Most uncertainties regarding the theoretical study of the neutrinoless double-$\beta$ decay are related to the accuracy of the nuclear matrix elements that appear in the expressions of the lifetimes. We calculate the nuclear matrix elements for the $0\nu \beta \beta$ decay of ${}^{130}\mathrm{Te}$ in a shell model approach, using a recently proposed effective Hamiltonian. To ensure the reliability of the results, we investigate this Hamiltonian by performing calculations of spectroscopic quantities and comparing them to the latest experimental data available, and we analyze the $2\nu \beta \beta$- and the $0\nu \beta \beta$-decay nuclear matrix elements of ${}^{136}\mathrm{Xe}$. Finally, we report new nuclear matrix elements for the ${}^{130}\mathrm{Te}$ considering the light neutrino exchange and heavy neutrino exchange mechanisms, alongside an overview of some recent values reported in the literature.

A new approach is presented to determine the proton-nucleus interactions from the analysis of the accompanying photon bremsstrahlung. We study the scattering of $p+{}^{208}\mathrm{Pb}$ at the proton incident energies of 140 and 145 MeV, and the scattering of $p+{}^{12}\mathrm{C},p+{}^{58}\mathrm{Ni},p+{}^{107}\mathrm{Ag}$, and $p+{}^{197}\mathrm{Au}$ at the proton incident energy of 190 MeV. The model determines contributions of the coherent emission (formed by an interaction between the scattering proton and nucleus as a whole without the internal many-nucleon structure), incoherent emission (formed by interactions between the scattering proton and nucleus with the internal many-nucleon structure), and transition between them in dependence on the photon energy. The radius parameter of the proton-nucleus potential for these reactions is extracted from the experimental bremsstrahlung data analysis. We explain the hump-shaped plateau in the intermediate- and high-energy regions of the spectra by the essential presence of the incoherent emission, while at low energies the coherent emission predominates which produces the logarithmic shape spectrum. We provide our predictions (in absolute scale) for the angular distribution of the bremsstrahlung photons in order to test our model, results, and analysis in further experiments.

Three-body nuclear reactions in two-nucleon plus core systems are described in the framework of exact scattering equations including the core excitation. A nucleon-core optical potential is constructed that can be easily adjusted to the reference potential and thereby to the experimental two-body data, if available. This constitutes an important improvement over the simple deformation of the potential used previously that violated the original fit to the data. Predictions for elastic, inelastic, and transfer reactions involving ${}^{10}\mathrm{Be}$ and ${}^{24}\mathrm{Mg}$ nuclear cores are obtained. The new optical potential leads to a moderate increase of cross sections.

Electromagnetic (EM) radiation off strongly interacting matter created in high-energy heavy-ion collisions (HICs) encodes information on the high-temperature phases of nuclear matter. Microscopic calculations of thermal EM emission rates are usually rather involved and not readily accessible to broad applications in models of the fireball evolution which are required to compare with experimental data. An accurate and universal parametrization of the microscopic calculations is thus key to honing the theory behind the EM spectra. Here we provide such a parametrization for photon emission rates from hadronic matter, including the contributions from in-medium $\rho$ mesons (which incorporate effects from baryons and antibaryons), as well as bremsstrahlung from $\pi \pi$ scattering. Individual parametrizations for each contribution are numerically determined through nested fitting functions for photon energies from 0.2 to 5 GeV in chemically equilibrated matter of temperatures 100–180 MeV and baryon chemical potentials 0–400 MeV. Special care is taken to extent the parametrizations to chemical off-equilibrium as encountered in HICs after chemical freeze-out. This provides a functional description of thermal photon rates within a 20% variation of the microscopically calculated values.

This work aims at a global assessment of the effect of the density dependence of the zero-range pairing interaction. Systematic Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface, and mixed pairing forces are carried out to study the pairing gaps in even-even nuclei over the whole nuclear chart. Calculations are also done in coordinate representation for unstable semimagic even-even nuclei. The calculated pairing gaps are compared with empirical values from four different odd-even staggering formulas. Calculations with the three pairing interactions are comparable for most nuclei close to the $\beta$-stability line. However, the surface interaction calculations predict neutron pairing gaps in neutron-rich nuclei that are significantly stronger than those given by the mixed and volume pairing. On the other hand, calculations with volume and mixed pairing forces show noticeable reduction of neutron pairing gaps in nuclei far from stability.

