We describe the ground state of the isovector pairing Hamiltonian in self-conjugate nuclei by a product of collective quartets of different structures built from two neutrons and two protons coupled to total isospin $T=0$. The structure of the collective quartets is determined by an iterative variational procedure based on a sequence of diagonalizations of the pairing Hamiltonian in spaces of reduced size. The accuracy of the quartet model is tested for $N=Z$ nuclei carrying valence nucleons outside the ${}^{16}O$, ${}^{40}\mathrm{Ca}$, and ${}^{100}\mathrm{Sn}$ cores. The comparison with the exact solutions of the pairing Hamiltonian, obtained by shell model diagonalization, shows that the quartet model is able to describe the isovector pairing energy with very high precision. The predictions of the quartet model are also compared to those of the simpler quartet condensation model in which all the collective quartets are assumed to be identical.

We have investigated the survival probability of different charmonium states in a high baryon density parton plasma, expected to be produced in nuclear collisions at the Facility for Antiproton and Ion Research. Charmonia are assumed to undergo complete dissociation by color screening if the in-medium Debye radius becomes comparable to the spatial size of the corresponding bound state. Results indicate a nontrivial dependence of the suppression pattern on the plasma evolution dynamics. A much larger magnitude of suppression is foreseen induced by cold nuclear matter compared to that due to plasma screening.

We study the $P$-odd effects related to the vorticity of the medium formed in noncentral heavy-ion collisions. Using the kinetic quark-gluon strings model, we perform numerical simulations of the vorticity and hydrodynamical helicity for various atomic numbers, energies, and centralities. We observed vortical structures typically occupy the relatively small fraction of the fireball volume. In the course of numerical simulations, the noticeable hydrodynamical helicity was observed to manifest specific mirror behavior with respect to the reaction plane. The effect is maximal at the Nuclotron based Ion Collider fAcility and Facility for Antiproton and Ion Research in Europe energy range.

Background: For nuclei heavier than ${}^{208}$Pb $\alpha$ decay is a dominating decay mode, and in the search of new superheavy elements one often observes chains of $\alpha$ decays.

Purpose: Explore and test microscopic descriptions of $\alpha$ decay based on theories with effective nuclear interactions.

Methods: The nuclear ground states are calculated with the Hartree-Fock-Bogoliubov (HFB) method using the Skyrme interaction. Microscopic $\alpha$-decay formation amplitudes are calculated from the HFB wave functions, and the $R$-matrix formalism is utilized to obtain decay probabilities.

Results: Using a large harmonic-oscillator basis we obtain converged $\alpha$-decay widths. A comparison with experiment including all spherical even-even $\alpha$ emitting nuclei shows that the model consistently predicts too small formation amplitudes while relative values are in good agreement with experiment.

Conclusions: The method was found to be numerically practical even with a large basis size. The comparison of formation amplitudes suggests that the pairing type correlations included in the HFB approach cannot produce sufficient $\alpha$-particle clustering.

In this work we present the results for the investigation of intermediate-mass fragment (IMF) production with the proton-induced reaction at 660 MeV on ${}^{238}$U and ${}^{237}$Np target. The data were obtained with the LNR Phasotron U-400M Cyclotron at Joint Institute for Nuclear Research (JINR), Dubna, Russia. A total of 93 isotopes, in the mass range of $30<A<200$, were unambiguously identified with high precision. The fragment production cross sections were obtained by means of the induced-activation method in an off-line analysis. Mass-yield distributions were derived from the data and compared with the results of the simulation code CRISP for multimodal fission. A discussion of the superasymmetric fragment production mechanism is also given.

A calculation of the pion-production operator up to next-to-next-to-leading order for $s$-wave pions is performed within chiral effective field theory. In the previous study [Phys. Rev. C 85, 054001 (2012)] we discussed the contribution of the pion-nucleon loops at the same order. Here we extend that study to include explicit delta degrees of freedom and the $1/m_N^2$ corrections to the pion-production amplitude. Using the power counting scheme where the delta-nucleon mass difference is of the order of the characteristic momentum scale in the production process, we calculate all tree-level and loop diagrams involving delta up to next-to-next-to-leading order. The long-range part of the delta loop contributions is found to be of similar size to that from the pion-nucleon loops which supports the counting scheme. The net effect of pion-nucleon and delta loops is expected to play a crucial role in understanding of the neutral pion production data.

