We perform a systematic study of the structure and properties of the krypton isotopic chain including both even-even and odd-A nuclei based on the axially deformed relativistic Hartree-Bogoliubov approach. Five effective interactions of three families of covariant density functionals, i.e., PC-L3R, DD-PCX, DD-PC1, DD-MEX, and DD-ME2, are employed to calculate potential energy surfaces of krypton isotopes. ^74,75Kr and ^90,91,92Kr are determined as typical candidates of shape coexistence. The potential surfaces originating from the PC-L3R, DD-PCX, and DD-MEX interactions exhibit an abrupt shape transition from oblate to prolate for ^73-74Kr, whereas DD-PC1 and DD-ME2 preserve an oblate ground-state shape. Such discrepancies are attributed to the occupations of single-particle levels at the vicinity of the Fermi surface described by these functionals. Moreover, the comparison between spherical and deformed calculations verifies the indispensability of deformation degrees of freedom in this region. The consideration of deformation effects improves the description of two-neutron separation energies, of which its evolution clearly demonstrates the N=50 and 82 shell closures. Interestingly, PC-L3R predicts a more extended two-neutron drip line up to ^132Kr, in agreement with the NL3* and PC-PK1 nonlinear effective interactions, whereas other functionals estimate a rather short isotopic chain up to ^119Kr. This anomalous extension implies a significant softening or even collapse of the traditional N=82 shell closure near the neutron-rich drip line, highlighting the need for future studies based on triaxial deformation and beyond-mean-field correlations in this nuclear region.

We present a new development in the multireference covariant density functional theory (MR-CDFT) for the low-lying states of odd-mass nuclei by mixing configurations with different intrinsic quadrupole shapes and different K quantum numbers. All configurations are projected onto the good particle numbers and angular momenta. The success of this newly developed framework is illustrated in its application to the low-lying states of ^43 S near the neutron magic number N=28 with shape coexistence. Our results indicate that the ground state, 3/2^-_1 , is predominantly composed of the intruder prolate one-quasiparticle (1qp) configuration ν 1/2^-[321] . In contrast, the 7/2^-_1 state is identified as a high-K isomer, primarily built on the prolate 1qp configuration ν 7/2^-[303] . Additionally, the 3/2^-_2 state is found to be an admixture dominated by an oblate configuration with K^π = 1/2^- , along with a small contribution from a prolate configuration with K^π = 3/2^- . These results demonstrate the capability of MR-CDFT to capture the intricate interplay among shape coexistence, configuration mixing, and isomerism in the low-energy structure of odd-mass nuclei around N = 28 , without invoking triaxiality.

The simultaneous reconciliation of the 1σ estimations on the mass (M) and radius (R) of the PSR J0030+0451 pulsar and the HESS J1731-347 remnant requires a region in the M-R plane where the slope dM/dR is positive. The latter reflects that the equation of state (EOS) should stiffen as the density increases, which requires a sufficiently large value for the speed of sound in dense matter. However, based on different theoretical assumptions, the sound velocity manifests an upper bound leading to a constraint on how stiff the resulting EOS can be. In the present contribution, we present our recent work on the possible simultaneous explanation of the aforementioned measurements in the context of hybrid EOSs, by describing the high-density phase as maximally incompressible (considering different suggestions for the upper speed of sound bound). A relevant discussion on possible constraints on the properties of first order transitions is also included.

We discuss recent applications of covariant density functional the­ory to the investigation of the full deformation space of the superheavy nucleus 286No. The calculations were performed on a three-dimensional lattice in a mi­croscopic and self-consistent manner. For the ground state of 286No, we find a novel pure non-axial octupole shape. This state coexists with a tetrahedral isomeric state at an excitation energy of 0.12 MeV.

