Large-scale shell-model calculations are performed for even-even, odd-mass, and doubly odd nuclei of Pb, Bi, Po, At, Rn, and Fr isotopes in the neutron rich region ($N>126$) assuming ${}^{208}\mathrm{Pb}$ as a doubly magic core. Seven orbitals above the magic number 126, the $1g_{9/2}$, $0i_{11/2}$, $0j_{15/2}$, $2d_{5/2}$, $3s_{1/2}$, $1g_{7/2}$, and $2d_{3/2}$ orbitals, are considered for neutrons and all the six orbitals between the magic numbers 82 and 126, the $0h_{9/2}$, $1f_{7/2}$, $0i_{13/2}$, $2p_{3/2}$, $1f_{5/2}$, and $2p_{1/2}$ orbitals, are considered for protons. For a phenomenological effective two-body interaction, one set of the monopole-pairing, quadrupole-quadrupole, and multipole-pairing interactions is adopted for all the nuclei considered. The calculated energies and electromagnetic properties are compared with the experimental data. Many isomeric states are analyzed in terms of the shell-model configurations. The spins and parities of some experimentally ambiguous states are suggested.

A recent experiment on $s$-wave neutron scattering from ${}^{192,194,196}\mathrm{Pt}$ found that the reduced neutron width distributions deviate significantly from the expected Porter-Thomas distribution (PTD), and several explanations have been proposed within the statistical model of compound nucleus reactions. Here, we study the statistics of reduced neutron widths in the reaction $n+{}^{194}\mathrm{Pt}$ within a model that combines the standard statistical model with a realistic treatment of the neutron channel. We find that, if the correct secular energy dependence of the average neutron widths is used, the reduced neutron width distribution is in excellent agreement with the PTD for a reasonable range of the neutron-nucleus coupling strength and depth of the neutron channel potential. Within our parameter range, there can be a near-threshold bound or virtual state of the neutron channel potential that modifies the energy dependence of the average width from the $\sqrt{E}$ dependence, commonly assumed in experimental analysis, in agreement with the proposal of Weidenmüller [Phys. Rev. Lett. 105, 232501 (2010)]. In these cases, the reduced neutron width distributions extracted using the $\sqrt{E}$ dependence are broader than the PTD. We identify a relatively narrow range of parameters where this effect is significant.

I argue that, because of the peculiar properties of the ${\eta }^{\prime }$ meson, it is a promising probe of chiral dynamics. In particular, I show that a rotating gluon-dominated plasma might lead to an enhanced production of ${\eta }^{\prime }$ with respect to statistical model expectations. The presence of a strong topological susceptibility might give a similar effect. In both cases, unlike the statistical model, I expect a nontrivial dependence on event geometry, such as initial volume and impact parameter. Hence, an observation of ${\eta }^{\prime }/\pi$ ratio depending strongly on impact parameter might be a good indication of chiral effects, either from vorticity or topological phases of QCD.

This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $\eta /s\left(T\right)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $\eta /s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.

We study the property of $\alpha$ aggregates distributed on Archimedean solids within a microscopic framework, which takes full account of the Pauli principle. We pay special attention to the Coulomb energy for such exotic shapes of nuclei, and we discuss the advantage of $\alpha$ clusters with geometric configurations compared with the uniform density distributions in reducing the repulsive effect. We consider four kinds of configurations of $\alpha$ clusters distributed on Archimedean solids: dual polyhedra composed of a dodecahedron and an icosahedron, an octacontahedron, and two types of truncated icosahedrons, that is, two kinds of Archimedean solids. The latter two are an icosidodecahedron and a fullerene shape. Putting an $\alpha$ cluster on each vertex of the polyhedra, four $\alpha$-cluster aggregates correspond to the following four nuclei: Gd (64 protons), Po (84 protons), Nd (60 protons), and a nucleus with 120 protons, respectively.

A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors, corresponding to two high-$j$ quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the single-particle configuration and the asymmetry measure $\gamma$. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schrödinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum passes the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two $h_{11/2}$ quasiparticles, with the results used for the description of the chiral doublet bands in ${}^{134}\mathrm{Pr}$.

