Central nucleus-nucleus collisions produce many new baryons and the nuclear clusters can be formed from these species. The phenomenological coalescence models were used extensively for description of light nuclei from these baryons in a very broad range of collision energies. We suggest that the coalescence nucleation process can be effectively considered as (1) the formation of low-density baryon matter which can be subdivided into primary diluted clusters with the limited excitation energy, and (2) the following statistical decay of such clusters leading to the final cold nuclei production. We argue that the nuclei formation from the interacting baryons is a natural consequence of the nuclear interaction at subnuclear densities resulting in the nuclear liquid-gas-type phase transition in finite systems. In this way one can provide a consistent interpretation of the experimental fragment yields (FOPI data), including the important collision energy dependence of He isotope production in relativistic ion reactions. We investigate the regularities of this new kind of fragment production, for example, their yield, isospin, and kinetic energy characteristics. A generalization of such a clusterization mechanism for hypernuclear matter is suggested. The isotope yields and particle correlations should be adequate for studying these phenomena.

Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiment's sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $\beta$-decay spectrum, we assess a high-precision $\beta$-decay experiment's sensitivity to the neutrino mass scale and ordering for one assumed design scenario. We find that such an experiment could measure the electron-weighted neutrino mass within $\sim 40$ meV after 1 year (90% credibility). Neutrino masses $>500$ meV could be measured within $\approx 5$ meV. Using only $\beta$ decay and external reactor neutrino data, we find that next-generation $\beta$-decay experiments could potentially constrain the mass ordering using a two-neutrino spectral model analysis. By calibrating mass ordering results, we identify reporting criteria that can be tuned to suppress false ordering claims. In some cases, a two-neutrino analysis can reveal that the mass ordering is inverted, an unobtainable result for the traditional one-neutrino analysis approach.

In this paper we study mass relations of mirror nuclei in terms of Coulomb energies calculated by the microscopic relativistic continuum Hartree-Bogoliubov theory. An additional term corresponding to the Nolen-Schiffer anomaly is assumed to take the same form as the well-known empirical formula. The resultant root-mean-square deviations of these mass relations are typically less than 100 keV. Based on these relations, 61 unknown proton-rich nuclear masses are predicted for $18⩽A⩽87$ with positive two-proton separation energies and are tabulated in the Supplemental Material of this paper.

The structure of ${}^{208}\mathrm{Po}$ populated through the EC/${\beta }^{+}$ decay of ${}^{208}\mathrm{At}$ is investigated using $\gamma$-ray spectroscopy at the ISOLDE Decay Station. The presented level scheme contains 27 new excited states and 43 new transitions, as well as a further 50 previously observed $\gamma$ rays which have been (re)assigned a position. The level scheme is compared to shell model calculations. Through this analysis approximately half of the $\beta$-decay strength of ${}^{208}\mathrm{At}$ is found to proceed via allowed decay and half via first-forbidden decay. The first-forbidden transitions predominantly populate core excited states at high excitation energies, which is qualitatively understood using shell model considerations. This mass region provides an excellent testing ground for the competition between allowed and first-forbidden $\beta$-decay calculations, important for the detailed understanding of the nucleosynthesis of heavy elements.

We extend, from operators with one derivative to operators with three derivatives, the analysis of two-body hadronic parity violation in a combined pionless effective field theory (${\mathrm{EFT}}_{\pi /}$) and large-$N_c$ expansion, where $N_c$ is the number of colors in quantum chromodynamics (QCD). In elastic scattering, these operators contribute to $S\text{−}P$ and $P\text{−}D$ wave transitions, with five operators and their accompanying low energy coefficients (LECs) characterizing the $S\text{−}P$ transitions and six operators and LECs those in $P\text{−}D$ transitions. We show that the large-$N_c$ analysis separates them into leading order in $N_c$, next-to-leading order in $N_c$, etc. Relationships among ${\mathrm{EFT}}_{\pi /}$ LECs emerge in the large-$N_c$ expansion. We also discuss the renormalization group (RG) scale dependence of these LECs by considering two distinct limits: one in which large-$N_c$ relationships among LECs hold but RG-related approximate expansions do not, and vice versa. Our analysis can complement lattice QCD calculations and help prioritize future parity-violating experiments.