In the present study, we employ three distinct, physically motivated speed of sound bounds to construct hybrid models, where the high-density phase is described by the maximally stiff equation of state. In particular, we consider the bounds related to special relativity, relativistic kinetic theory and conformality. The low-density hadronic phase is described by a state-of-the-art microscopic relativistic Brueckner-Hartree-Fock theory. This work aims to access the effect of the different speed of sound constraints on the relevant parameter space of the key parameters of first-order phase transitions by utilizing recent astronomical data. This involves a systematic analysis that also includes two distinct schemes for the construction of hybrid models (abrupt and smooth). Finally, a relevant discussion is conducted on the possible occurrence of a thermodynamic inconsistency that is related to the stability of the high-density phase over hadronic matter at large densities.

The relativistic Vlowk is developed from a renormalization group method for the first time, to provide softened NN interactions for relativistic abinitio calculations. Starting from a given bare NN interaction, the renormalization group method eliminates the repulsive core while keeping the low-energy on-shell T-matrix and, consequently, the two-body observables unchanged. We derive the relativistic Vlowk interactions from the relativistic Bonn NN interactions across a wide range of cutoffs and study nuclear matter using the relativistic Brueckner-Hartree-Fock theory in the full Dirac space. Our results demonstrate that the resulting relativistic Vlowk interactions provide a proper description of nuclear saturation, exhibiting only mild cutoff dependence. Therefore, the relativistic Vlowk shows promise for providing reliable softened NN interactions for future relativistic abinitio calculations of finite nuclei.

Within the relativistic Brueckner-Hartree-Fock theory in the full Dirac space, the tensor-force effects on infinite nuclear matter are elucidated by subtracting the matrix elements of tensor forces from the realistic nucleon-nucleon interaction. The tensor-force effects for the binding energy per particle of symmetric nuclear matter (SNM) as well as the symmetry energy are attractive and are more pronounced around the empirical saturation density, while the tensor forces have little impact on the pure neutron matter. By tuning the tensor-force strength, an infinite (negative) scattering length in the spin-triplet channel is found. This locates the dilute SNM with only the $^3S_1$-$^3D_1$ channel interaction at the unitary limit. Its ground-state energy is found proportional to the energy of a free Fermi gas with a scaling factor 0.38, revealing good universal properties. This work paves the way to study the tensor-force effects in neutron stars as well as finite nuclei from realistic nucleon-nucleon interactions, highlights the role of the tensor force on the deviation of the nuclear physics to the unitary limit, and provides valuable reference for studies of the four-component unitary Fermi gas.

A relativistic microscopic optical model potential for nucleon-nucleus scattering is developed based on the \emph{ab initio} relativistic Brueckner-Hartree-Fock (RBHF) theory with the improved local density approximation, which is abbreviated as the RBOM potential. Both real and imaginary parts of the single-particle potentials in symmetric and asymmetric nuclear matter at various densities are determined uniquely in the full Dirac space. The density distributions of the target nuclei are calculated by the covariant energy density functional theory with the density functional PC-PK1. The central and spin-orbit terms of the optical potentials are quantitatively consistent with the relativistic phenomenological optical potentials. The performance of the RBOM potential is evaluated by considering proton scattering with incident energy $E\leq 200$ MeV on five target nuclei, $\prescript{208}{}{\text{Pb}}$, $\prescript{120}{}{\text{Sn}}$, $\prescript{90}{}{\text{Zr}}$, $\prescript{48}{}{\text{Ca}}$, and $\prescript{40}{}{\text{Ca}}$. Scattering observables including the elastic scattering angular distributions, analyzing powers, spin rotation functions, and reaction cross sections are analyzed. Theoretical predictions show good agreements with the experimental data and the results derived from phenomenological optical potentials. We anticipate that the RBOM potential can provide reference for other phenomenological and microscopic optical model potentials, as well as reliable descriptions for nucleon scattering on exotic nuclei in the era of rare-isotope beams.

The shape of 286No is investigated with the relativistic density functional theory on a three-dimensional lattice space without any symmetry restriction in a microscopic and self-consistent way. It is found that the ground state of 286No has a pure non-axial octupole shape and coexists with a tetrahedral isomeric state. The energy difference between the two states is only 0.12 MeV, and they are separated by a potential barrier of about 0.5 MeV. The occurrence of the octupole correlations is analyzed with the evolution of the single-particle levels near the Fermi surface driven by the octupole deformations.

