Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required of energies for nuclear physics and astrophysics applications is of the order of 500 keV and much effort is undertaken to build EDFs that meet this requirement.

Purpose: Mean-field calculations have to be accurate enough to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for mean-field equations that can accommodate any kind of symmetry breaking.

Method: The method that we use is a particular implementation of three-dimensional mesh calculations. Its numerical accuracy is governed by three main factors: the size of the box in which the nucleus is confined, the way numerical derivatives are calculated, and the distance between the points on the mesh.

Results: We examine the dependence of the results on these three factors for spherical doubly magic nuclei, neutron-rich ${}^{34}\mathrm{Ne}$, the fission barrier of ${}^{240}\mathrm{Pu}$, and isotopic chains around $Z=50$.

Conclusions: Mesh calculations offer the user extensive control over the numerical accuracy of the solution scheme. When appropriate choices for the numerical scheme are made the achievable accuracy is well below the model uncertainties of mean-field methods.

Background: Despite the importance of light-ion fusion in nucleosynthesis, a limited amount of data exist regarding the de-excitation following fusion for such systems.

Purpose: To explore the characteristics of $\alpha$ emission associated with the decay of light fused systems at low excitation energy.

Method: $\alpha$ particles were detected in coincidence with evaporation residues (ER) formed by the fusion of ${}^{18}\mathrm{O}$ and ${}^{12}\mathrm{C}$ nuclei. Both $\alpha$ particles and ERs were identified on the basis of their energy and time-of-flight. ERs were characterized by their energy spectra and angular distributions while the $\alpha$ particles were characterized by their energy spectra, angular distributions, and cross sections.

Results: While the energy spectra and angular distributions for the $\alpha$ particles are relatively well reproduced by the statistical model codes, evapor and pace4 the measured cross section is substantially underpredicted by the models. Examination of the relative $\alpha$ emission probability for similar systems reveals that this underprediction is a more general feature of such light-ion reactions.

Conclusion: Comparison of the measured relative $\alpha$ cross section at low $E_{\mathrm{c}.\mathrm{m}.}$ for ${}^{18}\mathrm{O}+{}^{12}\mathrm{C},{}^{16}\mathrm{O}+{}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}+{}^{13}\mathrm{C}$ indicates that the $\alpha$ cluster structure of the initial projectile and target nuclei influences the $\alpha$ emission following fusion. The underprediction of the relative $\alpha$ emission by the statistical model codes emphasizes that the failure of these models to account for $\alpha$ cluster structure is significant.

We consider a system composed of two identical light quarks ($qq$) and two identical antiquarks ($\overline{Q}\overline{Q}$) that can be linked either as two mesons or as a tetraquark, incorporating quantum correlations between identical particles and an effective many-body potential between particles. We perform a three-dimensional Monte Carlo simulation of the system, considering the configurations allowed to form: i) Only two mesons, ii) only tetraquark, and iii) two mesons and a tetraquark. We characterize each case and determine whether it is energetically more favorable to form a tetraquark or two mesons, as a function of the interparticle separation distance which, for a fixed number of particles, can be identified as a particle density. We determine how the two mesons, which dominate the low density regime, mixes with a tetraquark state as the density increases. Properties like the mean square radius and the two-particle correlation function are found to reflect such transition, and we provide a parametrization of the diquark correlation function in the isolated case. We track the dynamical flipping among configurations to determine the recombination probability, exhibiting the importance of the tetraquark state. We analyze the four-body potential evolution and show that its linear behavior is preserved, although the slope can reflect the presence of a mixed state. Results are shown for several light-quarks to heavy-antiquarks mass ratios whenever they are found to be relevant.