We study the weak interaction processes taking place within a combustion flame that converts dense hadronic matter into quark matter in a compact star. Using the Boltzmann equation we follow the evolution of a small element of just deconfined quark matter all along the flame interior until it reaches chemical equilibrium at the back boundary of the flame. We obtain the reaction rates and neutrino emissivities of all the relevant weak interaction processes without making any assumption about the neutrino degeneracy. We analyze systematically the role the initial conditions of unburnt hadronic matter, such as density, temperature, neutrino trapping, and composition, focusing on typical astrophysical scenarios such as cold neutron stars, proto–neutron stars, and post-merger compact objects. We find that the temperature within the flame rises significantly in a timescale of 1 nanosecond. The increase in $T$ strongly depends on the initial strangeness of hadronic matter and tends to be more drastic at larger densities. Typical final values range between 20 and $60\mathrm{MeV}$. The nonleptonic process $u+d\to u+s$ is always dominant in cold stars, but in hot objects the process $u+e^{-}\leftrightarrow d+{\nu }_e$ becomes relevant, and in some cases dominant, near chemical equilibrium. The rates for the other processes are orders of magnitude smaller. We find that the neutrino emissivity per baryon is very large, leading to a total energy release per baryon of $2–60\mathrm{MeV}$ in the form of neutrinos along the flame. We discuss some astrophysical consequences of the results.

We present an analysis of hot and dilute isospin-asymmetric nuclear matter employing the temperature-dependent effective-relativistic mean-field theory (E-RMF). We consider nuclear matter to be homogeneous and study the equation of state (EoS) for densities, temperature, and asymmetry which are relevant for astrophysical simulations such as supernovae explosion and neutron-star crust. The two recently developed E-RMF parameter sets IOPB-I and G3 are used here to study various physical observables at finite temperatures. These sets are known to reproduce the nuclear matter properties, in agreement with various experimental and observational constraints. The effect of temperature is investigated in reference to the density-dependent free symmetry energy and its higher-order derivatives using the well-known parabolic approximation. The larger value of ${\lambda }_{\omega }$ cross coupling in G3 in addition to the $\delta$ meson coupling in G3 smoothen the free symmetry energy. Thermal effects on various state variables are examined at fixed temperature and isospin asymmetry by separating their $T=0$ and the finite-$T$ expressions. The thermal effects are governed by effective mass where larger effective mass corresponds to larger thermal contribution. The effect of temperature on isothermal and isentropic incompressibility is discussed, which is in harmony with various microscopic calculations. The liquid-gas phase-transition properties are examined in asymmetric matter in the context of different slope parameter and comparable symmetry energy in the IOPB-I and G3 set. The spinodal instability, binodal curve, and critical properties are found to be influenced by the slope parameter $L_{\mathrm{sym}}$. Finally, we consider a more realistic system (with the inclusion of electrons) and analyze the effect on instability and adiabatic index of isospin asymmetric nuclear matter.

In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in nuclear structure theory. Here we address the problem in terms of self-consistent mean-field calculations of collective deformation-energy surfaces, and the framework of the interacting boson approximation. In addition to quadrupole shape vibrations and rotations, the explicit coupling to pairing vibrations is taken into account by a boson-number nonconserving Hamiltonian, specified by a choice of a universal density functional and pairing interaction. An illustrative calculation for ${}^{128}\mathrm{Xe}$ and ${}^{130}\mathrm{Xe}$ shows the importance of dynamical pairing degrees of freedom, especially for structures built on low-energy $0^{+}$ excited states, in $\gamma$-soft and triaxial nuclei.

Using a fusion-evaporation reaction and a gas-filled recoil separator, an isomeric state $[T_{\frac{1}{2}}=83\left(8\right)\mu \mathrm{s}]$ with a most likely spin and parity of ${\frac{13}{2}}^{+}$ has been identified in ${}^{211}\mathrm{Th}$. The isomeric state is mainly depopulated via a hindered internal $M2$ transition [$B\left(M2\right)=0.0025\left(5\right)$ W.u.], but also a weak $\alpha$-decay branch of 4(3)% was observed. The present observations fit well to the systematic pattern set by the previously identified states of the same spin and parity in this region of the nuclear chart.

