We study the resonant neutrinoless double-electron capture ($0\nu$ECEC) in ${}^{152}\mathrm{Gd}$, ${}^{164}\mathrm{Er}$, and ${}^{180}\mathrm{W}$ atoms, associated with the ground-state to ground-state nuclear transitions. The corresponding matrix elements are calculated within the deformed quasiparticle random-phase approximation using the realistic charge-dependent Bonn (CD-Bonn) nucleon-nucleon interaction. The half-lives are estimated with the use of the most recent precision data on the $Q$ values of these processes. Perspectives of experimental search for the $0\nu$ECEC with the isotopes ${}^{152}\mathrm{Gd}$, ${}^{164}\mathrm{Er}$, and ${}^{180}\mathrm{W}$ are discussed.

Low energy incomplete fusion has been studied in ${}^{12}$C+${}^{159}$Tb system at energies $\approx$ 4–7 MeV/nucleon. The excitation functions of individual reaction channels have been measured using off-line $\gamma$ spectroscopy, and analyzed in the framework of statistical model code pace4 based on the concept of equilibrated compound nucleus decay. A significant fraction of incomplete fusion has been found in the production of residues involving $\alpha$ particle(s) in the exit channels. For better insights into the onset and strength of incomplete fusion, the incomplete fusion strength function has been deduced as a function of various entrance channel parameters. Large influence of incomplete fusion has been observed at slightly above barrier energies, and increases smoothly with incident projectile energy. Present results have been compared with the results obtained in the interactions of ${}^{12}$C with nearby targets to probe the dependence of incomplete fusion on entrance channel mass asymmetry. It has been found that the percentage fraction of incomplete fusion increases linearly with mass asymmetry of interacting partners in the studied mass region.

Spectra of positively charged kaons in $p+\text{C}$ interactions at 31 GeV/$c$ were measured with the NA61/SHINE spectrometer at the CERN SPS. The analysis is based on the full set of data collected in 2007 with a graphite target with a thickness of 4$\%$ of a nuclear interaction length. Interaction cross sections and charged pion spectra were already measured using the same set of data. These new measurements in combination with the published ones are required to improve predictions of the neutrino flux for the T2K long-baseline neutrino oscillation experiment in Japan. In particular, the knowledge of kaon production is crucial for precisely predicting the intrinsic electron neutrino component and the high-energy tail of the T2K beam. The results are presented as a function of laboratory momentum in two intervals of the laboratory polar angle covering the range from 20 to 240 mrad. The kaon spectra are compared with predictions of several hadron production models. Using the published pion results and the new kaon data, the $K^{+}$/${\pi }^{+}$ ratios are computed.

We use distorted wave electron scattering calculations to extract the weak charge form factor $F_W\left(\overline{q}\right)$, the weak charge radius $R_W$, and the point neutron radius $R_n$ of ${}^{208}$Pb from the Lead Radius Experiment (PREX) parity-violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer $\overline{q}=0.475$ fm${}^{-1}$. We find $F_W\left(\overline{q}\right)=0.204\pm 0.028\left(\exp \right)\pm 0.001\left(\mathrm{model}\right)$. We use the Helm model to infer the weak radius from $F_W\left(\overline{q}\right)$. We find $R_W=5.826\pm 0.181\left(\exp \right)\pm 0.027\left(\mathrm{model}\right)\mathrm{fm}$. Here the experimental error includes PREX statistical and systematic errors, while the model error describes the uncertainty in $R_W$ from uncertainties in the surface thickness $\sigma$ of the weak charge density. The weak radius is larger than the charge radius, implying a “weak charge skin” where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius $R_n=5.751\pm 0.175\left(\exp \right)\pm 0.026\left(\mathrm{model}\right)\pm 0.005\left(\mathrm{strange}\right)\mathrm{fm}$ from $R_W$. Here there is only a very small error (strange) from possible strange quark contributions. We find $R_n$ to be slightly smaller than $R_W$ because of the nucleon's size. Finally, we find a neutron skin thickness of $R_n-R_p=0.302\pm 0.175\left(\exp \right)\pm 0.026$ (model) $\pm$ 0.005 (strange) fm, where $R_p$ is the point proton radius.

Background: Phase-equivalent transformations (PETs) are well known in quantum scattering and inverse-scattering theory. PETs do not affect scattering phase shifts and bound-state energies of a two-body system but are conventionally supposed to modify two-body bound-state observables such as the rms radius and electromagnetic moments.

Purpose: In order to preserve all bound-state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound-state (deuteron) binding energy but also the bound-state wave function.

Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of ${}^3$H and ${}^4$He binding energies in the no-core full configuration (NCFC) approach based on extrapolations of the no-core shell model (NCSM) basis space results to the infinite basis space.

Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of ${}^3$H and ${}^4$He nuclei and their correlation (Tjon line).

Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of ${}^3$H (in the range of approximately 1.5 MeV) and ${}^4$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei.

