Rotation of triaxially deformed nucleus has been an interesting subject in the study of nuclear structure. In the present series of work, we investigate wobbling motion and chiral rotation by employing the microscopic framework of angular-momentum projection from cranked triaxially deformed mean-field states. In this first part, the wobbling motion is studied in detail. The consequences of the three-dimensional cranking are investigated. It is demonstrated that the multiple wobbling rotational bands naturally appear as a result of fully microscopic calculation. They have the characteristic properties that are expected from the macroscopic triaxial-rotor model or the phenomenological particle-triaxial-rotor model, although quantitative agreement with the existing data is not achieved. It is also found that the excitation spectrum reflects dynamics of the angular-momentum vector in the intrinsic frame of the mean field (transverse vs longitudinal wobbling). The results obtained by using the Woods-Saxon potential and the schematic separable interaction are mainly discussed, while some results with the Gogny D1S interaction are also presented.

In the sequel of the present study, we have investigated the rotational motion of triaxially deformed nucleus by using the microscopic framework of angular-momentum projection. The Woods-Saxon potential and the schematic separable-type interaction are employed as a microscopic Hamiltonian. As the first example, nuclear wobbling motion was studied in detail in part I of the series. This second part reports on another interesting rotational mode, chiral doublet bands: two prototype examples, ${}^{128}\mathrm{Cs}$ and ${}^{104}\mathrm{Rh}$, are investigated. It is demonstrated that the doublet bands naturally appear as a result of the calculation in this fully microscopic framework without any kind of core, and they have the characteristic properties of the $B\left(E2\right)$ and $B\left(M1\right)$ transition probabilities, which are expected from the phenomenological triaxial particle-rotor coupling model.

We study the shape evolution of $N=Z$ nuclei ${}^{24}\mathrm{Mg},{}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$ in the axially symmetric deformed Woods-Saxon model, taking into account both $T=0$ and $T=1$ pairing interactions. We find the coexistence of $T=0$ and $T=1$ superfluidity phases in the large deformation region $|{\beta }_2|>0.3$ in these three nuclei. The interplay between the two pairing interactions has an important effect on determining the deformation of the ground states in these nuclei. The self-energy contributions from the pairing correlations to the single particle (s.p.) energies are also examined.

A collective band of positive as well as negative parity could be composed of vibrational and rotational motions. The octupole vibrational configurations can be based either on axial or nonaxial octupole excitations. A consistent approach to the quadrupole-octupole collective vibrations coupled with the rotational motion enables us to distinguish between various scenarios of disappearance of the $E2$ transitions in negative-parity bands observed in several nuclei. The theoretical estimates presented here are compared with the very recent experimental energies and transition probabilities in and between the ground-state and low-energy negative-parity bands in ${}^{156}\mathrm{Dy}$. A realistic collective Hamiltonian contains the potential-energy term obtained through the macroscopic-microscopic Strutinsky-like method with a particle-number-projected BCS approach and a deformation-dependent mass tensor. The potential energy and the inertia parameters are defined in the vibrational-rotational, nine-dimensional collective space of the multipole-deformation parameters and Euler angles. The symmetrization procedure applied to the eigenstates of the collective Hamiltonian ensures their uniqueness with respect to the laboratory coordinate system. This quadrupole-octupole collective approach may also allow us to find and/or verify some fingerprints of possible high-rank symmetries (e.g., tetrahedral, octahedral, ...) in nuclear collective bands.

The incomplete fusion dynamics of ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the platypus code is used to understand and quantify the impact of both ${}^6\mathrm{Li}$ resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as ${}^8\mathrm{Be}$ and ${}^5\mathrm{Li}$) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of ${}^6\mathrm{Li}$ reduces the incomplete fusion cross sections and (ii) the neutron-stripping channel practically determines those cross sections.

Recent STAR data on the bulk observables in the energy range of the beam energy scan program at the Relativistic Heavy Ion Collider are analyzed within the model of three-fluid dynamics (3FD). The simulations are performed with different equations of state (EoS's). The purely hadronic EoS fails to reproduce the data. A good, though imperfect, overall reproduction of the data is found within the deconfinement scenarios. The crossover EoS turns out to be slightly preferable. For this reproduction a fairly strong baryon stopping in the quark-gluon phase is required. The 3FD model does not need two separate freeze-outs (i.e., kinetic and chemical ones) to describe the STAR data. A unified freeze-out is applied at all energies.