Lifetimes of low-spin excited states in ${}^{112}\mathrm{Pd}$ were measured using the recoil-distance Doppler-shift technique. The nucleus of interest was populated in a ${}^{110}\mathrm{Pd}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{112}\mathrm{Pd}$ reaction using the Cologne FN Tandem accelerator. Three lifetimes of ground-state band members and one lifetime of the $\gamma$ band were measured. From these lifetimes reduced transition probabilities were extracted and compared to interacting boson model, $\gamma$-soft calculations, and Davydov calculations. The lifetime of the $2_{\gamma }^{+}$ gives some insights on the nuclear shape and structure of the $\gamma$ band. The deduced transition rates show an indicator for a rigid triaxial nucleus as well as more indicators for a $\gamma$-soft nucleus.

We investigate proton systematics in terms of the barrier penetration and formation probability. To this purpose we approximate the realistic proton-core interaction by a parabolic dependence describing the nuclear part matched to a pure Coulomb potential. In this way we can use analytic semiclassical solutions to describe the proton dynamics inside the barrier. We then carefully investigate effects induced by the centrifugal barrier and quadrupole deformation. It turns out that the nuclear centrifugal and deformation effects are much smaller than their Coulomb counterparts. On the other hand, the Coulomb action defining the semiclassical penetrability is larger by one order of magnitude than its nuclear counterpart. We evidence a dependence of the Coulomb action upon the Coulomb parameter in terms of two parallel lines separated by $A=145$. Such a dependence was previously discovered for the logarithm of the experimental decay width corrected by the Coulomb centrifugal barrier. We also evidence an additional but smaller residual linear decrease of the proton formation probability versus $A^{1/3}$ along two parallel lines separated by $A=145$, induced by the internal proton wave function. Therefore, the dependence between the experimental decay width corrected by the centrifugal barrier and the Coulomb penetrability multiplied by the proton formation probability in the doubly logarithmic scale can be fitted within a factor of two by a universal straight line.

Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy ranges 0–15 MeV at NLO and 0–25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T=0$ and the other for $T=1$ channels. The cutoffs are taken to vary in the ranges $R_0=(1.5$–2.3) fm and $R_1=(1.5$–3.0) fm. The 780 (1100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a ${\chi }^2/\mathrm{datum}$ about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers $A=3$–6 and 16 obtained with selected LO and NLO $2N$ models both by themselves as well as in combination with a LO three-nucleon ($3N$) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental ${}^3\mathrm{H}$ binding energy. The inclusion of the $3N$ interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ binding energies that cluster around 7.8 and 30 MeV, respectively. However, in ${}^{16}\mathrm{O}$ this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with $A=40$, 48, and 90.

The ground-state pairing correlations in finite fermionic systems are described with a high degree of accuracy within a variational approach based on a combined coupled-cluster and particle-number-projected BCS ansatz. The flexibility of this symmetry-preserving wave function enables a unified picture valid from weak to strong coupling, both in small and large systems. The present variational approach consistently yields an energy upper bound while operating at the same level of precision as the nonvariational particle-number-projected Bogoliubov-coupled-cluster theory [Phys. Rev. C 99, 044301 (2019)].

The $\alpha$ (${}^4\mathrm{He}$)-clustering structure is a common phenomenon in light nuclei due to the decreasing contribution of the mean field in few-body systems. In this work, we presented calculations of giant dipole resonance (GDR) excitations for two non-$\alpha$-conjugate light nuclei, namely ${}^6\mathrm{Li}$ and ${}^9\mathrm{Be}$, within a framework of an extended quantum molecular dynamics model. For ${}^6\mathrm{Li}$, we investigated the GDR spectra from the two-body clustering structure with $\alpha +$ deuteron as well as the three-body structure with $\alpha +n+p$, and found that the major $\alpha$-clustering contribution on the GDR peak is located at around 31 MeV, while the resonance contributions between clusters, namely $\alpha$ and deuteron or $(n+p)$, are located on the lower energy side, which can be regarded as the pygmy dipole resonance (PDR). For ${}^9\mathrm{Be}$, a mixture configuration contribution for the chain-like structure and Borromean-like structure of the $\alpha +n+\alpha$ configuration can explain its GDR results.