The present work discusses, from an ab initio standpoint, the definition, the meaning, and the usefulness of effective single-particle energies (ESPEs) in doubly closed shell nuclei. We perform coupled-cluster calculations to quantify to what extent selected closed-shell nuclei in the oxygen and calcium isotopic chains can effectively be mapped onto an effective independent-particle picture. To do so, we revisit in detail the notion of ESPEs in the context of strongly correlated many-nucleon systems and illustrate the necessity of extracting ESPEs through the diagonalization of the centroid matrix, as originally argued by Baranger. For the purpose of illustration, we analyze the impact of correlations on observable one-nucleon separation energies and nonobservable ESPEs in selected closed-shell oxygen and calcium isotopes. We then state and illustrate the nonobservability of ESPEs. Similarly to spectroscopic factors, ESPEs can indeed be modified by a redefinition of inaccessible quantities while leaving actual observables unchanged. This leads to the absolute necessity of employing consistent structure and reaction models based on the same nuclear Hamiltonian to extract the shell structure in a meaningful fashion from experimental data.

The relativistic optical model potential (OMP) for nucleon-nucleus scattering is investigated in the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-B one-boson-exchange potential for the bare nucleon-nucleon interaction. Both real and imaginary parts of isospin-dependent nucleon self-energies in the nuclear medium are derived from the DBHF approach based on the projection techniques within the subtracted $T$-matrix representation. The Dirac potentials as well as the corresponding Schrödinger equivalent potentials are evaluated. An improved local density approximation is employed in this analysis, where a range parameter is included to account for a finite-range correction of the nucleon-nucleon interaction. As an example the total cross sections, differential elastic scattering cross sections, analyzing powers for $n$, $p$ $+$ ${}^{27}$Al at incident energy 100 keV $\le E\le$ 250 MeV are calculated. The results derived from this microscopic approach of the OMP are compared to the experimental data, as well as the results obtained with a phenomenological OMP. A good agreement between the theoretical results and the measurements can be achieved for all incident energies using a constant value for the range parameter.

Multiplicity fluctuations at midrapidity in $pp$ collisions at high energies are described by a negative binomial distribution and exhibit approximate Koba-Nielsen-Olesen (KNO) scaling. We find that these KNO fluctuations are important also for reproducing the multiplicity distribution in $d+\mathrm{Au}$ collisions observed at the Relativistic Heavy-Ion Collider (RHIC), adding to the Glauber fluctuations of the number of binary collisions or participants. We predict that the multiplicity distribution in $p+\mathrm{Pb}$ collisions at the Large Hadron Collider (LHC) also deviates little from the KNO scaling function. Finally, we analyze various moments of the eccentricity of the collision zone in $A+A$ collisions at RHIC and LHC and find that particle production fluctuations increase fluctuation dominated moments such as the triangularity ${\epsilon }_3$ substantially.

Two-pion Hanbury-Brown–Twiss (HBT) correlations for central Pb-Pb collisions at the Large-Hadron-Collider (LHC) energy of $\sqrt{s_{NN}}=2.76$ TeV are investigated with the microscopic transport model ultrarelativistic quantum molecular dynamics. The transverse momentum dependence of the Pratt-Bertsch HBT radii is extracted from a three-dimensional Gaussian fit to the correlator in the longitudinal comoving system. Qualitative agreement with the ALICE data is obtained, however $R_{\mathrm{out}}$ is overpredicted by nearly 50$\%$. The LHC results are also compared to data from the STAR experiment at RHIC. For both energies we find that the calculated $R_O:R_S$ ratio is always larger than data, indicating that the emission in the model is less explosive than observed in the data.

We report the first extraction of the pion-nucleon multipoles near the production threshold for the $n{\pi }^{+}$ channel at relatively high momentum transfer ($Q^2$ up to 4.2 ${\mathrm{GeV}}^2$). The dominance of the $s$-wave transverse multipole ($E_{0+}$), expected in this region, allowed us to access the generalized form factor $G_1$ within the light-cone sum-rule (LCSR) framework as well as the axial form factor $G_A$. The data analyzed in this work were collected by the nearly $4\pi$ CEBAF Large Acceptance Spectrometer (CLAS) using a 5.754-GeV electron beam on a proton target. The differential cross section and the $\pi$-$N$ multipole $E_{0+}/G_D$ were measured using two different methods, the LCSR and a direct multipole fit. The results from the two methods are found to be consistent and almost $Q^2$ independent.

We report observation of a narrow peak structure at $\sim$1.54 GeV with a Gaussian width $\sigma =6$ MeV in the missing mass of $K_S$ in the reaction $\gamma +p\to p{K}_S{K}_L$. The observed structure may be due to the interference between a strange (or antistrange) baryon resonance in the $p{K}_L$ system and the $\phi \left(K_S{K}_L\right)$ photoproduction leading to the same final state. The statistical significance of the observed excess of events estimated as the log-likelihood ratio of the resonant signal + background hypothesis and the $\phi$-production-based background-only hypothesis corresponds to $5.3\sigma$.