The nuclear structure of the ${}^{17}\mathrm{O}$ nucleus has been investigated using shell model and self-consistent Hartree-Fock calculations. In particular, elastic and inelastic electron scattering form factors, energy levels, and transition probabilities are calculated for positive and negative low-lying states. Two different shell model spaces have been used for this purpose. The first one is the psdpn model space for positive parity states and the second one is $p_{1/2}sd$ model space for negative parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been confirmed that combining the shell model plus Hartree-Fock mean field method with the Skyrme interaction can accommodate very well the nuclear excitation properties, and work better for low lying states than for higher excitations. Furthermore, the combination can be used to reproduce the positive and negative parity states after choosing the suitable model space, effective two-body interaction, and parameterization to reach highly descriptive and predictive results.

We present a fully three-dimensional model providing initial conditions for energy and net-baryon density distributions in heavy-ion collisions at arbitrary collision energy. The model includes the dynamical deceleration of participating nucleons or valence quarks, depending on the implementation. The duration of the deceleration continues until the string spanned between colliding participants is assumed to thermalize, which is either after a fixed proper time, or a fluctuating time depending on sampled final rapidities. Energy is deposited in space time along the string, which in general will span a range of space-time rapidities and proper times. We study various observables obtained directly from the initial-state model, including net-baryon rapidity distributions, two-particle rapidity correlations, as well as the rapidity decorrelation of the transverse geometry. Their dependence on the model implementation and parameter values is investigated. We also present the implementation of the model with 3+1-dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial-state model at proper times greater than the initial time for the hydrodynamic simulation.

Baryon and energy densities, which are reached in central Au+Au collisions at collision energy of $\sqrt{s_{NN}}=$ 39 GeV, are estimated within the model of three-fluid dynamics. It is shown that the initial thermalized mean proper baryon and energy densities in a sizable central region approximately are $n_B/n_0\approx 10$ and $\varepsilon \approx 40$ GeV/${\mathrm{fm}}^3$, respectively. The study indicates that the deconfinement transition at the stage of interpenetration of colliding nuclei makes the system quite opaque. The final fragmentation regions in these collisions are formed not only by primordial fragmentation fireballs, i.e., the baryon-rich matter passed through the interaction region (containing approximately 30% of the total baryon charge), but also by the baryon-rich regions of the central fireball pushed out to peripheral rapidities by the subsequent almost one-dimensional expansion of the central fireball along the beam direction.

One-proton ($1p$) radioactive emission under the influence of the ${\mathrm{\Lambda }}^0$-hyperon inclusion is discussed. I investigate the hyper-$1p$ emitter, ${}_{\mathrm{\Lambda }}{}^6\mathrm{Li}$, with a time-dependent three-body model. Two-body interactions for $\alpha$-proton and $\alpha -{\mathrm{\Lambda }}^0$ subsystems are determined consistently to their resonant and bound energies, respectively. For a proton-${\mathrm{\Lambda }}^0$ subsystem, a contact interaction, which can be linked to the vacuum-scattering length of the proton-${\mathrm{\Lambda }}^0$ scattering, is employed. A noticeable sensitivity of the $1p$-emission observables to the scattering length of the proton-${\mathrm{\Lambda }}^0$ interaction is shown. The ${\mathrm{\Lambda }}^0$-hyperon inclusion leads to a remarkable fall of the $1p$-resonance energy and width from the hyperonless $\alpha$-proton resonance. For some empirical values of the proton-${\mathrm{\Lambda }}^0$ scattering length, the $1p$-resonance width is suggested to be of the order of $0.1–0.01$ MeV. Thus, the $1p$ emission from ${}_{\mathrm{\Lambda }}{}^6\mathrm{Li}$ may occur in the time scale of ${10}^{-20}–{10}^{-21}$ seconds, which is sufficiently shorter than the self-decay lifetime of ${\mathrm{\Lambda }}^0,{10}^{-10}$ seconds. By taking the spin-dependence of the proton-${\mathrm{\Lambda }}^0$ interaction into account, a remarkable split of the $J^{\pi }=1^{-}$ and $2^{-} 1p$-resonance states is predicted. It is also suggested that, if the spin-singlet proton-${\mathrm{\Lambda }}^0$ interaction is sufficiently attractive, the $1p$ emission from the $1^{-}$ ground state is forbidden. From these results, I conclude that the $1p$ emission can be a suitable phenomenon to investigate the basic properties of the hypernuclear interaction, for which a direct measurement is still difficult.

