic blocking procedure is adopted, in which the orbital with the lowest quasiparticle energy is blocked during the iteration. This procedure is justified by comparing with the results from the orbital-fixed blocking calculations, in which the blocked orbital near the Fermi surface is fixed during the iteration. The ground states for both light and heavy nuclei can be provided by the automatic blocking procedure as the orbital-fixed blocking procedure, but with considerably reduced computational cost. Results: The numerical details for even-even nuclei, including the convergence on the energy cutoff, angular momentum cutoff, and Legendre expansion, are found to be valid for odd-A and odd-odd nuclei as well. The ground-state properties of odd-A Nd isotopes are calculated with the density functional PC-PK1. The calculated physical observables, such as binding energies, two-neutron and one-neutron separation energies, and charge radii, are in good agreement with the available experimental data for the whole Nd isotopic chain. Conclusions: The point-coupling DRHBc theory is extended to odd-A and odd-odd nuclei by including the blocking effect. Taking Nd isotopes including both even-even and odd-A ones as examples, the calculated ground-state properties with PC-PK1 are in good agreement with the available experimental data. This paper paves the way to construct the DRHBc mass table including all even-even, odd-A, and odd-odd nuclei in the nuclear chart.6 MoreReceived 4 May 2022Accepted 12 July 2022DOI:https://doi.org/10.1103/PhysRevC.106.014316©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesEnergy levels & level densitiesNuclear bindingNuclear charge distributionNuclear many-body theoryNuclear spin & parityNuclear structure & decaysNucleon distributionNuclear Physics

Ground state properties of polonium isotopes using covariant density functional theory

In the framework of the Relativistic Hartree-Bogoliubov (RHB) mean-field model, a Covariant Density Functional Theory (CDFT) is used to systematically investigate the triaxial shape evolution of even–even polonium isotopic chain (N = 102–148). Two different effective interactions, i.e. the Density-Dependent Meson-Exchange (DD-ME2) and the new parameter set of Density-Dependent Point-Coupling (DD-PCX) interactions, are utilized in the current study. Besides, the new parameter-free proxy-SU(3) model is used to investigate the ground state shapes of polonium isotopes. CDFT calculations with both parameter sets, predict shape coexistence in the neutron deficient side of polonium isotopic chain, which meets the same prediction of the proxy-SU(3) scheme. The predicted shapes of nuclei are in good agreement with several experimental studies, as well as other theoretical models presented in the current paper. Also, one triaxial ground state is predicted by DD-ME2, DD-PCX, and proxy-SU(3) but for three different nuclei. Different ground state properties like binding energy per nucleon, two-neutron separation energy and proton- neutron- and charge radii are presented in comparison with available experimental data as well as other theoretical models, like the Finite-Range Droplet Model (FRDM), the Infinite Nuclear Matter Model (INMM) and Deformed Relativistic Hartree-Bogoliubov theory in Continuum (DRHBc).

Systematic study of α decay half-lives for even–even nuclei within a deformed two-potential approach

In this work, we systematically study the α decay half-lives of 196 even–even nuclei using a two-potential approach improved by considering nuclear deformation. The results show that the accuracy of this model has been improved after considering nuclear deformation. In addition, we extend this model to predict the α decay half-lives of Z = 118 and 120 isotopes by inputting the α decay energies extracted from the Weizsacker–Skyrme-type (WS-type) mass model, a simple nuclear mass formula, relativistic continuum Hartree–Bogoliubov theory and Duflo-Zuker-19 (DZ19) mass model. It is useful for identifying the new superheavy elements or isotopes for future experiments. Finally, the predicted α decay energies and half-lives of Z = 118 and 120 isotopes are analyzed, and the shell structure of superheavy nuclei is discussed. It shows that the shell effect is obvious at N = 184, while the shell effect at N = 178 depends on the nuclear mass model.

Finite amplitude method on the deformed relativistic Hartree-Bogoliubov theory in continuum: The isoscalar giant monopole resonance in exotic nuclei

Finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc-FAM) is developed and applied to study isoscalar giant monopole resonance in exotic nuclei. Validation of the numerical implementation is examined for $^{208}\textrm{Pb}$. The isoscalar giant monopole resonances for even-even calcium isotopes from $^{40}\textrm{Ca}$ to the last bound neutron-rich nucleus $^{80}\textrm{Ca}$ are calculated, and a good agreement with the available experimental centroid energies is obtained for $^{40-48}\textrm{Ca}$. For the exotic calcium isotopes, e.g., $^{68}\textrm{Ca}$ and $^{80}\textrm{Ca}$, the DRHBc-FAM calculated results are closer to the energy weighted sum rule than the calculations on the harmonic oscillator basis, which highlights the advantages of DRHBc-FAM in describing giant resonances for exotic nuclei. In order to explore the soft monopole mode in the exotic nuclei, the giant monopole resonance for the deformed exotic nucleus $^{200}\textrm{Nd}$ is investigated, where the prolate shape and the oblate shape coexist. A soft monopole mode near 6.0 MeV is found in the prolate case, and another one near 4.5 MeV is found in the oblate case. The transition density of the soft monopole mode shows in phase or out-of-phase vibrations near the surface region, which is generated by quadrupole vibrations.

Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum * *Supported by the National Natural Science Foundation of China (11875225, 12005175, 11935003, 11875075, 11975031, 12070131001, 11790325), the Fundamental Research Funds for the Central Universities, the National Key R&D Program of China (2017YFE0116700, 2018YFA0404400), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2020ZZ01)

We extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to go beyond-mean-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 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 by 17%. Furthermore, it is found that the DCEs are quite sensitive to the pairing correlations; taking Nd as an example, a 10% enhancement of pairing strength can raise the DCE by 37%.