A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual, and resonant states based on numerical solutions of the Schrödinger equation. This method is well known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to \infty$. Concrete calculations are performed for the $1^{+}$ ground state of ${}^{14}\mathrm{N}$, the resonance ${}^{15}\mathrm{F}$ states ($1/2^{+}$, $5/2^{+}$), low-lying states of ${}^{11}\mathrm{Be}$ and ${}^{11}\mathrm{N}$, and the subthreshold resonance in the proton-proton system. We also demonstrate that in the case of broad resonances, their energy and width can be found from the fitting the experimental phase shifts using the analytical expression for the elastic-scattering $S$ matrix. We compare the $S$-matrix pole and the $R$ matrix methods for broad resonances in the ${}^{14}\mathrm{O}$-$p$ and in ${}^{26}\mathrm{Mg}$-$n$ systems.

We calculate rapidity distribution of photons due to Compton and annihilation processes from quark gluon plasma with pre-equilibrium momentum-space anisotropy. We also include contributions from hadronic matter with late-stage transverse expansion. A phenomenological model has been used for the time evolution of hard momentum scale, $p_{\mathrm{hard}}(\tau )$, and anisotropy parameter, $\xi (\tau )$. As a result of pre-equilibrium momentum-space anisotropy, we find significant modification of photons rapidity distribution. For example, with the fixed initial condition (FIC) free-streaming ($\delta =2$) interpolating model we observe significant enhancement of photon rapidity distribution at fixed $p_T$, where as for FIC collisionally broadened ($\delta =2/3$) interpolating model the yield increases till $y~1$. Beyond that suppression is observed. With fixed final multiplicity (FFM) free-streaming interpolating model we predict enhancement of photon yield which is less than the case of FIC. Suppression is always observed for FFM collisionally broadened interpolating model.

Radiative electron-proton scattering is studied in peripheral kinematics, where the scattered electron and photon move close to the direction of the initial electron. Even in the case of an unpolarized initial electron, the photon may have a definite polarization. The differential cross sections with longitudinally or transversity polarized initial electrons are calculated. The relevant effective degrees of polarization are explicitly derived. The same phenomena are considered for the production of an electron-positron pair by a photon, where the final positron (electron) can be also polarized. Differential distributions for the case of a polarized initial photon are given. We extend the results obtained for protons to atoms of any atomic number, including screening.

The isospin- and momentum-dependent MDI interaction, which has been extensively used in intermediate-energy heavy-ion reactions to study the properties of asymmetric nuclear matter, is extended to include the nucleon-hyperon and hyperon-hyperon interactions by assuming the same density, momentum, and isospin dependence as for the nucleon-nucleon interaction. The parameters in these interactions are determined from the empirical hyperon single-particle potentials in symmetric nuclear matter at saturation density. The extended MDI interaction is then used to study in the mean-field approximation the equation of state of hypernuclear matter and also the properties of hybrid stars by including the phase transition from hypernuclear matter to quark matter at high densities. In particular, the effects of attractive and repulsive $\Sigma$N interactions and different values of symmetry energies on the hybrid star properties are investigated.

Based on a microscopic cluster model that reproduces well the ${}^{17}\mathrm{C}$ spectrum below the neutron threshold, we study the spectrum of its mirror nucleus ${}^{17}\mathrm{Na}$. We find that the ${}^{17}\mathrm{Na}$ ground state should be located at $2.4$ MeV above the ${}^{16}\mathrm{Ne}$($0_1^{+})+p$ threshold, being a broad $1/2^{+}$ resonance with a width of $1.4$ MeV. However, there should exist at least four narrow excited states in ${}^{17}\mathrm{Na}$; three of them, $3/2_1^{+}$, $7/2_1^{+}$, and $9/2_1^{+}$, decay into the ${}^{16}\mathrm{Ne}$($2_1^{+})+p$ channel, and the other, $5/2_1^{+}$, decays mainly into the ${}^{16}\mathrm{Ne}$($0_1^{+})+p$ channel. Because the daughter nucleus ${}^{16}\mathrm{Ne}$ is a two-proton emitter, the narrow ${}^{17}\mathrm{Na}$ states must undergo a sequential three-proton decay via intermediate states in ${}^{16}\mathrm{Ne}$.

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

Isospin symmetry of atomic nuclei is explicitly broken by the charge-dependent interactions, primarily the Coulomb force. Within the nuclear density functional theory, isospin is also broken spontaneously. We propose a projection scheme rooted in a Hartree-Fock theory that allows the consistent treatment of isospin breaking in both ground and exited nuclear states. We demonstrate that this scheme is free from spurious divergences plaguing particle-number and angular-momentum restoration approaches. Applications of the new technique include excited high-spin states in medium-mass $N=Z$ nuclei, such as superdeformed bands and many-particle–many-hole terminating states. Owing to the large spin polarization and/or high seniority of these states, pairing correlations have been ignored.