Starting from the Bonn potential, the relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for nuclear matter in the full Dirac space, which provides a unique way to determine the single-particle potentials and avoids the approximations applied in the RBHF calculations in the Dirac space with positive-energy states (PESs) only. The uncertainties of the RBHF calculations in the Dirac space with PESs only are investigated, and the importance of RBHF calculations in the full Dirac space is demonstrated. In the RBHF calculations in the full Dirac space, the empirical saturation properties of symmetric nuclear matter are reproduced, and the obtained equation of state agrees with the results based on the relativistic Green's function approach up to the saturation density.

Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks, leads to isospin symmetry breaking. The isospin nonconservation affects a broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei.

Purpose: Recently, we constructed the charge-dependent density functional theory (DFT) that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of mirror and triplet displacement energies in a very broad range of masses. The aim of this work is to further test the charge-dependent functional by studying mirror energy differences (MEDs) in the function of angular momentum $I$.

Methods: To compute MEDs we use a DFT-rooted no core configuration interaction model. This post-mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants.

Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$, 45, 47, and 49 focusing on MEDs in the low-spin part (below band crossing), which allowed us to limit the model space to seniority one and three (one broken pair) configurations.

Conclusions: We demonstrate that, for spins $I\le 15/2$ being the subject of the present study, our model reproduces well experimental MEDs, which vary strongly in the function of $I$ and $A$. The quality of the model's predictions for MEDs is comparable to the nuclear shell-model results by Bentley et al. [Phys. Rev. C 92, 024310 (2015)].

The shape transition and possible occurrence of low-energy shape coexistence and rigid triaxial deformation are analyzed in the six even-even Er, Yb, Hf, W, Os, and Pt isotopic chains with the neutron number $102\le N\le 124$, using a five-dimensional collective Hamiltonian (5DCH) based on covariant density-functional theory. The potential-energy surfaces display a transition from prolate to oblate or triaxial, and then to near spherical shapes as the neutron number increases. The corresponding 5DCH model calculations reproduce the empirical isotopic trend of the characteristic collective observables and confirm the overall shape transition in this region. It is emphasized that a rapid shape transition between prolate and oblate shapes is predicted in Er and Yb isotopic chains while it becomes smooth for higher-$Z$ isotopic chains and signature for rigid triaxial deformation is found in the transitional isotopes, e.g., ${}^{194}\mathrm{W}$ and ${}^{192\text{–}196}\mathrm{Os}$ by analyzing the energy staggering and probability density distribution in the $\gamma$ bands. Finally, the calculated low-lying spectra for ${}^{184}\mathrm{Er}$ and ${}^{186}\mathrm{Yb}$ demonstrate a remarkable multishape coexistence of medium-deformed oblate, medium- and large-deformed prolate shapes in both nuclei.

We report on systematical optical model (OM) and continuum discretized coupled channel (CDCC) calculations applied to describe the elastic scattering angular distributions of exotic and stable nuclei projectiles on heavy targets. Our optical potential (OP) is composed of the nuclear microscopic double folding São Paulo potential (SPP), derived from the nonlocal nature of the interaction, and the Coulomb dipole polarization (CDP) potential, derived from the semiclassical theory of Coulomb excitation. The OP is compared to the trivial equivalent local potential (TELP), extracted from CDCC calculations. The OM and CDCC predictions corroborate each other and account for important differences in the nuclei reaction mechanisms, which are directly related to their structural properties. Thus, OM and CDCC establish a common basis for analyzing or even predicting exotic and stable nuclei reactions.

Three-body calculations of the $K\overline{K}N$ system with quantum numbers $I=1/2$, $J^{\pi }={\left(\frac{1}{2}\right)}^{+}$ were performed. Using separable potentials for two-body interactions, we calculated the $\pi \mathrm{\Sigma }$ mass spectra for the ${\left(\overline{K}N\right)}_{I=0}+K^{+}\to {\left(\pi \mathrm{\Sigma }\right)}^0{K}^{+}$ reaction on the basis of the three-body Alt-Grassberger-Sandhas equations in the momentum representation. In this regard, different types of $\overline{K}N\text{−}\pi \mathrm{\Sigma }$ potentials based on a phenomenological and chiral SU(3) approach were used. The possibility to observe the trace of the $\mathrm{\Lambda }\left(1405\right)$ resonance in the ${\left(\pi \mathrm{\Sigma }\right)}^0$ mass spectrum was studied. Using the ${\chi }^2$ fitting, it was shown that the mass of the $\mathrm{\Lambda }$(1405) resonance is about $1417\mathrm{MeV}/c^2$.