The evolution of the shape from the spherical to the axially deformed shapes of the neutron-rich, even-even ${}^{144\text{–}164}\mathrm{Sm}$ transitional nuclei is investigated. The investigations are performed with explicit density-dependent meson-nucleon and point-coupling models within the framework of the covariant density functional theory. A nonlinear meson-nucleon coupling model represented by the NL3* parametrization of the relativistic mean-field Lagrangian has also been used. The bulk and the microscopic properties of these nuclei have been investigated to analyze the phase-transition region and the critical-point behavior. The microscopic and self-consistent quadrupole deformation-constrained calculations show a clear shape change for even-even Sm isotopes with $N=82-102$. The potential energy surfaces for ${}^{148}\mathrm{Sm},{}^{150}\mathrm{Sm}$, and ${}^{152}\mathrm{Sm}$ obtained using different interactions are found to be relatively flat, which may be the possible critical-point nuclei. By examining the single-particle spectra, it is found that these nuclei distribute more uniformly as compared to other isotopes. Investigations also support the proposed shell-closure properties of ${}^{162}\mathrm{Sm}$. Overall good agreement is found within the different models used and between the calculated and experimental results wherever available.

We have performed continuum discretized coupled channel (CDCC) calculations for collisions of ${}^7\mathrm{Li}$ projectiles on ${}^{59}\mathrm{Co},{}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ targets at near-barrier energies, to assess the importance of the Coulomb and the nuclear couplings in the breakup of ${}^7\mathrm{Li}$, as well as the Coulomb-nuclear interference. We have also investigated scaling laws, expressing the dependence of the cross sections on the charge and the mass of the target. This work is complementary to that previously reported by us on the breakup of ${}^6\mathrm{Li}$. Here we explore the similarities and differences between the results for the two lithium isotopes. The relevance of the Coulomb dipole and quadrupole strengths at low energy for the two-cluster projectile is investigated in detail.

In recent models, the neutron-rich Ni isotopes around $N=40$ are predicted to exhibit multiple low-energy excited $0^{+}$ states attributed to neutron and proton excitations across both the $N=40$ and $Z=28$ shell gaps. In ${}^{68}\mathrm{Ni}$, the three observed $0^{+}$ states have been interpreted in terms of triple shape coexistence between spherical, oblate, and prolate deformed shapes. In the present work a new $\left(0_2^{+}\right)$ state at an energy of 1567 keV has been discovered in ${}^{70}\mathrm{Ni}$ by using $\beta$-delayed, $\gamma$-ray spectroscopy following the decay of ${}^{70}\mathrm{Co}$. The precipitous drop in the energy of the prolate-deformed $0^{+}$ level between ${}^{68}\mathrm{Ni}$ and ${}^{70}\mathrm{Ni}$ with the addition of two neutrons compares favorably with results of Monte Carlo shell-model calculations carried out in the large $fp{g}_{9/2}{d}_{5/2}$ model space, which predict a $0_2^{+}$ state at 1525 keV in ${}^{70}\mathrm{Ni}$. The result extends the shape-coexistence picture in the region to ${}^{70}\mathrm{Ni}$ and confirms the importance of the role of the tensor component of the monopole interaction in describing the structure of neutron-rich nuclei.

Background: One-phonon mixed-symmetry quadrupole excitations are a well-known feature of near-spherical, vibrational nuclei. Their interpretation as a fundamental building block of vibrational structures is supported by the identification of multiphonon states resulting from a coupling of fully-symmetric and mixed-symmetric quadrupole phonons. In addition, the observation of strong $M1$ transitions between low-lying $3^{-}$ and $4^{+}$ states has been interpreted as an evidence for one-phonon mixed-symmetry excitations of octupole and hexadecapole character.

Purpose: The aim of the present study is to identify collective one- and two-phonon excitations in the heaviest stable $N=52$ isotone ${}^{96}\mathrm{Ru}$ based on a measurement of absolute $M1$, $E1$, and $E2$ transition strengths.

Methods: Inelastic proton-scattering experiments have been performed at the Wright Nuclear Structure Laboratory (WNSL), Yale University, and the Institute for Nuclear Physics (IKP), University of Cologne. From the acquired proton-$\gamma$ and $\gamma \gamma$ coincidence data we deduced spins of excited states, $\gamma$-decay branching ratios, and multipole mixing ratios, as well as lifetimes of excited states via the Doppler-shift attenuation method (DSAM).

Results: Based on the new experimental data on absolute transition strengths, we identified the $2^{+}$ and $3^{+}$ members of the two-phonon mixed-symmetry quintuplet $(2_{1,\mathrm{ms}}^{+}\otimes 2_{1,\mathrm{s}}^{+})$. Furthermore, we observed strong $M1$ transitions between low-lying $3^{-}$ and $4^{+}$ states suggesting one-phonon symmetric and mixed-symmetric octupole and hexadecapole components in their wave functions, respectively. The experimental results are compared to $sdg$-IBM-2 and shell-model calculations.

