Proton pair correlations relevant for the neutrinoless double-$\beta$ decay of ${}^{76}$Ge have been probed via the ${}^{74,76}$Ge(${}^3$He,$n$) reactions at 16 MeV. No evidence for pairing vibrations in either nucleus is observed at sensitivity limits of $\sim$6$\%$ and $\sim$19$\%$ of the ground-state strength in ${}^{76}$Se and ${}^{78}$Se, respectively. These results are relevant for the understanding of matrix elements for neutrinoless double-$\beta$ decay. The lack of pairing vibrations is consistent with a simple BCS structure for the ground states of ${}^{76}$Ge and ${}^{76}$Se, assumed in quasiparticle random phase approximation (QRPA) models of the process.

The effects of the correlations in the ground state of ${}^{16}$O on the octupole and dipole excitations are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. It is found that the ground-state correlation effects are significant, especially in the octupole excitation. It is shown that the first $3^{-}$ state calculated in the random phase approximation (RPA) is shifted upward when the self-energy contributions are included in particle-hole pairs. The coupling to the two-particle–two-hole states plays a role in shifting the first $3^{-}$ state down to the right position. It is also found that the dipole strength is fragmented due to the partial occupation of the single-particle states and that the peak position of the giant dipole resonance calculated in ERPA is little changed from that in RPA due to the above-mentioned competing effects: the increase in particle-hole energy and the coupling to two-particle–two-hole configurations.

The odd-even staggerings (OESs) on nuclear binding energies are studied systematically within the spherical covariant density functional (CDF) theories, specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and the relativistic Hartree-Bogoliubov (RHB) theories. When taking the finite-range Gogny force D1S as an effective pairing interaction, both CDF models can provide appropriate descriptions on the OESs of nuclear binding energies for C, O, Ca, Ni, Zr, Sn, Ce, Gd, and Pb isotopes as well as for $N=50$ and 82 isotones. While there still exist some systematical discrepancies from the data, i.e., the underestimated OESs in light C and O isotopes and the overestimated ones in heavy regions, respectively, such discrepancies can be eliminated partially by introducing a $Z$- or $N$-dependent strength factor into the pairing force Gogny D1S. As an example of application, distinct improvements are achieved with the optimized pairing force in determining the single-particle configurations of ${}^{112,114,118,124}$Sn.

Background: Two important parametrizations of momentum-dependent nucleonic fields, proposed for the simulations of central heavy-ion collisions, one by Gale et al. [Phys. Rev. C 35, 1666 (1987)] and the other by Welke et al. [Phys. Rev. C 38, 2101 (1988)], suffer from practical limitations. The first gives rise to mean fields isotropic in momentum, even when underlying momentum distributions are anisotropic, making descriptions of early nonequilibrium stages of collisions unrealistic. The second parametrization gives rise to anisotropic mean fields, but is computationally expensive, because the mean field has to be computed separately for every location of a nucleon in phase space, through folding.

Purpose: Here we construct a parametrization of the nucleonic mean field that yields an anisotropic mean field for an anisotropic momentum distribution and is inexpensive computationally. To demonstrate the versatility of our parametrization, we take the case of results from the parametrization by Welke et al. [Phys. Rev. C 38, 2101 (1988)] and attempt to approximate them.

Method: In arriving at a suitable anisotropic mean-field potential, we draw, on one hand, from the idea behind the parametrization of Gale et al. [Phys. Rev. C 35, 1666 (1987)], of a separable expansion of the potential energy, and, on the other, from the idea of a parallel expansion of the energy and mean field in anisotropy.

Results: We show that using our novel parametrization we can qualitatively and partially quantitatively reproduce the features of the mean-field parametrization of Welke et al. [Phys. Rev. C 38, 2101 (1988)].

Conclusions: This opens up the possibility of exploring the effects of mean-field anisotropy in collisions, without the penalty of computational cost behind the folding parametrization.

We present theoretical predictions for electron scattering on oxygen and calcium isotopic chains. The calculations are done within the framework of the distorted-wave Born approximation and the proton and neutron density distributions are evaluated adopting a relativistic Dirac-Hartree model. We present results for the elastic and quasi-elastic cross sections and for the parity-violating asymmetry. As a first step, the results of the models are tested in comparison with some of the data available for elastic and quasi-elastic scattering on ${}^{16}$O and ${}^{40}$Ca nuclei. Then, the evolution of some nuclear properties is investigated as a function of the neutron number. We also present a comparison with the parity-violating asymmetry parameter obtained by the PREX Collaboration on ${}^{208}$Pb and give a prediction for the future experiment CREX on ${}^{48}$Ca.