Limited information is currently known on medium- and higher-spin states for ${}^{135}$Cs, a neutron-rich nucleus amenable to shell-model calculations due to its proximity to the shell closures in ${}^{132}$Sn. In order to extend the level structure of ${}^{135}$Cs to higher excitations, this nucleus was studied via prompt $\gamma$-ray spectroscopy of fragments following the fission of the compound nucleus ${}^{226}$Th formed in the ${}^{18}$O (91 MeV) $+$ ${}^{208}$Pb fusion-fission reaction. Medium-spin states up to spin (23/2) and $\sim$3.3 MeV excitation energy have been established. The observed states were compared with those in the neighboring $N=82$${}^{137}$Cs nucleus, as well as with states in the neighboring $N=80$ isotones. The coupling of the odd proton occupying the $g_{7/2}$ orbital to the yrast states in the ${}^{134}$Xe and ${}^{136}$Ba cores could account for the lower excited states of ${}^{135}$Cs. The experimental results are compared with predictions from shell-model calculations.

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g., ($d,p$) reactions, should be used. Those ($d,p$) reactions may be viewed as three-body reactions and described with Faddeev techniques.

Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. While there exist several separable representations for the nucleon-nucleon interaction, the optical potential between a neutron (proton) and a nucleus is not readily available in separable form. The purpose of this paper is to introduce a separable representation for complex phenomenological optical potentials of Woods-Saxon type.

Results: Starting from a global optical potential, a separable representation thereof is introduced based on the Ernst-Shakin-Thaler (EST) scheme. This scheme is generalized to non-Hermitian potentials. Applications to $n+{}^{48}\mathrm{Ca}$, $n+{}^{132}\mathrm{Sn}$, and $n+{}^{208}\mathrm{Pb}$ are investigated for energies from 0 to 50 MeV and the quality of the representation is examined.

Conclusions: We find a good description of the on-shell $t$ matrix for all systems with rank up to 5. The required rank depends inversely on the angular momentum. The resulting separable interaction exhibits a different off-shell behavior compared to the original potential, reducing the high-momentum contributions.

The generalized Baldin sum rule at finite four-momentum transfer $Q^2$ is evaluated utilizing a structure function parametrization fit to recent experimental data. The most recent measurements on $F_1$ from Hall C at Jlab, as well as the $F_2$ structure function data from Hall B at Jlab and SLAC, were used in constructing our parametrization. We find that at $Q^2$ below 1 GeV${}^2$ the dominant contribution to the electric and magnetic polarizabilities of the nucleon comes from the resonance region.

The model of coherent quadrupole and octupole motion is applied to describe non-yrast split parity-doublet spectra in odd-mass nuclei. The yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublet structures are obtained as higher-energy rotation-vibration modes coupled to excited s.p. states. It is shown that the extended model scheme describes both the yrast and non-yrast quasi parity-doublet spectra and the related $B\left(E1\right)$ and $B\left(E2\right)$ transition rates in different regions of heavy odd-$A$ nuclei. The involvement of the reflection-asymmetric deformed shell model to describe the single-particle motion and the Coriolis interaction on a deeper level is discussed.

Pairing fluctuations are self-consistently incorporated on the same footing as the quadrupole deformations in present state-of-the-art calculations including particle-number and angular-momentum conservation as well as configuration mixing. The approach is complemented by the use of the finite-range density-dependent Gogny force which, with a unique source for the particle-hole and particle-particle interactions, guarantees a self-consistent interplay in both channels. We have applied our formalism to study the role of the pairing degree of freedom in the description of the most relevant observables like spectra, transition probabilities, separation energies, etc. We find that the inclusion of pairing fluctuations mostly affects the description of excited states, depending on the excitation energy and the angular momentum. $E0$ transition probabilities experience rather big changes while $E2$'s are less affected. Genuine pairing vibrations are thoroughly studied with the conclusion that deformations strongly inhibits their existence. These studies have been performed for a selection of nuclei: spherical, deformed, and with different degrees of collectivity.

