The $4\alpha$ condensate state for ${}^{16}\mathrm{O}$ is discussed with the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function which has $\alpha$-particle condensate character. With a treatment of resonances, it is found that the $4\alpha$ THSR wave function yields a fourth $0^{+}$ state in the continuum above the $4\alpha$-breakup threshold, in addition to the three $0^{+}$ states obtained in a previous analysis. It is shown that this fourth $0^{+}$ $[(0_4^{+}){}_{\mathrm{THSR}}]$ state has a structure analogous to that of the Hoyle state because it has a very dilute density and a large component of $\alpha +{}^{12}\mathrm{C}(0_2^{+})$ configuration. Furthermore, single-$\alpha$ motions are extracted from the microscopic 16-nucleon wave function, and the condensate fraction and momentum distribution of $\alpha$ particles are quantitatively discussed. It is found that for the $(0_4^{+}){}_{\mathrm{THSR}}$ state a large $\alpha$-particle occupation probability concentrates on a single-$\alpha$ $0S$ orbit and the $\alpha$-particle momentum distribution has a $\delta$-function-like peak at zero momentum, both indicating that the state has a strong $4\alpha$ condensate character. It is argued that the $(0_4^{+}){}_{\mathrm{THSR}}$ state is the counterpart of the $0_6^{+}$ state which was obtained as the $4\alpha$ condensate state in the previous $4\alpha$ orthogonality condition model calculation and therefore is likely to correspond to the $0_6^{+}$ state observed at $15.1$ MeV. The necessity of including $\alpha +{}^{12}\mathrm{C}$ configurations in the THSR wave function is pointed out.

We carry out state-of-the-art optimization of a nuclear energy density of Skyrme type in the framework of the Hartree-Fock-Bogoliubov theory. The particle-hole and particle-particle channels are optimized simultaneously, and the experimental data set includes both spherical and deformed nuclei. The new model-based, derivative-free optimization algorithm used in this work has been found to be significantly better than standard optimization methods in terms of reliability, speed, accuracy, and precision. The resulting parameter set unedf0 results in good agreement with experimental masses, radii, and deformations and seems to be free of finite-size instabilities. An estimate of the reliability of the obtained parameterization is given, based on standard statistical methods. We discuss new physics insights offered by the advanced covariance analysis.

Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is shown that this definition of information is a more practical measure of the quality of a set of measured observables than whether the combination is a mathematically complete set. It is also shown that, when experimental uncertainty is introduced, complete sets of measurements do not necessarily remove ambiguities and that experiments should strive to measure as many observables as practical to extract amplitudes.

The generalized density-dependent cluster model (GDDCM) is extended to study cluster radioactivity in even-even and odd-$A$ nuclei decaying to the doubly magic nucleus ${}^{208}\mathrm{Pb}$ or its neighboring nuclei. The microscopic cluster-daughter potential is numerically constructed in the double-folding model with M3Y nucleon-nucleon interactions plus proton-proton Coulomb interactions. Instead of the WKB barrier penetration probability, the exact solution of the Schrödinger equation with outgoing Coulomb wave boundary conditions is presented. The cluster preformation factor is well taken into account based on some available experimental cases. The calculated half-lives are found to be in good agreement with the experimental data. This indicates that a unified description of $\alpha$ decay and cluster radioactivity has been achieved by the GDDCM. Predictions of cluster emission half-lives are made for promising emitters, which may guide future experiments.

A discussion on the nature of the $0^{+}$ states in ${}^{68}\mathrm{Ni}$ ($Z=28$, $N=40$) is presented and a comparison is made with its valence counterpart ${}^{90}\mathrm{Zr}$ ($Z=40$, $N=50$). Evidence is given for a $0^{+}$ proton-intruder state at only $~2.2$-MeV excitation energy in ${}^{68}\mathrm{Ni}$, while the analogous neutron-intruder states in ${}^{90}\mathrm{Zr}$ reside at $4126$ and $5441$ keV. The application of a shell-model description of $0^{+}$ intruder states reveals that many pair-scattered neutrons across $N=40$ have to be involved to explain the low excitation energy of the proton-intruder configuration in ${}^{68}\mathrm{Ni}$.