Transverse responses of the upper components, lower components, and crossed term of the bound single-nucleon Dirac-4 spinors of spin-orbit partners to elastic magnetic electron scattering are investigated. For the nuclear spin-orbit partners with $l\le 3$ or in the $s$-d $f$shell or lower, results show that in the elastic magnetic electron scattering process the lower component of the $j=(l-\frac{1}{2})$ partner may play a relatively more important role than that of the $j=(l+\frac{1}{2})$ partner, while the upper component of the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than that of $j=(l-\frac{1}{2})$ partner. The results also show that for the response of the crossed term the $j=(l+\frac{1}{2})$ partner may play a relatively more important role than the $j=(l-\frac{1}{2})$ partner. In addition, it is also found that the dominant $M1$ multipole of the magnetic form factors in the small momentum transfer region may mainly originate from the convection current transition density.

Motivated by the importance of ${}^{25}\mathrm{P}$ for the two-proton decay of ${}^{26}\mathrm{S}$ and for searches of the mirror analog of the island of inversion near $N=16$, we present the first predictions for the spectroscopy of the exotic isotope ${}^{25}\mathrm{P}$ obtained in the shell model, a potential model, and a microscopic-cluster model. All models predict ${}^{25}\mathrm{P}$ to be unbound, with an energy in the range $0.78–1.03$ MeV, which favors previous mass systematics over more recent revisions. We show that ${}^{25}\mathrm{P}$ possesses a rich low-lying spectrum that should be accessible by experimental studies. All of the predicted states below 7 MeV, except one, are narrow. Many of them are built on the excited-core states of ${}^{24}\mathrm{Si}$ for which the Coulomb barrier is raised. For decays into the ${}^{24}\mathrm{Si}\left(\text{g.s.}\right)+p$ channel we determined the proton widths based on their link to the asymptotic normalization coefficients (ANCs) of their mirror analogs in ${}^{25}\mathrm{Ne}.$ We determine these ANCs from the analysis of the transfer reaction ${}^{24}\mathrm{Ne}{(d,p)}^{25}\mathrm{Ne}$. The proton widths for decay into excited-state channels are obtained in model calculations. The only broad state is the intruder $3/2{}^{-}$, the mirror analog of which has been recently observed in ${}^{25}\mathrm{Ne}.$ The ${}^{25}\mathrm{P}(3/2^{-})$ energy is lower than that in ${}^{25}\mathrm{Ne}$, suggesting that the island of inversion may persist on the proton-rich side. All excited states of ${}^{25}\mathrm{P}$ have at least two decay modes and are expected to populate variously the $2_{1,2}^{+}$ and $4^{+}$ states in ${}^{24}\mathrm{Si}$, which then decay electromagnetically.

The ${}^{238}\mathrm{U}$ to ${}^{235}\mathrm{U}$ fission cross section ratio has been determined at n_TOF up to $\approx 1$ GeV, with two different detection systems, in different geometrical configurations. A total of four datasets has been collected and compared. They are all consistent to each other within the relative systematic uncertainty of 3–4%. The data collected at n_TOF have been suitably combined to yield a unique fission cross section ratio as a function of neutron energy. The result confirms current evaluations up to 200 MeV. Good agreement is also observed with theoretical calculations based on the $\mathrm{INCL}++/$Gemini$++$ combination up to the highest measured energy. The n_TOF results may help solve a long-standing discrepancy between the two most important experimental datasets available so far above 20 MeV, while extending the neutron energy range for the first time up to $\approx 1$ GeV.

The full relaxed-density potential between spherical nuclei is considered as a sum of the macroscopic and shell-correction contributions. The macroscopic part of the potential is related to a nucleus-nucleus potential obtained in the framework of the extended Thomas-Fermi approach with the Skyrme and Coulomb forces and the relaxed-density ansatz for evaluation of proton and neutron densities of interacting nuclei. A simple prescription for the shell-correction part of the total potential is discussed. The parameters of the shell-correction and macroscopic parts of the relaxed-density potential are found by fitting the empirical barrier heights of the 89 nucleus-nucleus systems as well as macroscopic potentials evaluated for 1485 nucleus-nucleus systems at 12 distances around touching points.