Using the relativistic Hartree–Bogoliubov approach with separable pairing force coupled with the latest point-coupling and meson-exchange covariant density functionals, i.e., PC-L3R, PC-X, DD-MEX, and DD-PCX, we systematically explore the ground-state properties of all isotopic chains from oxygen (Z=8) to darmstadtium (Z=110). These properties consist of the binding energies (Eb), one- and two-neutron separation energies (Sn and S2n), root-mean-square radii of matter (Rm), of neutron (Rn), of proton (Rp) and of charge (Rc) distributions, Fermi surfaces (λ), ground-state spins (J) and parities (π). We then use these calculated properties to predict the edges of nuclear landscape and bound nuclei for the isotopic chains of Z = 8–110. The number of bound nuclei predicted by PC-L3R, PC-X, DD-MEX, and DD-PCX, are 9004, 9162, 7112, and 6799, respectively. These latest covariant density functionals produce a set of rather similar proton drip lines due to the strong repulsive Coulomb force shifting up the single-proton energy of the proton-rich nuclei. PC-L3R and PC-X estimate more extended borders of the neutron-rich region compared with the neutron drip lines estimated by DD-MEX, and DD-PCX. Meanwhile, the root-mean-square deviations of one- (two-) neutron separation energies yielded from PC-L3R, PCX, DD-MEX, and DD-PCX are 0.962 (1.300) MeV, 0.920 (1.483) MeV, 1.010 (1.544) MeV, and 0.993 (1.753) MeV, respectively. The deviations of theoretical Sn, S2n, and charge radii from the available experimental ones increase at the regions further away from the proton magic numbers, indicating the important role of deformation in these regions. The root-mean-square deviations of charge radius distributions of comparing the available experimental values with the theoretical counterparts resulted from PC-L3R, PC-X, DD-MEX, and DD-PCX are 0.035 fm, 0.037 fm, 0.034 fm, and 0.035 fm, respectively. We compute and present the root-mean-square radii of neutron distributions for all isotopes of 8≤Z≤110 with respect to the empirical Rn. Basically, the systematic trends of the theoretical root-mean-square radii of neutron distributions generated from PC-L3R and PC-X closely follow the empirical Rn, except for the region of extreme neutron-rich nuclei, whereas DD-PCX produces a trend lower than the empirical Rn at the N<150 region. We notice pronounced differences between the empirical and theoretical Rn at nuclei near the neutron drip line of the Mg, Ca, and Kr isotopic chains, suggesting the possible existence of the halo or giant halo phenomena.

This Topical Collection of the European Physics Journal A is devoted to recent progress in the nuclear many-body problem. In particular, it aims at a comprehensive compilation of developments related to the work of a pioneer in that field, Peter Schuck, who passed away in 2022. Together with Peter Ring, he co-authored the book on “The Nuclear Many-Body Problem”. Different concepts presented in this seminal book have been elaborated further within a broad international collaboration. For instance, the quasi-particle approaches in connection with nuclear superfluidity and cluster formation in nuclear systems, in particular alpha-particle condensation and quartetting at subsaturation densities, have been put forward inspired by Peter Schuck. These advances obtained in the nuclear many-body problem can also be applied to other systems, for instance solid state physics. This Topical Collection is considered as addendum and continuation of the textbook of P. Ring and P. Schuck.

The rotational properties of the transfermium nuclei are investigated in the full deformation space by implementing a shell-model-like approach in the cranking covariant density functional theory on a three-dimensional lattice, where the pairing correlations, deformations, and moments of inertia are treated in a microscopic and self-consistent way. The kinematic and dynamic moments of inertia of the rotational bands observed in the transfermium nuclei ^{252}No, ^{254}No, ^{254}Rf, and ^{256}Rf are well reproduced without any adjustable parameters using a well-determined universal density functional. It is found for the first time that the emergence of the octupole deformation should be responsible for the significantly different rotational behavior observed in ^{252}No and ^{254}No. The present results provide a microscopic solution to the long-standing puzzle on the rotational behavior in No isotopes, and highlight the risk of investigating only the hexacontetrapole (β_{60}) deformation effects in rotating transfermium nuclei without considering the octupole deformation.