We present a method of filter diagonalization for shell-model calculations. This method is based on the Sakurai and Sugiura (SS) method, but extended with the help of the shifted complex orthogonal conjugate gradient (COCG) method. A salient feature of this method is that it can calculate eigenvalues and eigenstates in a given energy interval. We show that this method can be an alternative to the Lanczos method for calculating ground and excited states, as well as spectral strength functions. With an application to the $M$-scheme shell-model calculations we demonstrate that several inherent problems in the widely used Lanczos method can be removed or reduced.

Balance functions have been measured for charged-particle pairs, identified charged-pion pairs, and identified charged-kaon pairs in $\mathrm{Au}+\mathrm{Au}$, $d+\mathrm{Au}$, and $p+p$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider using the STAR detector. These balance functions are presented in terms of relative pseudorapidity, $\Delta \eta$, relative rapidity, $\Delta y$, relative azimuthal angle, $\Delta \varphi$, and invariant relative momentum, $q_{\mathrm{inv}}$. For charged-particle pairs, the width of the balance function in terms of $\Delta \eta$ scales smoothly with the number of participating nucleons, while hijing and urqmd model calculations show no dependence on centrality or system size. For charged-particle and charged-pion pairs, the balance functions widths in terms of $\Delta \eta$ and $\Delta y$ are narrower in central $\mathrm{Au}+\mathrm{Au}$ collisions than in peripheral collisions. The width for central collisions is consistent with thermal blast-wave models where the balancing charges are highly correlated in coordinate space at breakup. This strong correlation might be explained by either delayed hadronization or limited diffusion during the reaction. Furthermore, the narrowing trend is consistent with the lower kinetic temperatures inherent to more central collisions. In contrast, the width of the balance function for charged-kaon pairs in terms of $\Delta y$ shows little centrality dependence, which may signal a different production mechanism for kaons. The widths of the balance functions for charged pions and kaons in terms of $q_{\mathrm{inv}}$ narrow in central collisions compared to peripheral collisions, which may be driven by the change in the kinetic temperature.

We consider a rotating neutron star with the presence of hyperons in its core. We use an equation of state in an effective chiral model within the relativistic mean-field approximation. We calculate the hyperonic bulk viscosity coefficient caused by nonleptonic weak interactions. By estimating the damping time scales of the dissipative processes, we investigate its role in the suppression of gravitationally driven instabilities in the $r$ mode. We observe that $r$-mode instability remains very significant for hyperon core temperatures of around ${10}^8\hspace{0.5em}\mathrm{K}$, which results in a comparatively larger instability window. We find that such instability can reduce the angular velocity of the rapidly rotating star considerably up to $~0.04{\Omega }_{\mathrm{K}}$, with ${\Omega }_{\mathrm{K}}$ as the Keplerian angular velocity.

A new approach for the calculation of angular momentum projected potential energy surfaces (AMPPESs) is proposed which combines the projected shell model with a quadrupole constrained relativistic Hartree-Bogoliubov (RHB) theory in which the NL3 effective interaction is chosen for the relativistic mean-field effective Lagrangian and a separable Gogny D1S interaction for the pairing force (QCRHB-NL$3+$separable Gogny D1S force theory). We apply this approach to compute the AMPPESs of ${}^{80,82,84}\mathrm{Zr}$ nuclei up to high spins and investigate the spin-induced shape transitions and decay out of the superdeformed (SD) bands in these nuclei. We find that the shape transitions occur in ${}^{80}\mathrm{Zr}$ and ${}^{84}\mathrm{Zr}$, which are driven by the rotational alignments of the nucleons in the $1g_{9/2}$ orbitals, and a strong shape mixing happens in ${}^{82}\mathrm{Zr}$. Moreover, it is shown that the barrier separating the SD states and normal deformed (or spherical) states becomes lower and narrower for ${}^{82}\mathrm{Zr}$ and ${}^{84}\mathrm{Zr}$ at high spins, indicating that the decay out of the SD bands could occur at high spins. For ${}^{80}\mathrm{Zr}$, however, there is no decay out of the SD band because the barrier is so high and thick. Meanwhile, the QCRHB-NL$3+$separable Gogny D1S force theory is employed to calculate the ground-state potential energy surfaces and the single-particle levels of these nuclei, which in turn are used to determine and analyze the equilibrium shapes and discuss the shape coexistence of these nuclei. In addition, this theory is compared with other state-of-the-art mean-field theories to justify its use to study the ground-state potential energy surfaces of ${}^{80,82,84}\mathrm{Zr}$.