Fully constrained bubble chamber data on the $pp\to {\pi }^{+}pn$ and $pp\to {\pi }^{+}d$ reactions are used to investigate the ratio of the counting rates for the two processes as function of the $pn$ excitation energy $Q$. Though it is important to include effects associated with the $p$-wave nature of pion production, the data are insufficient to establish unambiguously the dependence on $Q$. The angular distributions show the presence of higher partial waves which seem to be anomalously large at small $Q$. The dispersion relation method to determine scattering lengths is extended to encompass cases where, as for the $pp\to {\pi }^{+}pn$ reaction, there is a bound state and, in a test example, it is shown that the values deduced for the low-energy neutron-proton scattering parameters are significantly influenced by the pion $p$-wave behavior.

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a rare earth nucleus ${}^{152}\mathrm{Sm}$. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach, and general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well-defined spins. In the exact-symmetry limit those bands involve no $E2$ transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers, and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape isomers and, possibly, new waiting point nuclei—impacting the nucleosynthesis processes in astrophysics—and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

$\beta$-decay properties of the odd-odd $N=Z{}^{70}\mathrm{Br}$ nucleus are self-consistently explored within the beyond-mean-field complex excited vampir variational model using an effective interaction obtained from a nuclear matter $G$-matrix based on the charge-dependent Bonn CD potential and an adequate model space. Results on superallowed Fermi $\beta$ decay of the ground state and Gamow-Teller decay of the $9^{+}$ isomer in ${}^{70}\mathrm{Br}$ correlated with the shape coexistence and mixing effects on the structure and electromagnetic properties of the populated states in the daughter nucleus ${}^{70}\mathrm{Se}$ are presented and compared with available data.

Background: Proton-induced knockout reactions of the form $(p,pN)$ have experienced a renewed interest in recent years due to the possibility of performing these measurements with rare isotopes, using inverse kinematics. Several theoretical models are being used for the interpretation of these new data, such as the distorted-wave impulse approximation (DWIA), the transition amplitude formulation of the Faddeev equations due to Alt, Grassberger, and Sandhas (FAGS) and, more recently, a coupled-channels method here referred to as transfer-to-the- continuum (TC).

Purpose: Our goal is to compare the momentum distributions calculated with the DWIA and TC models for the same reactions, using whenever possible the same inputs (e.g., distorting potential). A comparison with already published results for the FAGS formalism is performed as well.

Method: We choose the ${}^{15}\mathrm{C}(p,pn){}^{14}\mathrm{C}$ reaction at an incident energy of 420 MeV/u, which has been previously studied with the FAGS formalism. The knocked-out neutron is assumed to be in a $2s$ single-particle orbital. Longitudinal and transverse momentum distributions are calculated for different assumed separation energies.

Results: For all cases considered, we find a very good agreement between DWIA and TC results. The energy dependence of the distorting optical potentials is found to affect in a modest way the shape and magnitude of the momentum distributions. Moreover, when relativistic kinematics corrections are omitted, our calculations reproduce remarkably well the FAGS result.

Conclusions: The results found in this work provide confidence on the consistency and accuracy of the DWIA and TC models for analyzing momentum distributions for $(p,pn)$ reactions at intermediate energies.

The areas $d\sigma /d\mathrm{\Omega }$ of fitted quasifree scattering peaks from bound nucleons for continuum hadron-nucleus spectra measuring $d^2\sigma /d\mathrm{\Omega }d\omega$ are converted to sum rules akin to the Coulomb sums familiar from continuum electron scattering spectra from nuclear charge. Hadronic spectra with or without charge exchange of the beam are considered. These sums are compared to the simple expectations of a nonrelativistic Fermi gas, including a Pauli blocking factor. For scattering without charge exchange, the hadronic sums are below this expectation, as also observed with Coulomb sums. For charge exchange spectra, the sums are near or above the simple expectation, with larger uncertainties. The strong role of hadron-nucleon in-medium total cross sections is noted from use of the Glauber model.

Background: The fusion reaction ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$ is a link between heavier cases studied in recent years, and the light heavy-ion systems, e.g., ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}, {}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ that have a prominent role in the dynamics of stellar evolution. ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$ fusion itself is not a relevant process for astrophysics, but it is important to establish its behavior below the barrier, where couplings to low-lying collective modes and the hindrance phenomenon may determine the cross sections. The excitation function is presently completely unknown below the barrier for the ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$ reaction, thus no reliable extrapolation into the astrophysical regime for the C+C and O+O cases can be performed.