Relativistic Brueckner-Hartree-Fock(RBHF)theory is one of the most important ab initio methods in the relativist-ic framework,where the saturation properties of nuclear matter could be described satisfactorily with only considering two-body forces.By achieving the self-consistent solution of the RBHF equations for nuclear matter in the full Dirac space,the scalar and vector components of the single-particle potential have been determined uniquely,the uncertainties caused by the neglect of negative-energy states(NESs)have been avoided,and the long-standing problem over 40 years of not being able to uniquely determine the single-particle potential has been solved.The history of the RBHF theory is briefly reviewed,and the necessity of considering NESs is illustrated.The latest results of nuclear matter and neutron star matter by the RBHF theory in the full Dirac space are discussed,including the effective mass,the binding energy per particle of pure neutron matter,the pressure of symmetric nuclear matter and pure neutron matter,the particle fractions as well as the equation of state for neutron star matter,and the mass-radius relation as well as the tidal deformability of a neutron star.Possible applications of the RBHF theory in the full Dirac space are also discussed,including the calibration of the parameters in density functional theory,the microscopic description of nucleon-nucleus elastic scattering,and the research on the hadron-quark transition inside neutron stars.

Collective nuclear excitations, like giant resonances, are sensitive to nuclear deformation, as evidenced by alterations in their excitation energies and transition strength distributions. A common theoretical framework to study these collective modes, the random-phase approximation (RPA), has to deal with large dimensions spanned by all possible particle-hole configurations satisfying certain symmetries. This work aims to establish a new theoretical framework to study the impact of deformation on spin-isospin excitations, that can provide fast and reliable solutions of the RPA equations. The nuclear ground state is determined with the axially-deformed relativistic Hartree-Bogoliubov (RHB) model based on relativistic point-coupling energy density functionals (EDFs). To study the excitations in the charge-exchange channel, an axially-deformed proton-neutron relativistic quasiparticle RPA (pnRQRPA) is developed in the linear response approach. After benchmarking the axially-deformed pnRQRPA in the spherical limit, a study of spin-isospin excitations including Fermi, Gamow-Teller (GT), and Spin-Dipole (SD) is performed for selected $pf$-shell nuclei. For GT transitions, it is demonstrated that deformation leads to considerable fragmentation of the strength function. A mechanism inducing the fragmentation is studied by decomposing the total strength to different projections of total angular momentum $K$ and constraining the nuclear shape to either spherical, prolate or oblate. A similar fragmentation is also observed for SD transitions, although somewhat moderated by the complex structure of these transitions, while the Fermi strength is almost shape-independent. The axially-deformed pnRQRPA introduced in this work opens perspectives for future studies of deformation effects on astrophysically relevant weak interaction processes, in particular beta decay and electron capture.

Photonuclear reactions of light nuclei below a mass of A=60 are planned to be studied experimentally and theoretically with the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual photon excitation by proton scattering and real photo absorption by a high-brilliance γ -ray beam produced by laser Compton scattering, will be applied to measure the photoabsorption cross sections and decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. anti-symmetrized molecular dynamics, mean-field and beyond-mean-field models, a large-scale shell model, and ab initio models, will be employed to predict the photonuclear reactions. The uncertainty in the model predictions will be evaluated based on the discrepancies between the model predictions and experimental data. The data and predictions will be implemented in the general reaction calculation code, TALYS. The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation.