The ability of a recently developed square-integrable discrete basis to represent the properties of the continuum of a two-body system is investigated. The basis is obtained performing a simple analytic local scale transformation to the harmonic oscillator basis. Scattering phase-shifts and the electric transition probabilities $B(E1)$ and $B(E2)$ have been evaluated for several potentials using the proposed basis. Both quantities are found to be in excellent agreement with the exact values calculated from the true scattering states. The basis has been applied to describe the projectile continuum in the ${}^6\mathrm{He}$ scattering by ${}^{12}\mathrm{C}$ and ${}^{208}\mathrm{Pb}$ targets at 240 MeV/nucleon and the ${}^{11}\mathrm{Be}$ scattering by ${}^{12}\mathrm{C}$ at 67 MeV/nucleon. The calculated breakup differential cross sections are found to be in very good agreement with the available experimental data for these reactions.

We investigate the effect of single-particle excitations on heavy-ion reactions at energies near the Coulomb barrier. To this end, we describe single-particle degrees of freedom with the random matrix theory and solve the coupled-channels equations for one-dimensional systems. We find that the single-particle excitations hinder the penetrability at energies above the barrier, leading to a smeared barrier distribution. This indicates that the single-particle excitations provide a promising way to explain the difference in a quasielastic barrier distribution recently observed in ${}^{20}\mathrm{Ne}$$+$${}^{90,92}\mathrm{Zr}$ systems.

We address the problem of whether the early thermalization and Hanbury-Brown–Twiss (HBT) puzzles in relativistic heavy-ion collisions may be solved by the assumption that the early dynamics of the produced matter is locally anisotropic. The hybrid model describing the purely transverse hydrodynamic evolution followed by the perfect-fluid hydrodynamic stage is constructed. The transition from the transverse to perfect-fluid hydrodynamics is described by the Landau matching conditions applied at a fixed proper time ${\tau }_{\mathrm{tr}}$. The global fit to the RHIC data reproduces the soft hadronic observables (the pion, kaon, and the proton spectra, the pion and kaon elliptic flow, and the pion HBT radii) with the accuracy of about $20\%$. These results indicate that the assumption of the very fast thermalization may be relaxed. In addition, the presented model suggests that a large part of the inconsistencies between the theoretical and experimental HBT results may be removed.

The statistical system of pions with zero total isospin is studied. The suppression effects for the average yields due to isospin conservation are the same for ${\pi }^0$, ${\pi }^{+}$, and ${\pi }^{-}$. However, a behavior of the corresponding particle number fluctuations are different. For neutral pions there is the enhancement of the fluctuations, whereas for charged pions the isospin conservation suppresses fluctuations. The correlations between the numbers of charged and neutral pions are observed for finite systems. This causes a maximum of the total pion number fluctuations for small systems. The thermodynamic limit values for the scaled variances of neutral and charged pions are calculated. The enhancements of the fluctuations due to Bose statistics are found and discussed.

We present new corrections for the polarization-dependent efficiency (PDE), which introduces a false asymmetry into measurements of $n\text{−}p$ analyzing power $A_y(\theta )$ caused by double scattering in the neutron side detectors. To accomplish this, we created a new database of ${}^{12}\mathrm{C}$$(\mathrm{n⃗},n)$ $A_y(\theta )$ by using a combination of fits to data, phase-shift analysis, and $R$-matrix analysis. Our recorrection for PDE of previously reported $n\text{−}p$ $A_y(\theta )$ data at 7.6 and 12.0 MeV and new data at 7.6 MeV indicate that we have achieved a superior representation of ${}^{12}\mathrm{C}$$(\mathrm{n⃗},n)$. Our results continue to suggest a possible charge dependence of the pion-nucleon coupling constant.

