The development of nuclear collectivity in even-even ${}^{152\text{–}170}\mathrm{Yb}$ is studied with three types of mean-field calculations: the nonrelativistic Hartree-Fock plus BCS calculation using the Skyrme SLy4 force plus a density-dependent $\delta$ pairing force and the relativistic mean-field calculation using a point-coupling energy functional supplemented with either a density-independent $\delta$ pairing force or a separable pairing force. The low-lying states are obtained by solving a five-dimensional collective Hamiltonian with parameters determined from the three mean-field solutions. The energy surfaces, excitation energies, electric multiple transition strengths, and differential isotope shifts are presented in comparison with available data. Our results show that different treatments of pairing correlations have a significant influence on the speed of developing collectivity as the increase of neutron number. All the calculations demonstrate the important role of dynamic shape-mixing effects in resolving the puzzle in the dramatic increase of charge radius from ${}^{152}\mathrm{Yb}$ to ${}^{154}\mathrm{Yb}$ and the role of triaxiality in ${}^{160,162,164}\mathrm{Yb}$.

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferably small fractional power of the density $\rho$ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parametrizations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power.

Purpose: Beginning with the observation that the Fermi momentum $k_F$, i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a $k_F$ expansion can be inferred from the properties of homogeneous matter in a domain of densities, which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained.

Method: For the EDF, we fit systematically polynomial and other functions of ${\rho }^{1/3}$ to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters, which we found robust, and examine the parameters' naturalness and the quality of resulting extrapolations.

Results: A statistical analysis confirms that low-order terms such as ${\rho }^{1/3}$ and ${\rho }^{2/3}$ are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure neutron matter, supporting the need for more than one density-dependent term in nonrelativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic results, to which it has not been fitted. It also predicts a neutron-star mass-radius relation consistent with observations. The coefficients display naturalness.

Conclusions: Having been already determined for homogeneous matter, a functional of the present form can be mapped onto extended Skyrme-type functionals in a straightforward manner, as we outline here, for applications to finite nuclei. At the same time, the statistical analysis can be extended to higher orders and for different microscopic (ab initio) calculations with sufficient pseudodata points and for polarized matter.

Data for the ${}^{13}\mathrm{C}({}^6\mathrm{Li},t){}^{16}\mathrm{O}$ reaction, obtained in inverse kinematics at a ${}^{13}\mathrm{C}$ incident energy of 7.72 MeV, are presented. A distorted wave Born approximation (DWBA) analysis was used to extract spectroscopic factors and asymptotic normalization coefficients (ANCs) for the $〈{}^{16}\mathrm{O}\mid {}^{13}\mathrm{C}+{}^3\mathrm{He}〉$ overlaps, subject to the assumption of a fixed $〈{}^6\mathrm{Li}\mid {}^3\mathrm{He}+{}^3\mathrm{H}〉$ overlap. The variation of the extracted spectroscopic factors and ANCs as a function of various inputs to the DWBA calculations was explored. The extracted ANCs were found to vary as a cubic function of the radius of the potential well binding the transferred ${}^3\mathrm{He}$ to the ${}^{13}\mathrm{C}$ core while the spectroscopic factors varied as a quartic function of the radius. The ANC values could be determined to within a factor of two for this system.

It has recently been suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [Brown, Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a surrogate for the neutron skin is a welcome alternative. To test the validity of this assumption we perform calculations based on a set of relativistic energy density functionals that span a wide region of values of $L$. Our results confirm that the difference in charge radii between various neutron-deficient nickel isotopes and their corresponding mirror nuclei is indeed strongly correlated to both the neutron-skin thickness and $L$. Moreover, given that various neutron-star properties are also sensitive to $L$, a data-to-data relation emerges between the difference in charge radii of mirror nuclei and the radius of low-mass neutron stars.

Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we studied charged pion transverse and elliptic flows in semicentral ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at 600 MeV/nucleon. It is found that ${\pi }^{+}-{\pi }^{-}$ differential transverse flow and the difference of ${\pi }^{+}$ and ${\pi }^{-}$ transverse flows almost show no effects of the symmetry energy. Their corresponding elliptic flows are largely affected by the symmetry energy, especially at high transverse momenta. The isospin-dependent pion elliptic flow at high transverse momenta thus provides a promising way to probe the high-density behavior of the symmetry energy in heavy-ion collisions at the Facility for Antiproton and Ion Research (FAIR) at GSI, Darmstadt or at the Cooling Storage Ring (CSR) at HIRFL, Lanzhou.

Based on the relativistic Vlasov-Uehling-Uhlenbeck transport model, which includes relativistic scalar and vector potentials on baryons, we consider an $N-\mathrm{\Delta }-\pi$ system in a box with periodic boundary conditions to study the effects of energy conservation in particle production and absorption processes on the equilibrium properties of the system. The density and temperature of the matter in the box are taken to be similar to the hot dense matter formed in heavy ion collisions at intermediate energies. We find that to maintain the equilibrium numbers of $N,\mathrm{\Delta }$, and $\pi$, which depend on the mean-field potentials of $N$ and $\mathrm{\Delta }$, we must include these potentials in the energy conservation condition that determines the momenta of outgoing particles after a scattering or decay process. We further find that the baryon scalar potentials mainly affect the $\mathrm{\Delta }$ and pion equilibrium numbers, while the baryon vector potentials have considerable effect on the effective charged pion ratio at equilibrium. Our results thus indicate that it is essential to include in the transport model the effect of potentials in the energy conservation of a scattering or decay process, which is ignored in most transport models, for studying pion production in heavy ion collisions.