Measurements of the proton and deuteron $F_2$ structure functions are presented. The data, taken at Jefferson Lab Hall C, span the four-momentum transfer range $0.06<Q^2<2.8$ GeV${}^2$ and Bjorken $x$ values from 0.009 to 0.45, thus extending the knowledge of $F_2$ to low values of $Q^2$ at low $x$. Next-to-next-to-leading-order calculations using recent parton distribution functions start to deviate from the data for $Q^2<2$ GeV${}^2$ at the low and high $x$ values. Down to the lowest value of $Q^2$, the structure function is in good agreement with a parametrization of $F_2$ based on data that have been taken at much higher values of $Q^2$ or much lower values of $x$, and which are constrained by data at the photon point. The ratio of the deuteron and proton structure functions at low $x$ remains well described by a logarithmic dependence on $Q^2$ at low $Q^2$.

High-spin states in ${}^{73}\mathrm{Kr}$ were studied at the XTU tandem accelerator of the Laboratori Nazionali di Legnaro using the reaction ${}^{40}\mathrm{Ca}$(${}^{40}\mathrm{Ca}$,$\alpha 2\mathit{pn}$) at a beam energy of 185 MeV. Gamma rays were detected with the EUROBALL spectrometer. Particle detection enabled us to identify the reaction channel leading to ${}^{73}\mathrm{Kr}$. The yrast bands of positive and negative parity were established up to probable spins of $61/2^{+}$ and $63/2^{-}$, respectively. The energies of the two identified bands agree well with the predictions of the configuration-dependent Cranked Nilsson-Strutinsky approximation and indicate that the nucleus remains collective up to the maximum spins of the respective high-spin configurations. The positive-parity band represents one of the rare cases where band non-termination at the highest spin of the configuration could be established experimentally.

A complete kinematic measurement of the ${}^6\mathrm{Li}$(${}^3\mathrm{He}$,${}^3\mathrm{H}$)$\alpha \mathit{pp}$ reaction is performed at $E_{\mathrm{lab}}=50$ MeV, to investigate the cluster structure of ${}^6\mathrm{Be}$. The energy and angular distributions of the breakup particles, emitted from the ground and first excited states of ${}^6\mathrm{Be}$, are compared to three-body resonance and two-body sequential decay calculations. The results indicate a rather pure three-body configuration of the $2^{+}$ state of ${}^6\mathrm{Be}$ but they are not conclusive regarding the decay mode of the $0^{+}$ state. No branching ratio between sequential and three-body decay paths could be extracted. Excitations above the $2^{+}$ state were populated at $E_x=1.67$–23 MeV. Decay through ${}^5\mathrm{Li}$-$p$ and ${}^2\mathrm{He}$-${}^4\mathrm{He}$ channels is identified in the continuum of ${}^6\mathrm{Be}$, and the reaction mechanism is discussed.

Differential cross sections for the $0_2^{+}$ state at $E_x=7.654$ MeV in ${}^{12}\mathrm{C}$ were measured with the ($p,p^{\prime }$) reaction at an incident energy of $E$${}_p=300$ MeV, and in an angular range from ${\theta }_{\mathrm{Lab}}=2.7$${}^{°}$ to ${40}^{°}$. The cross-section data were compared with the distorted-wave Born-approximation calculations employing three types of transition densities obtained in a macroscopic collective model, a microscopic $\alpha$-cluster model, and a microscopic $\alpha$-cluster condensation model. It is concluded that the measured angular distribution of the differential cross sections for the ${}^{12}\mathrm{C}$($p,p^{\prime }$) reaction at 300 MeV is consistently described with the assumption that the $0_2^{+}$ state at $E_x=7.654$ MeV is the dilute $\alpha$-cluster condensed state.

We investigate reaction mechanisms occurring in heavy-ion collisions at low energy ($~20$ MeV/nucleon). In particular, we focus on the competition between fusion and breakup processes (deep inelastic and fragmentation) in semiperipheral collisions, where the formation of excited systems under various conditions of shape and angular momentum is observed. Adopting a Langevin treatment for the dynamical evolution of the system configuration, described in terms of shape observables such as quadrupole and octupole moments, we derive fusion and fission probabilities, from which the corresponding fusion and breakup cross sections can finally be evaluated. The dependence of the results on shape, angular momentum, and excitation energy is discussed.