Background: A complete set is a minimum set of observables which allows one to determine the underlying reaction amplitudes unambiguously. Pseudoscalar-meson photoproduction from the nucleon is characterized by four such amplitudes and complete sets involve single- and double-polarization observables.

Purpose: Identify complete sets of observables and study how measurements with finite error bars impact their potential to determine the reaction amplitudes unambiguously.

Method: The authors provide arguments to employ the transversity representation in order to determine the amplitudes in pseudoscalar-meson photoproduction. It is studied whether the amplitudes in the transversity basis for the $\gamma p\to K^{+}\Lambda$ reaction can be estimated without ambiguity. To this end, data from the GRAAL collaboration and simulations from a realistic model are analyzed.

Results: It is illustrated that the moduli of normalized transversity amplitudes can be determined from precise single-polarization data. Starting from simulations with achievable experimental resolution, it is quite likely to obtain imaginary solutions for the relative phases of the amplitudes. Also the real solutions face a discrete phase ambiguity which makes it impossible to obtain a statistically significant solution for the relative phases at realistic experimental conditions.

Conclusions: Single polarization observables are effective in determining the moduli of the amplitudes in a transversity basis. Determining the relative phases of the amplitudes from double-polarization observables is far less evident. The availability of a complete set of observables does not allow one to unambiguously determine the reaction amplitudes with statistical significance.

Resonances just above the proton threshold in ${}^{30}\mathrm{S}$ affect the ${}^{29}\mathrm{P}{(p,\gamma )}^{30}\mathrm{S}$ reaction under astrophysical conditions. The ($p$,$\gamma$)-reaction rate is currently determined indirectly and depends on the properties of the relevant resonances. We present here a method for finding the ratio between the proton and $\gamma$ partial widths of resonances in ${}^{30}\mathrm{S}$. The widths are determined from the $\beta$2$p$- and $\beta$$p$$\gamma$-decay of ${}^{31}\mathrm{Ar}$, which is produced at the ISOLDE radioactive ion beam facility at the European research organization CERN. Experimental limits on the ratio between the proton and $\gamma$ partial widths for astrophysical relevant levels in ${}^{30}\mathrm{S}$ have been found for the first time. A level at $4689.2\left(24\right)\mathrm{keV}$ is identified in the $\gamma$ spectrum, and an upper limit on the ${\Gamma }_p/{\Gamma }_{\gamma }$ ratio of $0.26$ ($95\%$ C.L.) is found. In the two-proton spectrum two levels at $5227\left(3\right)\mathrm{keV}$ and $5847\left(4\right)\mathrm{keV}$ are identified. These levels were previously seen to $\gamma$ decay and upper limits on the ${\Gamma }_{\gamma }/{\Gamma }_p$ ratio of $0.5$ and 9, respectively, ($95\%$ C.L.) are found, where the latter differs from previous calculations.

The phase diagram of a system constituted of neutrons, protons, $\Lambda$ hyperons, and electrons is evaluated in the mean-field approximation in the complete three-dimensional space given by the baryon, lepton, and strange charge. It is shown that the phase diagram at subsaturation densities is strongly affected by the electromagnetic interaction, while it is almost independent of the electric charge at suprasaturation density. As a consequence, stellar matter under the condition of strangeness equilibrium is expected to experience a first as well as a second-order strangeness-driven phase transition at high density, while the liquid-gas phase transition is expected to be quenched. An RPA calculation indicates that the presence of this critical point might have sizable implications for the neutrino propagation in core-collapse supernovae.

Excited states in ${}^{132,134}$Nd were populated in the ${\beta }^{+}$/$\epsilon$ decay of ${}^{132,134}$Pm and studied through off-beam $\gamma$-ray spectroscopy. Level spins and multipole mixing ratios of transitions were determined through an angular correlation analysis. In ${}^{132}$Nd, a new excited $0^{+}$ state is identified and in ${}^{134}$Nd the level scheme is significantly extended. Differences in the location of the $0_2^{+}$ state and the $\gamma$ bandhead above and below $N=82$ suggest that the lighter isotopes are much more $\gamma$-soft than the heavier Nd and that a first-order phase transitional description is not applicable in the $N<82$ region.