Conclusions: Both the $sdg$-IBM-2 and the shell-model calculations are able to describe key features of mixed-symmetry excitations of ${}^{96}\mathrm{Ru}$. Moreover, they support the one-phonon mixed-symmetry hexadecapole assignment of the experimental $4_2^{+}$ state.

We studied transition rates for the lowest $1/2^{+}$ and $5/2^{+}$ excited states of ${}^{17}\mathrm{C}$ through lifetime measurements with the GRETINA array using the recoil-distance method. The present measurements provide a model-independent determination of transition strengths giving the values of $B(M1;1/2^{+}\to 3/2_{\mathrm{g}.\mathrm{s}.}^{+})=1.{04}_{-0.12}^{+0.03}\times {10}^{-2}{\mu }_N^2$ and $B(M1;5/2^{+}\to 3/2_{\mathrm{g}.\mathrm{s}.}^{+})=7.{12}_{-0.96}^{+1.27}\times {10}^{-2}{\mu }_N^2$. The quenched $M1$ transition strength for the $1/2^{+}\to 3/2_{\mathrm{g}.\mathrm{s}.}^{+}$ transition, with respect to the $5/2^{+}\to 3/2_{\mathrm{g}.\mathrm{s}.}^{+}$ transition, has been confirmed with greater precision. The current data are compared to importance-truncated no-core shell model calculations addressing effects due to continuum and three-body forces.

Background: Recent microscopic studies, based on the theoretical framework of nuclear energy density functionals, have analyzed dynamic (least action) and static (minimum energy) fission paths, and it has been shown that in addition to the important role played by nonaxial and/or octupole collective degrees of freedom, fission paths crucially depend on the approximations adopted in calculating the collective inertia.

Purpose: To analyze effects of triaxial and octupole deformations, as well as approximations to the collective inertia, on the symmetric and asymmetric spontaneous fission dynamics, and compare with results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method.

Methods: Deformation energy surfaces, collective potentials, and perturbative and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic Hartree-Bogoliubov (MDC-RHB) model, with the energy density functionals PC-PK1 and DD-PC1. Pairing correlations are treated in the Bogoliubov approximation using a separable pairing force of finite range. The least-action principle is employed to determine dynamic spontaneous fission paths.

Results: The dynamics of spontaneous fission of ${}^{264}\mathrm{Fm}$ and ${}^{250}\mathrm{Fm}$ is explored. The fission paths, action integrals, and the corresponding half-lives predicted by the functionals PC-PK1 and DD-PC1 are compared and, in the case of ${}^{264}\mathrm{Fm}$, discussed in relation with recent results obtained using the HFB model based on the Skyrme functional ${\mathrm{SkM}}^{*}$ and a density dependent mixed pairing interaction.

Conclusions: The inclusion of nonaxial quadrupole and octupole shape degrees of freedom is essential for a quantitative analysis of fission dynamics. The action integrals and, consequently, the half-lives crucially depend on the approximation used to calculate the effective collective inertia along the fission path. The perturbative cranking approach underestimates the effects of structural changes at the level crossings and the resulting collective inertia varies relatively smoothly in the $({\beta }_{20},{\beta }_{22})$ and $({\beta }_{20},{\beta }_{30})$ planes. In contrast, the nonperturbative collective mass is characterized by the occurrence of sharp peaks on the surface of collective coordinates, that can be related to single-particle level crossings near the Fermi surface. This enhances the effective inertia, increases the values of the action integral, and results in longer fission half-lives.

Using the $\hslash$ expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.

We study the sensitivity of the higher-order moments of produced particle multiplicity distributions to the chemical freeze-out parameters in relativistic heavy ion collisions using the hadron resonance gas model. We compare the obtained sensitivity level to the one extracted from the ratios of particle yields. We find that, for certain final state hadrons, the fluctuation measurements add significant information to the determination of the hadrochemical freeze-out properties of the deconfined phase of matter obtained at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.