The complete and incomplete fusion along with one neutron stripping and pickup cross sections for the ${}^6\mathrm{Li}+{}^{124}\mathrm{Sn}$ system are measured using online and offline characteristic $\gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier are found to be suppressed by $\sim 34\%$ 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., $d$ capture is found to be dominant than $\alpha$ capture at all the measured energies, contrary to the data available for ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi},{}^{197}\mathrm{Au}$ systems. The total fusion cross section ratio between ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ induced reactions shows an increasing trend as the energy decreases below the barrier while it remains unity at above-barrier energies. A simultaneous explanation of complete, incomplete, and total fusion (TF) data is 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 shows the dominance of ICF at below-barrier energies and CF at above-barrier energies.

The decay mechanism of compound nucleus (CN) ${}^{202}\mathrm{Po}^{*}$, formed in ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Gd}$ reaction, is studied within the dynamical cluster-decay model (DCM) at various excitation energies $E_{\mathrm{CN}}^{*}$, where neutron emission $xn$, $x=3\text{–}5$, are the predominant decay modes. The study is of interest since ${}^{202}\mathrm{Po}^{*}$ decays to the ground state (g.s.) of ${}^{198}\mathrm{Po}$ by emission of $4n$ and to metastable states ${}^{199m}\mathrm{Po}$ and ${}^{197m}\mathrm{Po}$ via ($3n,5n$) emission, respectively. The DCM is applied here for the first time to the decays of metastable states. Both types of decays are analyzed separately, using neck-length $\mathrm{\Delta }R$ (equivalently, barrier-lowering) parameter, the only parameter in the DCM, to best fit the evaporation residue or channel cross section (${\sigma }_{xn}$) data and predict the quasifissionlike (qf-like) noncompound (${\sigma }_{\mathrm{qf}}$) and fusion-fission (${\sigma }_{\mathrm{ff}}$) cross sections. For g.s. to g.s. decay of ${}^{202}\mathrm{Po}^{*}$, possibly due to involving the deformed rare-earth lanthanide target ${}^{154}\mathrm{Gd}$, the observed $4n$ decay channel requires the noncompound nucleus (nCN) contribution, treated as the qf-like process. On the other hand, the decay mechanism of ${}^{202}\mathrm{Po}^{*}$ to metastable states (m.s.) ${}^{199m}\mathrm{Po}$ and ${}^{197m}\mathrm{Po}$, is a pure CN decay, i.e., the ${\sigma }_{\mathrm{qf}}$ is zero. In this study, we have included the deformation effects up to quadrupole deformations ${\beta }_{2i}$ and optimum orientations ${\theta }_i^{\mathrm{opt}.}$ for coplanar ($\mathrm{\Phi }=0^0$) nuclei, using hot-compact configurations, supporting asymmetric fission of CN ${}^{202}\mathrm{Po}^{*}$. The variation of CN formation probability $P_{\mathrm{CN}}$ and survival probability $P_{\mathrm{surv}}$ with excitation energy $E_{\mathrm{CN}}^{*}$ is in complete agreement with the known systematic of other radioactive CN studied so far, thereby giving credence to the predicted ${\sigma }_{\mathrm{qf}}$ in g.s. to g.s. decay and fusion-fission cross section ${\sigma }_{\mathrm{ff}}$ of ${}^{202}\mathrm{Po}^{*}$. Interestingly, both the observed g.s. to g.s. and g.s. to m.s. processes occur at a fixed $\mathrm{\Delta }R=2.45\pm 0.20\mathrm{fm}$, which is within the nuclear proximity limit of $\sim 2.5\mathrm{fm}$, and hence useful for making predictions.

Friction coefficients for the fusion reaction ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{32}\mathrm{S}$ are extracted based on both the time-dependent Hartree-Fock and the time-dependent density matrix methods. The latter goes beyond the mean-field approximation by taking into account the effect of two-body correlations, but in practical simulations of fusion reactions we find that the total energy is not conserved. We analyze this problem and propose a solution that allows for a clear quantification of dissipative effects in the dynamics. Compared to mean-field simulations, friction coefficients in the density-matrix approach are enhanced by about $20\%$. An energy dependence of the dissipative mechanism is also demonstrated, indicating that two-body collisions are more efficient at generating friction at low incident energies.