Neutrinoless double-$\beta$ decay ($0\nu \beta \beta$) is a unique process that could reveal physics beyond the Standard Model. Essential ingredients in the analysis of $0\nu \beta \beta$ rates are the associated nuclear matrix elements. Most of the approaches used to calculate these matrix elements rely on the closure approximation. Here we analyze the light neutrino-exchange matrix elements of ${}^{48}$Ca $0\nu \beta \beta$ decay and test the closure approximation in a shell-model approach. We calculate the $0\nu \beta \beta$ nuclear matrix elements for ${}^{48}$Ca using both the closure approximation and a nonclosure approach, and we estimate the uncertainties associated with the closure approximation. We demonstrate that the nonclosure approach has excellent convergence properties which allow us to avoid unmanageable computational cost. Combining the nonclosure and closure approaches we propose a new method of calculation for $0\nu \beta \beta$ decay rates which can be applied to the $0\nu \beta \beta$ decay rates of heavy nuclei, such as ${}^{76}$Ge or ${}^{82}$Se.

Isoscalar giant resonances and low spin states in ${}^{32}$S have been measured with inelastic $\alpha$ scattering at extremely forward angles including zero degrees at $E$${}_{\alpha }=386$ MeV. By applying multipole decomposition analysis, various excited states are classified according to their spins and parities (J${}^{\pi }$), and are discussed in relation to the superdeformed and ${}^{28}$Si $+$ $\alpha$ cluster bands.

The spontaneous fission lifetime of ${}^{264}$Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the nonperturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used.

The recently developed treatment of Brownian shape evolution is refined to take account of the gradual decrease in microscopic effects as the nuclear excitation energy is raised. We construct effective potential-energy surfaces by multiplying the shell-plus-pairing correction term by a suppression factor that depends on the local excitation energy. While this approach is equivalent to the modification of the Fermi-gas level density parameter suggested by Ignatyuk et al. [Sov. J. Nucl. Phys. 29, 450 (1979)], we adopt a more general functional form for the suppression factor, which is adjusted to measured charge yields for ${}^{234}\mathrm{U}(E^{*}\approx 11\mathrm{MeV})$. The resulting model is benchmarked by comparison with 70 measured yields.

The odd-even staggering of the yield of final reaction products has been studied as a function of proton ($Z$) and neutron $\left(N\right)$ numbers for the collisions ${}^{84}\mathrm{Kr}+{}^{112}\mathrm{Sn}$ and ${}^{84}\mathrm{Kr}+{}^{124}\mathrm{Sn}$ at 35 MeV/nucleon in a wide range of elements (up to $Z\approx 20$). The experimental data show that staggering effects rapidly decrease with increasing size of the fragments. Moreover the staggering in $N$ is definitely larger than the one in $Z$. Similar general features are qualitatively reproduced by the gemini code. Concerning the comparison of the two systems, the staggering in $N$ is in general rather similar, being slightly larger only for the lightest fragments produced in the $n$-rich system. In contrast the staggering in $Z$, although smaller than that in $N$, is sizably larger for the $n$-poor system with respect to the $n$-rich one.

The in-medium ${\eta }^{\prime }$ mass and the ${\eta }^{\prime }N$ interaction are investigated in an effective theory based on the linear realization of the SU(3) chiral symmetry. We find that a large part of the ${\eta }^{\prime }$ mass is generated by the spontaneous breaking of chiral symmetry through the U${}_A$(1) anomaly. As a consequence of this observation, the ${\eta }^{\prime }$ mass is reduced in nuclear matter where chiral symmetry is partially restored. In our model, the mass reduction is found to be 80 MeV at the saturation density. Estimating the ${\eta }^{\prime }N$ interaction based on the same effective theory, we find that the ${\eta }^{\prime }N$ interaction in the scalar channel is attractive sufficiently to form a bound state in the ${\eta }^{\prime }N$ system with a several MeV binding energy. We discuss the origin of attraction by emphasizing the special role of the $\sigma$ meson in the linear sigma model for the mass generation of ${\eta }^{\prime }$ and $N$.

We point out that the mixed-event method for two-particle acceptance correction, widely used in particle correlation measurements at the BNL Realtivistic Heavy Ion Collider and the CERN Large Hadron Collider (LHC), is wrong in cases where the single-particle pseudorapidity distribution is significantly nonuniform. The correct acceptance should be the convolution of two single-particle efficiency $\times$ acceptance functions. The error of the mixed-event method, which guarantees a uniform $\Delta \eta$ two-particle combinatorial density, is, however, small in correlation analyses where the two particles are integrated over an extended pseudorapidity $\eta$ range. With one particle fixed in $\eta$ and the right acceptance correction, the background-subtracted correlated pair density may reveal not only a short-range but also a long-range $\Delta \eta$ dependence. This has important physics implication and may provide crucial information to disentangle physics mechanisms for the recently observed long-range ridge correlation in asymmetric proton-lead collisions at the LHC.