Starting from a realistic constituent quark model for the nucleon-nucleon interaction, we derive the equation of state (EOS) of nuclear matter within the Bethe-Brueckner-Goldstone approach up to the three-hole-line level, without the need to introduce three-nucleon forces. To estimate the uncertainty of the calculations both the gap and the continuous choices for the single-particle potential are considered and compared. The resultant EOS is compatible with the phenomenological analysis of the saturation point, the incompressibility, the symmetry energy at a low density, and its slope at saturation, together with the high-density pressure extracted from flow data on heavy-ion collisions. Although the symmetry energy is appreciably higher in the gap choice in the high-density region, the maximum neutron star masses derived from the continuous-choice EOS and the gap-choice EOS are similar and close to two solar masses, which is again compatible with recent observational data. A comparison with other microscopic equations of state is presented and discussed.

Excited states in ${}^{167}\mathrm{Lu}$ were populated in the ${}^{123}\mathrm{Sb}({}^{48}\mathrm{Ca},4n)$ reaction at 203 MeV and decay $\gamma$ rays measured using the Gammasphere spectrometer array. Two triaxial strongly deformed bands were identified previously and interpreted as zero- and one-phonon wobbling excitations. As a result of more extensive band search, the level scheme has been considerably extended to include ten new rotational bands and some $630\gamma$-ray transitions. A number of interband linking transitions were revealed, so that all but two bands could be connected with each other. Configurations are proposed for all new bands based on measured observables, with the help of cranked shell model calculations. A $\gamma$-ray sequence, previously suggested as a triaxial strongly deformed band based on quasiparticle excitations coexisting with the wobbling excitation in the triaxial potential well, has now been determined to be a signature partner of a coupled band, associated with a normal deformed five-quasiparticle configuration. The possibility of two new bands being associated with triaxial deformation is discussed.

We compute the quark-gluon-plasma suppression of $\mathrm{{\rm Y}}\left(1s\right), \mathrm{{\rm Y}}\left(2s\right), \mathrm{{\rm Y}}\left(3s\right), {\chi }_{b1}$, and ${\chi }_{b2}$ states in $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb collisions. Using the suppression of each of these states, we estimate the inclusive $R_{AA}$ for the $\mathrm{{\rm Y}}\left(1s\right)$ and $\mathrm{{\rm Y}}\left(2s\right)$ states as a function of $N_{\mathrm{part}}, y$, and $p_T$ including the effect of excited-state feed down. We find that our model provides a reasonable description of preliminary CMS results for the $N_{\mathrm{part}}, y$, and $p_T$ dependence of $R_{AA}$ for both the $\mathrm{{\rm Y}}\left(1s\right)$ and $\mathrm{{\rm Y}}\left(2s\right)$. Comparing with our previous model predictions, we find a flatter rapidity dependence, thereby reducing some of the tension between our model and ALICE forward-rapidity results for $\mathrm{{\rm Y}}\left(1s\right)$ suppression.

Renormalization-group (RG) methods used to soften Hamiltonians for nuclear many-body calculations change the effective resolution of the interaction. For nucleon knockout processes, these RG transformations leave cross sections invariant, but initial-state wave functions, interaction currents, and final-state interactions are individually altered. This has implications for the factorization of nuclear structure and reactions. We use deuteron electrodisintegration as a controlled laboratory for studying how structure and reaction components are modified under RG evolution, without the complication of three-body forces or currents. The dependence of these changes on kinematics is explored.

Both $E1$ and $M1 \gamma$-strength functions below the neutron separation energy were analyzed based on experimental data from ${}^{143}\mathrm{Nd}(n,\gamma ){}^{144}\mathrm{Nd}$ and ${}^{143}\mathrm{Nd}(n,\gamma \alpha ){}^{140}\mathrm{Ce}$ reactions. It is confirmed that the commonly adopted $E1$ model based on the temperature dependence of the width of the giant dipole resonance works well. The popular $M1$ strength function due to the spin-flip magnetic resonance located near the neutron binding energy is not capable of reproducing experimental data. The low-energy enhancement of the $M1$ strength or the energy-independent model of Weisskopf, both leading to the low-energy strength sizable to $E1$ one, fit experimental data best.