Based on an isospin and momentum-dependent transport model, we studied the effect of the momentum-dependent symmetry potential on the free neutron-to-proton ratio of pre-equilibrium nucleon emission. It is found that, for the ${}^{132}\text{Sn}{+}^{124}\text{Sn}$ reaction at 400 MeV/nucleon incident beam energy, the free $n/p$ ratio of pre-equilibrium nucleon emission mainly probes the momentum dependence of the symmetry potential at a nucleon momentum around 400–600 MeV/$c$, whereas for 200 MeV/nucleon incident beam energy this observable mainly probes the momentum dependence of the symmetry potential at a nucleon momentum around 200–400 MeV/$c$. To probe the symmetry energy/potential using free $n/p$ ratio, not all the details of the momentum dependence of the symmetry potential are important: the values of symmetry potential in only a certain momentum range are crucial for an observable. It is important to input reasonable density and momentum dependence of the symmetry potential according to the magnitude of incident beam energy of heavy-ion collisions. The present experimental data on the symmetry potential are not enough for probing the density-dependent symmetry energy. More experimental data (such as nucleon and nuclei scattering experiments at different nucleonic momenta and densities) on the symmetry potential are therefore needed to pin down the density-dependent symmetry energy.

In this paper we revisit spin $I$ ground state probabilities (denoted by $P\left(I\right))$ of a few integrable systems under random interactions. We obtain explicit and simple formulas of $P\left(I\right)$ for $d$-boson systems and fermions in a $j=5/2$ shell.

An inelastic excitation experiment was performed with a ${}^{12}\mathrm{Be}$ beam at 29 MeV/u on a carbon target. New resonances close to the respective cluster separation thresholds were observed in ${}^{12}\mathrm{Be}$ for the ${}^4\mathrm{He}+{}^8\mathrm{He}$ and ${}^6\mathrm{He} + {}^6\mathrm{He}$ decay channels, confirming the previously proposed molecular rotational bands. Using the model-independent angular correlation analysis, a $0^{+}$ spin parity is assigned to the remarkably large peak at 10.3 MeV in the ${}^4\mathrm{He} + {}^8\mathrm{He}$ channel. A distorted wave Born approximation (DWBA) calculation was compared to the experimental differential cross section of this state, resulting in a largely enhanced monopole transition matrix element of $7.0\pm 1.0{\mathrm{fm}}^2$, in good agreement with the generalized two-center cluster model (GTCM) prediction assuming a preformed $\alpha \text{−}4n\text{−}\alpha$ configuration. Together with the previously reported large cluster spectroscopic factor, the strong clustering in ${}^{12}\mathrm{Be}$ is well demonstrated. The detection focused on the most forward angles, by using a zero-deg telescope, is essential in the present measurement.

We present blast wave fits to elliptic flow [$v_2\left(p_{\mathrm{T}}\right)$] data in minimum bias collisions from $\sqrt{s_{\mathit{\text{NN}}}}=7.7–200$ GeV at the BNL Relativistic Heavy Ion Collider, and also at the CERN Large Hadron Collider energy of 2.76 TeV. The fits are performed separately for particles and corresponding antiparticles. The mean transverse velocity parameter $\beta$ shows an energy-dependent difference between particles and corresponding antiparticles, which increases as the beam energy decreases. Possible effects of feed down, baryon stopping, antiparticle absorption, and early production times for antiparticles are discussed.

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of $p$- and lower-$sd$-shell nuclei. As a first application we concentrate on energy levels of the ${}^9\mathrm{Be}$ system for which all excited states lie above the n-${}^8\mathrm{Be}$ threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the ${\frac{1}{2}}^{+}$ resonance energy, which is of astrophysical interest, in good agreement with experiment.

