A many-body Hamiltonian involving the mean field for a projected spherical single-particle basis, the pairing interactions for like nucleons, a repulsive dipole-dipole proton-neutron interaction in the particle-hole channel, and an attractive dipole-pairing interaction is treated by a gauge-restored and fully renormalized proton-neutron quasiparticle random-phase approximation formalism. The resulting wave functions and energies for the parent and the daughter nuclei are used to calculate the $2\nu \beta \beta$ decay rate and the process half-life for the emitters: ${}^{48}$Ca, ${}^{76}$Ge, ${}^{82}$Se, ${}^{96}$Zr, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te, ${}^{148,150}$Nd, ${}^{154}$Sm, and ${}^{160}$Gd. The results of our calculations are compared with the corresponding experimental data as well as with those obtained through other methods. The Ikeda sum rule is obeyed.

Post-accelerated isomerically purified radioactive beams, available at the CERN On-Line Isotope Mass Separator facility using the resonant ionization laser technique, have been used to study the Coulomb excitation of the $I^{\pi }$ = 3${}^{-}$ state in ${}^{70}$Cu ($Z=29$, $N=41$). While first results using a $I^{\pi }=6^{-}$ beam were reported previously, the present complementary experiment allows us to complete the study of the multiplet of states (3${}^{-}$, 4${}^{-}$, 5${}^{-}$, 6${}^{-}$) arising from the $\pi 2p_{3/2}\nu 1g_{9/2}$ configuration. Besides the known $\gamma$-ray transition deexciting the 4${}^{-}$ state, a ground-state $\gamma$ ray of 511(3) keV was observed for the first time and was unambiguously associated with the 5${}^{-}$ state deexcitation. This observation fixes the energy, spin, and parity of this state, completing the low-energy level scheme of ${}^{70}$Cu. $B\left(E2\right)$ values for all possible $E2$ transitions within the multiplet were determined. A comparison with large-scale shell model calculations using different interactions and valence spaces shows the importance of proton excitation across the $Z=28$ shell gap and the role of the $2d_{5/2}$ neutron orbital.

Excitation energies and transition probabilities of the first $2^{+}$ excitations in even tin and lead isotopes as well as the quadrupole moments of odd neighbors of these isotopes are calculated within the self-consistent theory of finite Fermi systems based on the energy density functional by Fayans et al. [Nucl. Phys. A 676, 49 (2000)]. The effect of the density dependence of the effective pairing interaction is analyzed in detail by comparing results obtained with volume and surface pairing. The effect is found to be noticeable. For example, the $2^{+}$ energies are systematically higher at 200–400 keV for the volume paring as compared with the surface-pairing case. However, on the average, both models reasonably agree with the data. Quadrupole moments of odd-neutron nuclei are very sensitive to the single-particle energy of the state $\lambda$ under consideration owing to the Bogolyubov factor ($u_{\lambda }^2-v_{\lambda }^2$). A reasonable agreement with experiment for the quadrupole moments has been obtained for the most part of odd nuclei considered. The method used gives a reliable possibility to predict quadrupole moments of unstable odd nuclei, including very neutron rich ones.

It has been shown experimentally that the ${}^6$Li nucleus shrinks by adding a $\Lambda$ particle while its spectrum is also compressed. We discuss the compatibility of these two effects, contrasting also with a relation between the shrinkage effect and the stability of the spectrum in the ${}_{\Lambda }^9$Be hypernucleus. To this end, we employ two-body $d$-${}_{\Lambda }^5$He and $\alpha$-${}_{\Lambda }^5$He cluster models for the ${}_{\Lambda }^7$Li and ${}_{\Lambda }^9$Be hypernuclei, respectively. We first argue that a Gaussian-like interaction between two clusters leads to a stabilization of the spectrum against an addition of a $\Lambda$ particle, even though the intercluster distance is reduced. In the case of ${}_{\Lambda }^7$Li, the spin-orbit interaction between the intercluster motion and the deuteron spin has to be considered also. We show that the shrinkage effect makes the expectation value of the spin-orbit potential larger, lowering the excitation energy for the ${}^6$Li($3^{+})\otimes \Lambda (1/2^{+})$ level.