The amplitudes for photoproduction of two pseudoscalars on a nucleon are expanded in the overall center-of-momentum (c.m.) frame in a model-independent way with respect to the contribution of the final-state partial wave of total angular momentum $J$ and its projection on the normal to the plane spanned by the momenta of the final particles. The expansion coefficients, which are analogs to the multipole amplitudes for single-meson photoproduction, contain the complete information about the reaction dynamics. Results of an explicit evaluation are presented for the moments $W_{jm}$ of the inclusive angular distribution of an incident photon beam with respect to the c.m. coordinate system defined by the final particles, taking photoproduction of ${\pi }^0{\pi }^0$ and ${\pi }^0\eta$ as an example.

Background: Nuclear structure plays a significant role on the rapid neutron capture process ($r$ process) since shapes evolve with the emergence of shells and subshells. There was some indication in neighboring nuclei that we might find examples of a new $N=56$ subshell, which may give rise to a doubly magic ${}_{34}^{90}$Se${}_{56}$ nucleus.

Purpose: $\beta$-decay half-lives of nuclei around ${}^{90}$Se have been measured to determine if this nucleus has in fact a doubly magic character.

Method: The fragmentation of a ${}^{136}$Xe beam at the National Superconducting Cyclotron Laboratory at Michigan State University was used to create a cocktail of nuclei in the $A=90$ region.

Results: We have measured the half-lives of 22 nuclei near the $r$-process path in the $A=90$ region. The half-lives of ${}^{88}$As and ${}^{90}$Se have been measured for the first time. The values were compared with theoretical predictions in the search for nuclear-deformation signatures of a $N=56$ subshell, and its possible role in the emergence of a potential doubly magic ${}^{90}$Se. The impact of such hypothesis on the synthesis of heavy nuclei, particularly in the production of Sr, Y, and Zr elements was investigated with a weak $r$-process network.

Conclusions: The new half-lives agree with results obtained from a standard global QRPA model used in $r$-process calculations, indicating that ${}^{90}$Se has a quadrupole shape incompatible with a closed $N=56$ subshell in this region. The impact of the measured ${}^{90}$Se half-life in comparison with a former theoretical predication associated with a spherical half-life on the weak $r$ process is shown to be strong.

High-resolution triple-$\alpha$ coincidence data were used to reconstruct the decay of the excited states in ${}^{12}$C at 7.65 MeV ($J^{\pi }=0^{+}$) and 9.64 MeV $(J^{\pi }=3^{-})$. These data are consistent with the $\alpha$-particle decay of both levels proceeding exclusively through ${}^8$Be${}_{g.s.}$. In the first of these cases, the Hoyle state, an upper limit of 0.45% (at the 99.75% confidence level) is set for a component producing three nearly equal-energy $\alpha$ particles.

We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of time-dependent Hartree-Fock $\left(\mathrm{TDHF}\right)+\mathrm{BCS}$, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in $\mathrm{TDHF}+\mathrm{BCS}$, but there are other problems with the BCS approximation that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the $U$ and $V$ Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schrödinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schrödinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.

Gamma-ray transitions have been observed in the proton-emitting $N=Z+2$ ($T_z=1$) isotope ${}^{112}$Cs. The transitions have been unambiguously assigned to ${}^{112}$Cs by correlation with the characteristic proton decay, using the method of recoil-decay tagging with mass selection. The measured proton-decay energy and half-life are $E_p=810\left(5\right)$ keV and $T_{1/2}=470\left(50\right)$ $\mu$s, respectively, which are consistent with previous measurements. Five $\gamma$-ray transitions have been observed which appear to form a rotational sequence. The energy differences between excited states in the sequence are consistent with an assignment as the favored signature of the $\nu \left(h_{11/2}\right)\otimes \pi \left(h_{11/2}\right)$ structure. Tentative evidence for fine structure in the ${}^{112}$Cs proton decay is also observed.

Within the quantum diffusion approach, the isotopic dependencies of capture cross section and mean-square angular momentum are studied in the reactions ${}^4$He, ${}^{16}$O, ${}^{36}$S, ${}^{48}$Ca $+$ ${}^{196,200,204,208}$Pb and ${}^{16}$O $+$ ${}^{70,72,74,76}$Ge. The results are in a reasonable agreement with existing experimental data.

The effects of including light clusters in nuclear matter at low densities are investigated within four different parametrizations of relativistic models at finite temperature. Both homogeneous and inhomogeneous matter (pasta phase) are described for neutral nuclear matter with fixed proton fractions. We discuss the effect of the density dependence of the symmetry energy, the temperature, and the proton fraction on the nonhomogeneous matter forming the inner crust of protoneutron stars. It is shown that the number of nucleons in the clusters, the cluster proton fraction, and the sizes of the Wigner-Seitz cell and of the cluster are very sensitive to the density dependence of the symmetry energy.