The isoscalar monopole excitation of ${}^4\mathrm{He}$ is studied within a few-body ab initio approach. We consider the transition density to the low-lying and narrow $0^{+}$ resonance, as well as various sum rules and the strength energy distribution itself at different momentum transfers $q$. Realistic nuclear forces of chiral and phenomenological nature are employed. Various indications for a collective breathing mode are found: (i) the specific shape of the transition density, (ii) the high degree of exhaustion of the non-energy-weighted sum rule at low $q,$ and (iii) the complete dominance of the resonance peak in the excitation spectrum. For the incompressibility $K$ of the $\alpha$ particle, two different definitions give two rather small values (22 and 36 MeV).

Employing the known experimental fact that the sub-barrier capture (fusion) enhancement in the reactions ${}^{40}\mathrm{Ca}+{}^{94,96}\mathrm{Zr}$ and ${}^{40}\mathrm{Ca}+{}^{116,124,132}\mathrm{Sn}$ is not proportional to the magnitudes of $Q$ values for the neutron transfer, the similarity of the structure of the target nuclei, and the conservation of the total reaction flux, we analyze the dependence of a few-neutron transfer probability on the magnitudes of $Q$ values. This analysis is checked by the calculations of nucleon transfer probabilities within the time-dependent Hartree-Fock plus BCS approach.

In this work we analyze the theoretical uncertainties on the predictions for the photoproduction of light vector mesons in coherent $pp$, $pA$, and $AA$ collisions at the CERN Large Hadron Collider energies using the color dipole approach. In particular, we present our predictions for the rapidity distribution for ${\rho }^0$ and $\varphi$ photoproduction and perform an analysis on the uncertainties associated to the choice of vector meson wave function and the phenomenological models for the dipole cross section. Comparison is done with the recent ALICE analysis on coherent production of ${\rho }^0$ at 2.76 TeV in PbPb collisions.

We systematically construct $I\left(J^P\right)=0\left(3^{+}\right)$ six-quark local interpolating currents without derivative operators. We discuss the best choice of operator and select three $\Delta \text{−}\Delta$-like operators to perform QCD sum rule analyses to calculate the mass of the $d^{*}\left(2380\right)$. The mass extracted from this analysis is $M_{d^{*}}=2.4\pm 0.2$ GeV, consistent with the $d^{*}\left(2380\right)$ mass observed by the WASA detector at COSY. We also obtain a sum rule lower mass bound $M_{d^{*}}>2.25$ GeV. We also consider the effect of mixing of singlet dibaryon fields with the same quantum numbers, and perform the QCD sum rule analysis of the mixed interpolating current and extract the mass of the $d^{*}\left(2380\right)$ and its lower mass bound. With optimized mixing parameters, we find that the mixed current does not change the numerical result significantly.

The nuclear symmetry energy $\left(E_{\mathrm{sym}}\left(\rho \right)\right)$ is a vital ingredient of our understanding of many processes, from heavy-ion collisions to neutron stars structure. While the total nuclear symmetry energy at nuclear saturation density $\left({\rho }_0\right)$ is relatively well determined, its value at supranuclear densities is not. The latter can be better constrained by separately examining its kinetic and potential terms and their density dependencies. The kinetic term of the symmetry energy, $E_{\mathrm{sym}}^{\mathrm{kin}}\left({\rho }_0\right)$, equals the difference in the per-nucleon kinetic energy between pure neutron matter (PNM) and symmetric nuclear matter (SNM), often calculated using a simple Fermi gas model. However, experiments show that tensor force induced short-range correlations (SRC) between proton-neutron pairs shift nucleons to high momentum in SNM, where there are equal numbers of neutrons and protons, but have almost no effect in PNM. We present an approximate analytical expression for $E_{\mathrm{sym}}^{\mathrm{kin}}\left({\rho }_0\right)$ of correlated nucleonic matter. In our model, $E_{\mathrm{sym}}^{\mathrm{kin}}\left({\rho }_0\right)=-10$ MeV, which differs significantly from +12.5 MeV for the widely-used free Fermi gas model. This result is consistent with our analysis of recent data on the free proton-to-neutron ratios measured in intermediate energy nucleus-nucleus collisions as well as with microscopic many-body calculations, and previous phenomenological extractions. We then use our calculated $E_{\mathrm{sym}}^{\mathrm{kin}}\left(\rho \right)$ in combination with the known total symmetry energy and its density dependence at saturation density to constrain the value and density dependence of the potential part and to extrapolate the total symmetry energy to supranuclear densities.