We study the propagation and diffusion of electric charge fluctuations in high-energy heavy-ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1-dimensional Bjorken hydrodynamical model. Limiting the speed of propagation of charge fluctuations increases the height and reduces the width of these balance functions when plotted versus rapidity. We also estimate the numerical value of the associated diffusion time constant from anti–de Sitter-space/conformal-field theory.

Differential cross sections and photon-beam asymmetries for the $\vec{\gamma }p\to {\pi }^{+}n$ reaction have been measured for $0.6<cos{\theta }_{\pi }<1$ and $E_{\gamma }=1.5\text{–}2.95\mathrm{GeV}$ at SPring-8/LEPS. The cross sections monotonically decrease as the photon beam energy increases for $0.6<cos{\theta }_{\pi }<0.9$. However, the energy dependence of the cross sections for $0.9<cos{\theta }_{\pi }<1$ and $E_{\gamma }=1.5\text{–}2.2\mathrm{GeV}$ ($W=1.9\text{–}2.2\mathrm{GeV}$) is different, which may be due to a nucleon or $\mathrm{\Delta }$ resonance. The present cross sections agree well with the previous cross sections measured by other groups and show forward peaking, suggesting significant $t$-channel contributions in this kinematical region. The asymmetries are found to be positive, which can be explained by $\rho$ exchange in the $t$ channel. Large positive asymmetries in the small-$\left|t\right|$ region, where the $\rho$-exchange contribution becomes small, could be explained by introducing $\pi$-exchange interference with the $s$ channel.

Using Laplace transform techniques, I calculate the longitudinal structure function $F_L(x,Q^2)$ from the scaling violations of the proton structure function $F_2(x,Q^2)$ and make a critical study of this relationship between the structure functions at leading order (LO) up to next-to-next-to leading order (NNLO) analysis at small $x$. Furthermore, I consider heavy quark contributions to the relation between the structure functions, which leads to compact formula for $N_f=3+\mathrm{Heavy}$. The nonlinear corrections to the longitudinal structure function at LO up to NNLO analysis are shown in the $N_f=4$ (light quark flavor) based on the nonlinear corrections at $R=2$ and $R=4{\text{GeV}}^{-1}$. The results are compared with experimental data of the longitudinal proton structure function $F_L$ in the range of $6.5\le Q^2\le 800{\text{GeV}}^2$.

Spectroscopic factors in ${}^{10}\mathrm{Be}$, ${}^{11}\mathrm{Be}$, and ${}^{12}\mathrm{Be}$, extracted from $(d,p)$, one-neutron knockout, and $(p,d)$ reactions, are interpreted within the rotational model. Assuming that the ground state and first excited state of ${}^{11}\mathrm{Be}$ can be associated with the $\frac{1}{2}\left[220\right]$ and $\frac{1}{2}\left[101\right]$ Nilsson levels, the strong-coupling limit gives simple expressions that relate the amplitudes of these wave functions (in the spherical basis) with the measured cross sections and derived spectroscopic factors. We obtain good agreement with both the measured magnetic moment of the ground state in ${}^{11}\mathrm{Be}$ and the reaction data.

The cross section for producing a heavy evaporation residue ${\sigma }_{\mathrm{EVR}}$ in a fusion reaction can be written as a product of three nonseparable factors, i.e., the capture cross section, the fusion probability $P_{\mathrm{CN}}$, and the survival probability $W_{\text{sur}}$. Each of these factors is dependent on the spin. However, one must remember that the $W_{\text{sur}}$ term is zero or very small for higher spin values, thus effectively limiting the capture and fusion terms. For a series of $\sim 287$ reactions leading to heavy evaporation residues with $Z_{\text{CN}}\le 110$, we point out the implications of this fact for capture cross sections for heavy element formation reactions. From a comparison of calculated and measured evaporation residue cross sections we deduce values of the fusion probability $P_{\text{CN}}$ for some of these reactions.

The anisotropic-hydrodynamics framework is used to describe a mixture of quark and gluon fluids. The effects of quantum statistics, finite quark mass, and finite baryon number density are taken into account. The results of anisotropic hydrodynamics are compared with exact solutions of the coupled kinetic equations for quarks and gluons in the relaxation time approximation. An overall very good agreement between the hydrodynamic and kinetic-theory results is found.

In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say $n$, typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between $n$ and the impact parameter $b$ of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about $b$ can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of $n$ for a fixed $b$ is Gaussian, we show that the probability distribution of the impact parameter in a narrow centrality bin can be accurately reconstructed up to $5\%$ centrality. We apply our methodology to data from the Relativistic Heavy Ion Collider and the Large Hadron Collider. We propose a simple measure of the precision of the centrality determination, which can be used to compare different experiments.