Theoretical uncertainties of various types are discussed for the nucleon-deuteron elastic scattering observables at incoming-nucleon laboratory energies up to 200 MeV. We are especially interested in the statistical errors arising from uncertainties of parameters of a nucleon-nucleon interaction. The obtained uncertainties of the differential cross section and numerous scattering observables are in general small, grow with the reaction energy, and amount up to a few percent at 200 MeV. We compare these uncertainties with the other types of theoretical errors like truncation errors, numerical uncertainties, and uncertainties arising from using the various models of nuclear interaction. We find the latter ones to be dominant source of uncertainties of modern predictions for the three-nucleon scattering observables. To perform above mentioned studies we use the One-Pion-Exchange Gaussian potential derived by the Granada group, for which the covariance matrix of its parameters is known, and solve the Faddeev equation for the nucleon-deuteron elastic scattering. Thus besides studying theoretical uncertainties we also show a description of the nucleon-deuteron elastic scattering data by the One-Pion-Exchange Gaussian model and compare it with results obtained with other nucleon-nucleon potentials, including chiral ${\mathrm{N}}^4\mathrm{LO}$ forces from the Bochum-Bonn and Moscow(Idaho)-Salamanca groups. In this way we confirm the usefulness and high quality of the One-Pion-Exchange Gaussian force.

In this work we calculate the energies odd $J^{+}$ states in selected even-even nuclei—${}^{44}\mathrm{Ti}{}^{52}\mathrm{Fe}$, and ${}^{96}\mathrm{Cd}$. Of particular interest is the fact that in many cases the first $T=0$ and the first $T=1$ state are close in energy. Whether the lowest odd $J$ state has $T=0$ or $T=1$ is here considered.

To study the properties of the $N^{*}$(1535) and $N^{*}$(1650), we calculate the mass distributions of $MB$ in the ${\mathrm{\Lambda }}_c\to {\overline{K}}^{0}MB$ decay, with $MB=\pi N(I=1/2),\eta p$, and $K\mathrm{\Sigma }(I=1/2)$. We do this by calculating the tree-level and loop contributions, mixing pseudoscalar-baryon and vector-baryon channels using the local hidden gauge formalism. The loop contributions for each channel are calculated using the chiral unitary approach. We observe that for the $\eta N$ mass distribution only the $N^{*}$(1535) is seen, with the $N^{*}$(1650) contributing to the width of the curve, but for the $\pi N$ mass distribution both resonances are clearly visible. In the case of $MB=K\mathrm{\Sigma }$, we found that the strength of the $K\mathrm{\Sigma }$ mass distribution is smaller than that of the mass distributions of the $\pi N$ and $\eta p$ in the ${\mathrm{\Lambda }}_c^{+}\to {\overline{K}}^0\pi N$ and ${\mathrm{\Lambda }}_c^{+}\to {\overline{K}}^0\eta p$ processes, in spite of this channel having a large coupling to the $N^{*}\left(1650\right)$. This is because the $K\mathrm{\Sigma }$ pair production is suppressed in the primary production from the ${\mathrm{\Lambda }}_c$ decay.

We investigated neutron-proton pairing correlations effects on the shell evolution of ground-state energies by the deformation for $N=Z$ nuclei in $pf$ shell, such as ${}^{44}\mathrm{Ti}$, ${}^{48}\mathrm{Cr}$, ${}^{52}\mathrm{Fe}$, ${}^{64}\mathrm{Ge}$, ${}^{68}\mathrm{Se}$, ${}^{72}\mathrm{Kr}$, and ${}^{76}\mathrm{Sr}$. We started from a simple shell-filling model constructed by a deformed Woods-Saxon potential with ${\beta }_2$ deformation, and included pairing correlations in the residual interaction, which give rise to smearing of the Fermi surface revealing interesting evolution of the Fermi energy along the shell evolution. In this work, like-pairing and unlike-pairing correlations decomposed as isovector $T=1$ and isoscalar $T=0$ components are explicitly taken into account. Finally, we estimate ground-state energies comprising the mean-field energy, the pairing energy, and the self-energy due to the pairing correlations, in terms of the deformation. The enhanced $T=0$ pairing interaction supports oblate deformations for ${}^{72}\mathrm{Kr}$ and ${}^{68}\mathrm{Se}$, whose features are different from other $pf$-shell $N=Z$ nuclei considered in this work.