High-energy-resolution magnetic spectrometer measurements have been used to determine the width of the 9.641 MeV ${}^{12}$C, 3${}^{-}$ excited state. The width is found to be 48(2) keV with an $R$-matrix analysis. This would correspond to 30$\%$ of the Wigner limit, indicating a significant $\alpha$-particle content to the state. This is a marked improvement on results of earlier studies that yielded 34(5) keV.

We have used the relationship between matter radius and separation energy to compute the matter radius as a function of the assumed separation energy for ${}^{34}$Na, whose mass has just recently been measured.

In previous papers we have presented a calculation describing electrodisintegration of the deuteron at GeV energies. The model is fully relativistic and incorporates full spin dependence of the final-state interactions (FSI), which were obtained from the said analysis. It was, however, limited kinematically due to lack of availability of the said amplitudes. This work rectifies this problem by implementing a Regge model to describe the FSI. We present an outline of the model and show comparisons between the two approaches in a region of overlap. We see good agreement between the models, and note observables which can provide additional insight due to model sensitivity.

We discuss $\gamma \gamma \to \pi \pi$ reactions, starting from the two-pion threshold up to about $\sqrt{s_{\gamma \gamma }}=6$ GeV. Several reaction mechanisms are identified. We include the dipion continuum owing to pion exchange (for ${\pi }^{+}{\pi }^{-}$) and ${\rho }^{\pm }$ exchange (for ${\pi }^0{\pi }^0$), as well as the pronounced dipion $\sigma \left(600\right)$, $f_0\left(980\right)$, and $f_2\left(1270\right)$ $s$-channel resonances. We discuss also a possible contribution of less pronounced scalar resonances $f_0\left(1500\right)$ and $f_0\left(1710\right)$, being glueball candidates, as well as the tensor resonances $f_2^{\prime }\left(1525\right)$, $f_2\left(1565\right)$, and $f_2\left(1950\right)$. While the contribution of $f_2^{\prime }\left(1525\right)$ is rather small, the contribution of $f_2\left(1565\right)$ changes the spectrum around the resonance position. We find that the inclusion of the spin-four $f_4\left(2050\right)$ resonant state improves the situation at $\sqrt{s_{\gamma \gamma }}\approx 2$ GeV. We estimate the relevant diphoton partial decay width to be ${\Gamma }_{f_4\to \gamma \gamma }\approx 0.7$ keV. At higher energies, Brodsky-Lepage and handbag mechanisms are included in addition. We nicely describe the world data for $\gamma \gamma \to \pi \pi$ for the first time both for the total cross section and for angular distributions for $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and $\gamma \gamma \to {\pi }^0{\pi }^0$ reactions simultaneously at all experimentally available energies. The cross section for the production of two pions in ultraperipheral ultrarelativistic heavy-ion collisions is calculated in the impact parameter space Equivalent Photon Approximation (EPA). We obtain the nuclear cross section of 46.7 mb for ${\pi }^{+}{\pi }^{-}$ and 8.7 mb for ${\pi }^0{\pi }^0$ at the LHC energy $\sqrt{s_{NN}}=3.5$ TeV and minimal cut on pion transverse momentum $p_t>0.2$ GeV. Differential distributions in impact parameter, dipion invariant mass, single-pion and dipion rapidity, pion transverse momentum, and pion pseudorapidity are shown. The $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ subprocess constitutes a background to the exclusive $AA\to A{\rho }^0(\to {\pi }^{+}{\pi }^{-})A$ process, initiated by photon-pomeron or pomeron-photon subprocesses. We find that only a part of the dipion invariant mass spectrum associated with $\gamma \gamma$ collisions can be potentially visible as the cross section for the $AA\to A{\rho }^{0}A$ reaction is very large.

The rate of muon capture in a muonic hydrogen atom is calculated in heavy-nucleon chiral perturbation theory up to next-to-next-to-leading order. To this order, we present the systematic evaluation of all the corrections due to the QED and electroweak radiative corrections and the proton-size effect. Since the low-energy constants involved can be determined from other independent sources of information, the theory has predictive power. For the hyperfine-singlet $\mu p$ capture rate ${\Gamma }_0$, our calculation gives ${\Gamma }_0=710\pm 5$ s${}^{-1}$, which is in excellent agreement with the experimental value obtained in a recent high-precision measurement by the MuCap Collaboration.