Recent years have seen considerable progress with ab-initio calculations of the nuclear structure by non-relativistic many-body methods. Dirac-Brueckner-Hartree-Fock Theory provides a relativistic ab-intio approach, which is able to reproduce saturation properties of symmetric nuclear matter without three-body forces. However, so far, the corresponding equations have been solved only for positive energy states. Negative energy states have been included for forty years in various approximations, leading to differences in the isospin dependence. This problem has been solved only recently by a complete solution of the self-consistent relativistic Brueckner-Hartree-Fock equations in asymmetric nuclear matter. Due to its numerical complexity, however, it is very difficult to extend the Relativistic Brueckner-Hartree-Fock theory to the study of finite nuclear systems. Recent efforts will be discussed to overcome this problem.

Pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the lower component of the Dirac spinor. Here, we investigate the conservation and breaking of PSS in the single-nucleon resonant states, as an example, using Green's function method that provides a novel way to precisely describe not only the resonant energies and widths but also the spacial density distributions for both narrow and wide resonances. The PSS conservation and breaking are perfectly displayed in the evolution of resonant parameters and density distributions with the potential depth: In the PSS limit, i.e., when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign, PSS is exactly conserved with strictly the same energy and width between the PS partners as well as identical density distributions of the lower components. As the potential depth increases, the PSS is broken gradually with energy and width splittings and a phase shift in the density distributions.

We propose a newly optimized nonlinear point-coupling parameterized interaction, PC-L3R, for the relativistic Hartree-Bogoliubov framework with a further optimized separable pairing force by fitting to observables, i.e., the binding energies of 91 spherical nuclei, charge radii of 63 nuclei, and 12 sets of mean pairing gaps consisting of 54 nuclei in total. The separable pairing force strengths of proton and neutron are optimized together with the point-coupling constants, and are justified in satisfactory reproducing the empirical pairing gaps. The comparison of experimental binding energies compiled in AME2020 for 91 nuclei with the ones generated from the present and other commonly used point-coupling interactions indicates that the implementation of PC-L3R in relativistic Hartree-Bogoliubov yields the lowest root-mean-square deviation. The charge radii satisfactory agree with experiment. Meanwhile, PC-L3R is capable of estimating the saturation properties of the symmetric nuclear matter and of appropriately predicting the isospin and mass dependence of binding energy. The experimental odd-even staggering of single nucleon separation energies is well reproduced. The comparison of the estimated binding energies for 7,373 nuclei based on the PC-L3R and other point-coupling interactions is also presented.

Nucleon effective masses in neutron-rich matter are studied with the relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space. The neutron and proton effective masses for symmetric nuclear matter are 0.80 times rest mass, which agrees well with the empirical values. In neutron-rich matter, the effective mass of the neutron is found larger than that of the proton, and the neutron-proton effective mass splittings at the empirical saturation density are predicted as 0.187α with α being the isospin asymmetry parameter. The result is compared to other ab initio calculations and is consistent with the constraints from the nuclear reaction and structure measurements, such as the nucleon-nucleus scattering, the giant resonances of ^208Pb, and the Hugenholtz-Van Hove theorem with systematics of nuclear symmetry energy and its slope. The predictions of the neutron-proton effective mass splitting from the RBHF theory in the full Dirac space might be helpful to constrain the isovector parameters in phenomenological density functionals.

We extend the multi-reference covariant density functional theory (MR-CDFT) by including fluctuations in quadrupole deformations and average isovector pairing gaps simultaneously for the nuclear matrix elements (NMEs) of neutrinoless double-beta $(0\nu\beta\beta)$ decay in the candidate nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe assuming the exchange of either light or heavy neutrinos. The results indicate a linear correlation between the predicted NMEs and the isovector pairing strengths, as well as the excitation energies of $2^{+}_1$ and $4^{+}_1$ states. By adjusting the pairing strengths based on the excitation energies of the $2^{+}_1$ states, we calculate the NMEs for $0\nu\beta\beta$ decay, which are reduced by approximately $12\%$ to $62\%$ compared to the results obtained in the previous studies by Song et al. [Phys. Rev. C95, 024305 (2017)]. Additionally, upon introducing the average isovector pairing gap as an additional generator coordinate in the calculation, the NMEs increase by a factor ranging from $56\%$ to $218\%$.