The region near $Z=28$ and $N=40$ is a subject of great interest for nuclear structure studies due to spectroscopic signatures in ${}^{68}\mathrm{Ni}$ suggesting a subshell closure at $N=40$. Trends in nuclear masses and their derivatives provide a complementary approach to shell structure investigations via separation energies. Penning trap mass spectrometry has provided precise measurements for a number of nuclei in this region; however, a complete picture of the mass surfaces has so far been limited by the large uncertainty remaining for nuclei with $N>40$ along the iron ($Z=26$) and cobalt ($Z=27$) chains because these species are not available from traditional isotope separator online rare isotope facilities. The Low-Energy Beam and Ion Trap Facility at the National Superconducting Cyclotron Laboratory is the first and only Penning trap mass spectrometer coupled to a fragmentation facility and therefore presents the unique opportunity to perform precise mass measurements of these elusive isotopes. Here we present the first Penning trap measurements of ${}^{68,69}\mathrm{Co}$, carried out at this facility. Some ambiguity remains as to whether the measured values are ground-state or isomeric-state masses. A detailed discussion is presented to evaluate this question and to motivate future work. In addition, we perform ab initio calculations of ground-state and two-neutron separation energies of cobalt isotopes with the valence-space in-medium similarity renormalization group approach based on a particular set of two- and three-nucleon forces that predict saturation in infinite matter. We discuss the importance of these measurements and calculations for understanding the evolution of nuclear structure near ${}^{68}\mathrm{Ni}$.

Excited band structures recently observed in ${}^{156}\mathrm{Dy}$ are investigated using the microscopic triaxial projected shell model (TPSM) approach and the quasiparticle random phase approximation (QRPA) based on the rotating mean field. It is demonstrated that new observed excited bands, tracking the ground-state band, are the $\gamma$ bands based on the excited two-quasineutron configurations as conjectured in the experimental work.

The complete and incomplete fusion cross sections for the ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ reaction were measured using online and offline characteristic $\gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $\sim 26\%$ compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $\mathit{t}$ capture is found to be dominant compared to $\alpha$ capture at all the measured energies. A simultaneous explanation of complete, incomplete, and total fusion (TF) data was also obtained from the calculations based on the continuum discretized coupled channel method with short range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations showed the dominance of ICF at below-barrier energies and CF at above-barrier energies.

The experimental results of the future Electron-Ion ($eA$) Collider are expected to constrain the dynamics of the strong interactions at small values of the Bjorken $x$ variable and large nuclei. Recently it has been suggested that Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. In this paper, we present a detailed investigation of the impact of the Coulomb corrections to some of the observables that will be measured in the future $eA$ collider. In particular, we estimate the magnitude of these corrections for the charm and longitudinal cross sections in inclusive and diffractive interactions. Our results demonstrate that the Coulomb corrections for these observables are negligible, which implies that they can be used to probe the QCD dynamics.

Background: Neutron stars are astronomical systems with nucleons subjected to extreme conditions. Due to the longer range Coulomb repulsion between protons, the system has structural inhomogeneities. Several interactions tailored to reproduce nuclear matter plus a screened Coulomb term reproduce these inhomogeneities known as nuclear pasta. These structural inhomogeneities, located in the crusts of neutron stars, can also arise in expanding systems depending on the thermodynamic conditions (temperature, proton fraction, etc.) and the expansion velocity.

Purpose: We aim to find the dynamics of the fragment formation for expanding systems simulated according to the little big bang model. This expansion resembles the evolution of merging neutron stars.

Method: We study the dynamics of the nucleons with semiclassical molecular dynamics models. Starting with an equilibrium configuration, we expand the system homogeneously until we arrive at an asymptotic configuration (i.e., very low final densities). We study, with four different cluster recognition algorithms, the fragment distribution throughout this expansion and the dynamics of the cluster formation.

Results: Studying the topology of the equilibrium states, before the expansion, we reproduced the known pasta phases plus a novel phase we called pregnocchi, consisting of proton aggregates embedded in a neutron sea. We have identified different fragmentation regimes, depending on the initial temperature and fragment velocity. In particular, for the already mentioned pregnocchi, a neutron cloud surrounds the clusters during the early stages of the expansion, resulting in systems that give rise to configurations compatible with the emergence of the $r$ process.

Conclusions: We showed that a proper identification of the cluster distribution is highly dependent on the cluster recognition algorithm chosen, and found that the early cluster recognition algorithm (ECRA) was the most stable one. This approach allowed us to identify the dynamics of the fragment formation. These calculations pave the way to a comparison between Earth experiments and neutron star studies.

A simple model of E2 strengths previously applied to several neutron-excess light nuclei is used to investigate the $1/2^{-}\to 5/2^{-}$ transition strength in ${}^{17}\mathrm{Ne}$, with the aid of mirror symmetry. The calculation is found to be in good agreement with results of a recent measurement and emphasizes a likely problem with the same transition in ${}^{17}\mathrm{N}$.

We present the first ab initio calculations of neutrinoless double-$\beta$ decay matrix elements in $A=6-12$ nuclei using variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton-number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we also study the impact of two-body short-range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.