We investigate the polarization parameters in low-energy antiproton-proton elastic ($\overline{p}p\to \overline{p}p$) and charge-exchange ($\overline{p}p\to \overline{n}n$) scattering. The predictions for unmeasured observables are based on our new energy-dependent partial-wave analysis of all antiproton-proton scattering data below 925 MeV/$c$ antiproton laboratory momentum, which gives an optimal description of the existing database. Sizable and remarkable spin effects are observed, in particular for charge-exchange scattering. These result from the spin dependence of the long- and medium-range one- and two-pion exchange antinucleon-nucleon potential and the state dependence of the parametrized short-range interaction. We study the possibility of polarizing a circulating antiproton beam with a polarized proton target by exploiting the spin dependence of the $\overline{p}p$ total cross section. It appears feasible to achieve a significant transverse polarization of an antiproton beam within a reasonable time.

Using a ${}^{13}$O beam, we have observed proton decays of ${}^{12}$N and ${}^{13}$O excited states following proton-knockout and inelastic interactions on a ${}^9$Be target. The excited states were determined from detected two- and three-body exit channels using the invariant mass method. The width of the second excited state of ${}^{12}$N was determined to be 55(20) keV, considerably smaller than the value listed in the ENSDF data base. Three new excited states of narrow width ($\Gamma <50$ keV) were observed in ${}^{13}$O from the $p$+${}^{12}$N and 2$p$+${}^{11}$C exit channels. One of these states ($E^{*}$ = 3.67 MeV) was found to sequentially decay to the second excited of ${}^{12}$N. We again found these data to be inconsistent with the listed decay width. The ramifications for the astrophysically interesting ${}^{11}$C($p$,$\gamma$)${}^{12}$N reaction are given.

We present updated predictions of effective elastic nucleon-nucleon cross sections intended for use in nucleus-nucleus reactions. A novel characteristic of the present approach combines all microscopic medium effects included in the Dirac-Brueckner-Hartree-Fock $G$-matrix with a Pauli blocking mechanism which is more appropriate for applications in ion-ion reaction models as compared to a previous approach. The effective in-medium cross section is found to be quite sensitive to the description of Pauli blocking in the final configurations.

Background: Detailed experimental knowledge of the level structure of light weakly bound nuclei is necessary to guide the development of new theoretical approaches that combine nuclear structure with reaction dynamics.

Purpose: The resonant structure of ${}^8$B is studied in this work.

Method: Excitation functions for elastic and inelastic ${}^7$Be+$p$ scattering were measured using a ${}^7$Be rare isotope beam. Excitation energies ranging between 1.6 and 3.4 MeV were investigated. An $R$-matrix analysis of the excitation functions was performed.

Results: New low-lying resonances at 1.9, 2.54, and 3.3 MeV in ${}^8$B are reported with spin-parity assignment 0${}^{+}$, 2${}^{+}$, and 1${}^{+}$, respectively. Comparison to the time-dependent continuum shell (TDCSM) model and ab initio no-core shell model/resonating-group method (NCSM/RGM) calculations is performed. This work is a more detailed analysis of the data first published as a Rapid Communication. J. P. Mitchell, G. V. Rogachev, E. D. Johnson, L. T. Baby, K. W. Kemper et al., [Phys. Rev. C 82, 011601(R) (2010)].

Conclusions: Identification of the 0${}^{+}$, 2${}^{+}$, 1${}^{+}$ states that were predicted by some models at relatively low energy but never observed experimentally is an important step toward understanding the structure of ${}^8$B. Their identification was aided by having both elastic and inelastic scattering data. Direct comparison of the cross sections and phase shifts predicted by the TDCSM and ab initio no-core shell model coupled with the resonating group method is of particular interest and provides a good test for these theoretical approaches.

Using the Langevin dynamical approach, the neutron multiplicity and the anisotropy of angular distribution of fission fragments in heavy ion fusion-fission reactions were calculated. We applied one- and two-dimensional Langevin equations to study the decay of a hot excited compound nucleus. The influence of the level-density parameter on neutron multiplicity and anisotropy of angular distribution of fission fragments was investigated. We used the level-density parameter based on the liquid drop model with two different values of the Bartel approach and Pomorska approach. Our calculations show that the anisotropy and neutron multiplicity are affected by level-density parameter and neck thickness. The calculations were performed on the ${}^{16}$O+${}^{208}$Pb and ${}^{20}$Ne+${}^{209}$Bi reactions. Obtained results in the case of the two-dimensional Langevin with a level-density parameter based on Bartel and co-workers approach are in better agreement with experimental data.