The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in ${}^{90,92}\mathrm{Zr}$ and ${}^{92}\mathrm{Mo}$ from “background-free” spectra of inelastic $\alpha$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including $0^{\circ }$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influenced by nuclear shell structure near $A\sim 90$, contrary to the claim in a recent measurement.

Exploiting the similarity between the bunched single-particle energy levels of nuclei and of random distributions around the Fermi surface, pairing properties of the latter are calculated to establish statistically based bounds on the basic characteristics of the pairing phenomenon. When the most probable values for the pairing gaps germane to the BCS formalism are used to calculate thermodynamic quantities, we find that while the ratio of the critical temperature $T_c$ to the zero-temperature pairing gap is close to its BCS Fermi gas value, the ratio of the superfluid to the normal phase specific heats at $T_c$ differs significantly from its Fermi gas counterpart. The largest deviations occur when a few levels lie closely on either side of the Fermi energy but other levels are far away from it. The influence of thermal fluctuations, expected to be large for systems of finite number of particles, were also investigated using a semiclassical treatment of fluctuations. When the average pairing gaps along with those differing by one standard deviation are used, the characteristic discontinuity of the specific heat at $T_c$ in the BCS formalism was transformed to a shoulderlike structure indicating the suppression of a second-order phase transition as experimentally observed in nanoparticles and several nuclei. Contrasting semiclassical and quantum treatments of fluctuations for the random spacing model is currently underway.

We propose a framework to calculate the dynamics at the scission point of nuclear fission, based as far as possible on a discrete representation of orthogonal many-body configurations. Assuming axially symmetric scission shapes, we use the $K$ orbital quantum number to build a basis of wave functions. Pre-scission configurations are stable under mean-field dynamics while post-scission configurations evolve to separated fragments. In this first exploratory study, we analyze a typical fission trajectory through to scission in terms of these configurations. We find that there is a major rearrangement of the $K$ occupancy factors at scission. Interestingly, very different fragment shapes occur in the post-scission configurations, even starting from the same pre-scission configuration.

We develop an ab initio, nonperturbative, time-dependent basis function (tBF) method to solve the nuclear structure and scattering problems in a unified manner. We apply this method to a test problem: the Coulomb excitation of a trapped deuteron by an impinging heavy ion. The states of the deuteron system are obtained by the ab initio nuclear structure calculation implementing a realistic internucleon interaction with a weak external trap to localize the center of mass and to discretize the continuum. The evolution of the internal state of the deuteron system is directly solved using the equation of motion for the scattering. We analyze the excitation mechanism of the deuteron system by investigating its internal transition probabilities and observables as functions of the exposure time and the incident speed. In this investigation, the dynamics of the Coulomb excitation are revealed by the time evolution of the system's internal charge distribution.

An open question in the field of heavy-ion collisions is to what extent the size of initial inhomogeneities in the system affects measured observables. Here we present a method to smooth out these inhomogeneities with minimal effect on global properties, to quantify the effect of short-range features of the initial state. We show a comparison of hydrodynamic predictions with original and smoothened initial conditions for four models of initial conditions and various observables. Integrated observables (integrated $v_n$, scaled $v_n$ distributions, normalized symmetric cumulants, event-plane correlations) as well as most differential observables $\left[v_n\left(p_T\right)\right]$ show little dependence on the inhomogeneity sizes and instead are sensitive only to the largest-scale geometric structure. However, other differential observables such as the flow factorization ratio and subleading principal components are more sensitive to the granularity and could be a good tool to probe the short-scale dynamics of the initial stages of a heavy-ion collision, which are not currently well understood.