Purpose: Our aim was to carry out a complete measurement of the fusion excitation function of ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$ from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of ${}^{30}\mathrm{Si}$, and whether the hindrance effect appears in this relatively light system which has a positive $Q$ value for fusion. This would have consequences for the extrapolated behavior to even lighter systems.

Methods: The inverse kinematics was used by sending ${}^{30}\mathrm{Si}$ beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin ${}^{12}\mathrm{C}$ ($50\mu \mathrm{g}/{\mathrm{cm}}^2$) targets enriched to $99.9\%$ in mass 12. The fusion evaporation residues (ER) were detected at very forward angles, following beam separation by means of an electrostatic deflector. Angular distributions of ER were measured at $E_{\mathrm{beam}}=45$, 59, and 80 MeV, and they were angle integrated to derive total fusion cross sections.

Results: The fusion excitation function of ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$ was measured with high statistical accuracy, covering more than five orders of magnitude down to a lowest cross section $\simeq 3\mu \mathrm{b}$. The logarithmic slope and the $S$ factor have been extracted and we have convincing phenomenological evidence of the hindrance effect. These results have been compared with the calculations performed within the model that considers a damping of the coupling strength well inside the Coulomb barrier.

Conclusions: The experimental data are consistent with the coupled-channels calculations. A better fit is obtained by using the Yukawa-plus-exponential potential and a damping of the coupling strengths inside the barrier. The degree of hindrance is much smaller than the one in heavier systems. Also a phenomenological estimate reproduces quite closely the hindrance threshold for ${}^{12}\mathrm{C}+{}^{30}\mathrm{Si}$, so that an extrapolation to the C+C and O+O cases can be reliably performed.

A detailed study of multiparticle azimuthal correlations is presented using $pp$ data at $\sqrt{s}=5.02$ and 13 TeV, and $p$+Pb data at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, recorded with the ATLAS detector at the CERN Large Hadron Collider. The azimuthal correlations are probed using four-particle cumulants $c_n\left\{4\right\}$ and flow coefficients $v_n\left\{4\right\}={(-c_n\left\{4\right\})}^{1/4}$ for $n=2$ and 3, with the goal of extracting long-range multiparticle azimuthal correlation signals and suppressing the short-range correlations. The values of $c_n\left\{4\right\}$ are obtained as a function of the average number of charged particles per event, $〈N_{\mathrm{ch}}〉$, using the recently proposed two-subevent and three-subevent cumulant methods, and compared with results obtained with the standard cumulant method. The standard method is found to be strongly biased by short-range correlations, which originate mostly from jets with a positive contribution to $c_n\left\{4\right\}$. The three-subevent method, on the other hand, is found to be least sensitive to short-range correlations. The three-subevent method gives a negative $c_2\left\{4\right\}$, and therefore a well-defined $v_2\left\{4\right\}$, nearly independent of $〈N_{\mathrm{ch}}〉$, which implies that the long-range multiparticle azimuthal correlations persist to events with low multiplicity. Furthermore, $v_2\left\{4\right\}$ is found to be smaller than the $v_2\left\{2\right\}$ measured using the two-particle correlation method, as expected for long-range collective behavior. Finally, the measured values of $v_2\left\{4\right\}$ and $v_2\left\{2\right\}$ are used to estimate the number of sources relevant for the initial eccentricity in the collision geometry. The results based on the subevent cumulant technique provide direct evidence, in small collision systems, for a long-range collectivity involving many particles distributed across a broad rapidity interval.

High energy proton-nucleus (pA) collisions provide an important constraint on the study of the chiral magnetic effect in QCD matter. Naively, in pA collisions one expects no correlation between the orientation of the event plane as reconstructed from the azimuthal distribution of produced hadrons and the orientation of the magnetic field. If this is the case, any charge-dependent hadron correlations can only result from the background. Nevertheless, in this paper we point out that in high multiplicity pA collisions a correlation between the magnetic field and the event plane can appear. This is because triggering on the high hadron multiplicity amounts to selecting Fock components of the incident proton with a large number of partons that are expected to have a transverse size much larger than the average proton size. We introduce the effect of the fluctuating proton size in the Monte Carlo Glauber model and evaluate the resulting correlation between the magnetic field and the second-order event plane in both pA and nucleus-nucleus (AA) collisions. The fluctuating proton size is found to result in a significant correlation between the magnetic field and the event plane in pA collisions, even though the magnitude of the correlation is still much smaller than in AA collisions. This result opens a possibility of studying the chiral magnetic effect in small systems.