We use the tools of hybrid intranuclear-cascade/nuclear-deexcitation models to evaluate the sensitivity of several physical observables to the inclusion of a multifragmentation stage in the deexcitation chain and assess the need for a multifragmentation model in the quantitative description of $p$ + ${}^{\text{5}6}$Fe and $p$ + ${}^{\text{1}36}$Xe reactions at 1-GeV incident energy. We seek clear signatures of multifragmentation by comparing different state-of-the-art deexcitation models coupled with intranuclear-cascade models and by focusing on discriminating observables such as correlations and fragment longitudinal-velocity distributions. None of the considered observables can be unambiguously interpreted as a multifragmentation footprint. The experimental data are best described as originating from sequential binary decays. However, no deexcitation model can reproduce the experimental longitudinal-velocity distributions from 1-GeV $p$ + ${}^{\text{1}36}$Xe.

The reaction ${}^8$Li + ${}^2$H has been studied in inverse kinematics at the incident energy of 3.15 MeV/nucleon, using the REX-ISOLDE post-accelerator. The reaction channels corresponding to $(d,p)$, $(d,d)$, and $(d,t)$ reactions populating ground states and low-lying excited states in ${}^{7–9}$Li have been identified and the related angular distributions extracted and compared with coupled-channels, distorted-wave Born approximation (DWBA), and coupled-reaction-channels calculations. For the inelastic and $(d,t)$ channels we find that higher order effects are very important and hence one needs to go beyond the simple DWBA to extract reliable structure information from these processes.

Deuteron production from intermediate-energy proton-nucleus interactions was investigated through experiments and model calculations, mainly to develop a theoretical model by elucidating the mechanism of cluster production. Spectral double-differential cross sections were measured for inclusive $(p,dx)$ reactions on five targets in the periodic table, namely ${}^{12}$C, ${}^{27}$Al, ${}^{51}$V, ${}^{93}$Nb, and ${}^{197}$Au, at beam energies of 300 and 392 MeV. The cross sections were determined in almost the entire outgoing energy range from the highest down to 30 MeV and at laboratory angles from 20${}^{\circ }$ to 104${}^{\circ }$. To interpret the measured spectra, we proposed a new model that includes the nucleon correlations of the initial- and final-state interactions to describe cluster knockout and pickup within the intranuclear cascade model. The results of the model calculations showed reasonable agreements with those of the experiments. Moreover, the model indicated reasonable predictive power for the ($p{,}^3\mathrm{He}x$), $(p,\alpha x)$, and $(d,d^{\prime }x)$ reactions measured elsewhere. The quantum molecular dynamics model underpredicts the results of the experiments by two to three orders except for low-energy portions of the $(p,dx)$ spectra.

Photoproduction of neutral pseudoscalar mesons ${\pi }^0,\eta \left(547\right)$, and ${\eta }^{\prime }\left(958\right)$ in the Coulomb field of an atomic nucleus is studied using a model which describes the Primakoff and nuclear parts of the production amplitude. At high energies the nuclear background is dominated by the exchange of $C$-parity odd Regge trajectories. In the coherent production the isospin filtering makes the $\omega \left(782\right)$ a dominant trajectory. The calculations are in agreement with ${\pi }^0$ data from JLAB provided the photon shadowing and final state interactions of mesons are taken into account. The kinematic conditions which allow to study the Primakoff effect in $\eta$ and ${\eta }^{\prime }$ photoproduction off nuclei are further discussed. We also give predictions for the higher energies available at the JLAB upgrade.

We investigated the superfluid properties of the inner crust of neutron stars, solving the Hartree-Fock-Bogoliubov equations in spherical Wigner-Seitz cells. Using realistic two-body interactions in the pairing channel, we studied in detail the Cooper-pair and the pairing-field spatial properties, together with the effect of the proton clusters on the neutron pairing gap. Calculations with effective pairing interactions are also presented, showing significant discrepancies with the results obtained with realistic pairing forces. At variance with recent studies on finite nuclei, the neutron coherence length is found to depend on the strength of the pairing interaction, even inside the nucleus. We also show that the spherical Wigner-Seitz approximation breaks down in the innermost regions of the inner crust, already at baryonic densities ${\rho }_b\ge 8\times {10}^{+13}$ g/cm${}^3$.