The high spin levels of a very neutron-rich ${}^{104}\mathrm{Zr}$ nucleus have been reinvestigated by measuring the prompt $\gamma$ rays in the spontaneous fission of ${}^{252}\mathrm{Cf}$. The ground-state band has been confirmed. A new sideband has been identified with a band-head energy at 1928.7 keV. The projected shell model is employed to investigate the band structure of ${}^{104}\mathrm{Zr}$. The results of calculated levels are in good agreement with the experimental data, and suggest that the new band in ${}^{104}\mathrm{Zr}$ may be based on the neutron $\nu 5/2^{-}[532]\otimes \nu 3/2^{+}[411]$ configuration.

Positive-parity doublet bands in the odd-odd nucleus ${}^{124}\mathrm{Cs}$ have been studied by using the two quasiparticles plus a triaxial rotor model. The energy spectra and electromagnetic properties are calculated and compared with the available experimental results. Good agreement is obtained in the present calculation. The chiral geometry and its evolution with angular momentum for doublet bands in ${}^{124}\mathrm{Cs}$ is also exhibited and discussed based on the analysis of the expectation values and the probability distributions of the angular momentum.

Covariance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-$j$ state can be visualized as being made up of $2j$ spinors which are represented by a constellation of $2j$ points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.

Proton-neutron correlations in nuclei above the $Z=50$ shell closure are investigated with the aim of understanding the behavior of the $2$${}^{+}$ and $4$${}^{+}$ states in Te and Xe isotopes, which remain at a rather constant energy as one approaches the shell closure at $N=50$. Our calculations reveal that standard quasiparticle random phase approximation calculations, involving a quadrupole-quadrupole (QQ) interaction with constant strengths, cannot explain this feature. It is found that to reproduce the experimental data within this model one has to include a variable proton-neutron interaction. It turns out that an increased proton-neutron QQ interaction increases the collectivity (i.e., $B(E2)$ values) when approaching the $N=50$ region, whereas an increased proton-neutron pairing interaction decreases the collectivity. We thus conclude that the ratio between the $B(E2)$ value and $2^{+}$ energy is a “fingerprint” of proton-neutron collectivity and it should be determined in future experiments concerning light Te isotopes. Based on this criterion, we conclude that the available experimental data indicate an enhanced proton-neutron pairing interaction by approaching doubly magic $Z=N=20$ and $Z=N=28$ regions.

Lifetimes of low-lying excited states of the neutron-rich ${}^{44,46}\mathrm{Ar}$ nuclei, populated via multinucleon transfer reactions, are measured by means of the differential recoil distance Doppler shift method. The extracted electromagnetic transition probabilities are compared with previous intermediate-energy Coulomb-excitation measurements and with large-scale shell-model calculations. The increase in the deduced $B$($E2;2^{+}\to 0^{+}$) transition probability from ${}^{44}\mathrm{Ar}$ to the closed-shell nucleus ${}^{46}\mathrm{Ar}$ contradicts the earlier results of Coulomb-excitation experiments. Shell-model calculations using different effective interactions agree with the new measured values.

The observation of large azimuthal anisotropy or $v_2$ for hadrons above $p_T>5$ GeV/$c$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{nn}}}=200$ GeV has been a longstanding challenge for jet quenching models based on perturbative QCD (pQCD). Using a simple jet absorption model, we seek to clarify the situation by exploring in detail how the calculated $v_2$ varies with choices of the collision geometry, as well as choices of the path-length dependence and thermalization time ${\tau }_0$ in the energy-loss formula. Besides the change of eccentricity owing to distortion from gluon saturation or event-by-event fluctuation, we find that the $v_2$ is also sensitive to the centrality dependence of multiplicity and the relative size between the matter profile and the jet profile. We find that the $v_2$ calculated for the naive quadratic path-length dependence of energy loss, even including eccentricity fluctuation and the gluon saturation, is not enough to describe the experimental data at high $p_T$ ($~$$6$ GeV/$c$) in $\mathrm{Au}+\mathrm{Au}$ collisions. However, it can match the full centrality dependence of $v_2$ data if higher-power path-length dependence of energy loss is allowed. We also find that the calculated $v_2$ is sensitive to the assumption of the early time dynamics but generally increases with ${\tau }_0$, opposite to what one expects for elliptic flow. This study attests to the importance of confining the initial geometry, possibly by combining jet quenching $v_2$ with elliptic flow and other jet quenching observables, for proper interpretation of the experimental data.