The relative $\gamma$-decay probabilities of the ${}^{162}\mathrm{Dy}$ to ${}^{161}\mathrm{Dy}$ and ${}^{162}\mathrm{Dy}$ to ${}^{164}\mathrm{Dy}$ residual nuclei, produced using light-ion-induced direct reactions, were measured as a function of excitation energy using the CACTUS array at the Oslo Cyclotron Laboratory. The external surrogate ratio method (SRM) was used to convert these relative $\gamma$-decay probabilities into the ${}^{161}\mathrm{Dy}$($n$,$\gamma$) cross section in an equivalent neutron energy range of 130–560 keV. The directly measured ${}^{161}\mathrm{Dy}$($n$,$\gamma$) cross section, obtained from the Evaluated Nuclear Data Files (ENDF/B-VII.0), was compared to the experimentally determined surrogate ${}^{161}\mathrm{Dy}$($n$,$\gamma$) cross section obtained using compound-nucleus pairs with both similar (${}^{162}\mathrm{Dy}$ to ${}^{164}\mathrm{Dy}$) and dissimilar (${}^{162}\mathrm{Dy}$ to ${}^{161}\mathrm{Dy}$) nuclear structures. A $\gamma$-ray energy threshold was identified, based upon pairing gap parameters, that provides a first-order correction to the statistical $\gamma$-ray tagging approach and improves the agreement between the surrogate cross-section data and the evaluated result.

Scaling studies of inclusive quasielastic electron scattering reactions have been used in the past as a basic tool to obtain information on the nucleon momentum distribution in nuclei. However, the connection between the scaling function, extracted from the analysis of cross-section data, and the spectral function only exists assuming very restricted approximations. We revisit the basic expressions involved in scaling studies and how they can be linked to the nucleon momentum distribution. In particular, the analysis applied in the past to the so-called scaling region, that is, negative values of the scaling variable $y$, is extended here to positive $y$, as a “universal” superscaling function has been extracted from the analysis of the separated longitudinal data. This leads to results that clearly differ from those based solely on the negative-$y$ scaling region, providing new information on how the energy and momentum are distributed in the spectral function.

Nuclear multifragmentation in intermediate-energy heavy-ion collisions has long been associated with liquid-gas phase transition. We calculate the shear viscosity to entropy density ratio $\eta /s$ for an equilibrated system of nucleons and fragments produced in multifragmentation within an extended statistical multifragmentation model. The temperature dependence of $\eta /s$ exhibits behavior surprisingly similar to that of ${\mathrm{H}}_2$O. In the coexistence phase of fragments and light particles, the ratio $\eta /s$ reaches a minimum of depth comparable to that for water in the vicinity of the critical temperature for liquid-gas phase transition. The effects of freeze-out volume and surface symmetry energy on $\eta /s$ in multifragmentation are studied.

We have made a new time-dependent calculation of the supernova production ratio of the long-lived isomeric state ${}^{180}\mathrm{Ta}$${}^m$. Such a time-dependent solution is crucial for understanding the production and survival of this isotope. We include the explicit linking between the isomer and all known excited states. We have also calculated the properties of possible links to a conjectured excited state that might decrease the final isomer residual ratio. We find that the explicit time evolution of the synthesis of ${}^{180}\mathrm{Ta}$ using the available nuclear data avoids the overproduction relative to ${}^{138}\mathrm{La}$ for a $\nu$-process neutrino temperature of 4 MeV.

We discuss elastic electron-deuteron ($\mathit{ed}$) scattering beyond the Born approximation. The reaction amplitude contains six generalized form factors, but only three linearly independent combinations of them (generalized charge, quadrupole, and magnetic form factors) contribute to the reaction cross section in second-order perturbation theory. We examine the two-photon exchange and find that it includes two types of diagrams, where two virtual photons are interacting with the same nucleon and where the photons are interacting with different nucleons. It is shown that the two-photon-exchange amplitude is strongly connected with the deuteron wave function at short distances.

The evolution of system observables at critical points of quantum phase transitions in atomic nuclei is explored within the context of the interacting boson model-1. The evolution of energies and transition strengths in the ground state band at the infinite-size critical point are examined with respect to system size. Properties of first-order phase transitions away from the U(5)-SU(3) leg of the Casten triangle are examined, and the effects of angular momentum on the evolution of system observables at the critical point are investigated for the first time.

Inclusive ($\mathrm{direct}+\mathrm{compound}$) $\alpha$ production for the ${}^6\mathrm{Li}+{}^{90}\mathrm{Zr}$ system is measured at near barrier energies, namely, $15,17,19,21,25$, and 30 MeV. The data are treated in the statistical model and distorted-wave Born approximation framework to disentangle the degree of competition between direct and compound reaction channels. A substantial contribution from the compound reaction channels is obtained but the direct reaction channels are found to be the dominant mechanism for $\alpha$ production at these energies. Estimation of the breakup and transfer reaction around the barrier shows that the latter is the dominant channel. Universal behavior of the $\alpha$-production cross section is observed over a large range of target nuclei.