Model predictions of the amount of the radioisotope ${}^{26}$Al produced in hydrogen-burning environments require reliable estimates of the thermonuclear rates for the ${}^{26\mathrm{g}}$Al($p$,γ) ${}^{27}$Si and ${}^{26\mathrm{m}}$Al($p$,γ)${}^{27}$Si reactions. These rates depend upon the spectroscopic properties of states in ${}^{27}$Si within about 1 MeV of the ${}^{26\mathrm{g}}$Al + $p$ threshold ($S_p$ = 7463 keV). We have studied the ${}^{28}$Si(${}^3$He,α)${}^{27}$Si reaction at 25 MeV using a high-resolution quadrupole-dipole-dipole-dipole magnetic spectrograph. For the first time with a transfer reaction, we have constrained $J^{\pi }$ values for states in ${}^{27}$Si over $E_x$ = 7.0–8.1 MeV through angular distribution measurements. Aside from a few important cases, we generally confirm the energies and spin-parity assignments reported in a recent γ-ray spectroscopy study. The magnitudes of neutron spectroscopic factors determined from shell-model calculations are in reasonable agreement with our experimental values extracted using this reaction.

The triple differential cross section of the ${}^{208}{\mathrm{Pb}(}^6\mathrm{Li},{\alpha d)}^{208}\mathrm{Pb}$ quasielastic breakup is calculated at a collision energy of 156 MeV and a scattering angle range of $2^{\circ }–6^{\circ }$. We fit the parameters of the Woods-Saxon potential using the experimental $\alpha -d$ phase shifts for different states to describe the relative motion of the $\alpha$ particle and deuteron. To check the validity of the two particle approach for the $\alpha -d$ system, we apply a potential model to describe the ${}^2\mathrm{H}{(\alpha ,\gamma )}^6\mathrm{Li}$ radiative capture. We calculate the Coulomb breakup using the semiclassical method while an estimation of the nuclear breakup is made on the basis of the diffraction theory. A comparison of our calculation with the experimental data of Kiener et al. [Phys. Rev. C 44, 2195 (1991)] gives evidence for the dominance of the Coulomb dissociation mechanism and the contribution of nuclear distortion, but is essentially smaller than the value reported by Hammache et al. [Phys. Rev. C 82, 065803 (2010)]. The results of our calculation for the triple cross sections (contributed by the Coulomb and nuclear mechanisms) of the ${}^6\mathrm{Li}$ breakup hint toward a forward-backward asymmetry in the relative direction of the $\alpha$ particle and deuteron emission, especially at smaller scattering angles, in the ${}^6\mathrm{Li}$ center-of-mass (c.m.) system.

The effect of the symmetry energy on the properties of compact stars is discussed. It is shown that, for stars with masses above $1M_{\odot }$, the radius of the star varies linearly with the symmetry energy slope $L$. We also analyze the dependence of the hyperon content and onset density of the direct Urca process on the symmetry energy and meson coupling parametrization.

The role of the particle-particle $p$-wave spin interaction in Fermi liquids with an $s$-wave pairing is studied. Depending on the sign of the interaction, there arises either a new exciton collective mode below the pair-breaking threshold or a diffusive excitation mode above the threshold. The Landau parameters that control the interaction strength are evaluated for various systems: dilute fermion gases, a degenerate electron liquid, metals, atomic nuclei, and neutron matter. The interaction removes also the square-root singularity in the phase space of pair-breaking processes. How these effects influence the neutrino emissivity in neutron Cooper-pair recombinations in neutron stars is shown.

$E0$ transitions are a sensitive indicator of structure in nuclei, reflecting shape transitional regions, deformation, and intruder states. Attention has generally focused on $E0$ transitions to the ground state or low-lying yrast levels. In this paper we look at all $E0$ transitions connecting $0^{+}$ states in a rather general collective model. We deduce a new selection rule and map out calculated strengths throughout the spectrum. The distributions of $E0$ strengths for several different collective structures are discussed.

The roles of nuclear deformation and neutron transfer in sub-barrier capture process are studied within the quantum diffusion approach. The change of the deformations of colliding nuclei with neutron exchange can crucially influence the sub-barrier fusion. The comparison of the calculated capture cross section and the measured fusion cross section in various reactions at extreme sub-barrier energies gives us information about the quasifission.

We investigate the influence of the nucleon-nucleon collision profile (probability of interaction as a function of the nucleon-nucleon impact parameter) in the wounded-nucleon model and its extensions on several observables measured in relativistic heavy-ion collisions. We find that the participant eccentricity coefficient, ${\epsilon }^{*}$, as well as the higher harmonic coefficients, ${\epsilon }_n^{*}$, are reduced by 10–20$\%$ for midperipheral collisions when the realistic (Gaussian) profile is used, as compared to the case with the commonly used hard-sphere profile. Similarly, the multiplicity fluctuations, treated as the function of the number of wounded nucleons in one of the colliding nuclei, are reduced by 10–20$\%$. This demonstrates that the Glauber Monte Carlo codes should necessarily use the realistic nucleon-nucleon collision profile in precision studies of these observables. Our study is relevant for hydrodynamic calculations which use the Glauber-model initial conditions. The Gaussian collision profile is built-in in glissando.

The transverse-momentum distributions of identified hadrons produced in Pb-Pb collisions at the Large Hadron Collider (LHC) are studied in the low and intermediate range for $p_T<5$ GeV/$c$. All four spectra ($\pi ,K,p,\Lambda$) can be well reproduced in the recombination model based on a common thermal parton distribution of light and strange quarks and on shower partons emitted in hard and semihard jets. Two essential parameters are adjusted to fit the data, one being the inverse slope of the thermal distribution and the other revealing the degree of momentum degradation in the medium. Various combinations of thermal and shower-parton components are calculated, showing the dominance of minijets. The effect of minijets is to produce harder baryons than mesons, resulting in their ratio to peak at around $p_T\sim 3$ GeV/$c$. A substantial portion of the jet energy is found to be lost to the dense medium before the partons emerge at the surface to undergo hadronization by recombination.

A chiral quark-model approach is adopted to study the $\gamma p\to {\eta }^{\prime }p$ and $\gamma n\to {\eta }^{\prime }n$. Good descriptions of the recent observations from CLAS and CBELSA/TAPS are obtained. Both of the processes are governed by $S_{11}\left(1535\right)$ and $u$ channel background. Strong evidence of an $n=3$ shell resonance $D_{15}\left(2080\right)$ is found in the reactions, which accounts for the bump-like structure around $W=2.1$ GeV observed in the total cross section and excitation functions at very forward angles. The $S_{11}\left(1920\right)$ seems to be needed in the reactions, with which the total cross section near threshold for the $\gamma p\to {\eta }^{\prime }p$ is improved slightly. The polarized beam asymmetries show some sensitivities to $D_{13}\left(1520\right)$, although its effects on the differential cross sections and total cross sections are negligible. There is no obvious evidence of the $P$-, $D_{13}$-, $F$-, and $G$-wave resonances with a mass around 2.0 GeV in the reactions.

Nuclear attenuation of the single hadron at low energies of the virtual photon $\nu$ ($\nu <5\text{GeV}$) is considered in the framework of the improved two-scale model, which is one of the versions of the string model. The model is used for a description of the ratio of the multiplicities of pions electroproduced on nuclear and deuterium targets as a function of the energy of virtual photons and the fractional energy of the pions. The final state interactions, which are essential in this energy range, are taken into account. A comparison with two sets of the experimental data obtained at JLab is performed. A satisfactory agreement of the theoretical calculations with the first set of data for the ratio of the multiplicities of positively charged pions on carbon, iron, and lead targets to that on the deuterium one is obtained. However, agreement with the second set of data for the ratio of the multiplicities of positively and negatively charged pions on the aluminum target to those on the deuterium one is poor. Possible reasons for this situation are discussed.

New measurements of the interaction cross sections of ${}^{22,23}$O at 900$A$ MeV performed at the GSI, Darmstadt are reported that address the unsolved puzzle of the large cross section previously observed for ${}^{23}$O. The matter radii for these oxygen isotopes extracted through a Glauber model analysis are in good agreement with the new predictions of the ab initio coupled-cluster theory reported here. They are consistent with a ${}^{22}\mathrm{O}+\mathrm{neutron}$ description of ${}^{23}$O as well.