Relatively neutron-rich thorium isotopes lie at the heart of a nuclear region of nuclei exhibiting octupole correlation effects. The detailed level structure of ${}^{223}\mathrm{Th}$ has been investigated in measurements of $\gamma$ radiation following the fusion-evaporation channel of the ${}^{208}\mathrm{Pb}({}^{18}\mathrm{O},3n){}^{223}\mathrm{Th}$ reaction at 85 MeV beam energy. The level structure has been extended up to spin $49/2$, and 33 new $\gamma$ rays have been added using triple-$\gamma$ coincidence data. The spins and parities of the newly observed states have been confirmed by angular distribution ratios. In addition to the two known yrast bands based on a $K=5/2$ configuration, a non-yrast band has been established up to spin $35/2$. We interpret this new structure as based on the same configuration as the yrast band in ${}^{221}\mathrm{Th}$ having dominant $K=1/2$ contribution. At the highest spin a backbending occurs around a rotational frequency of $\hslash \omega =0.23$ MeV, very close to the one predicted in ${}^{222}\mathrm{Th}$, where a sharp transition to a reflection-symmetric shape is expected.

In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. This work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding $1+1$ dimensional causal relativistic hydrodynamical evolution at nonzero baryon density. We demonstrate that the critically enhanced bulk viscosity induces a substantial nonequilibrium pressure, effectively softening the equation of state, and leads to sizable effects in the flow velocity and single-particle distributions at the freeze-out. The observable effects that may arise due to the enhanced bulk viscosity in the vicinity of the QCD critical point can be used as complementary information to facilitate searches for the QCD critical point.

The ${}^{16}\mathrm{O}(\alpha ,{\alpha }^{\prime })$ reaction was studied at ${\theta }_{\mathrm{lab}}=0^{\circ }$ at an incident energy of $E_{\mathrm{lab}}=200$ MeV using the K600 magnetic spectrometer at iThemba LABS. Proton decay and $\alpha$ decay from the natural parity states were observed in a large-acceptance silicon strip detector array at backward angles. The coincident charged-particle measurements were used to characterize the decay channels of the $0_6^{+}$ state in ${}^{16}\mathrm{O}$ located at $E_x=15.097\left(5\right)$ MeV. This state is identified by several theoretical cluster calculations to be a good candidate for the $4\text{−}\alpha$ cluster state. The results of this work suggest the presence of a previously unidentified resonance at $E_x\approx 15$ MeV that does not exhibit a $0^{+}$ character. This unresolved resonance may have contaminated previous observations of the $0_6^{+}$ state.

Lifetimes of excited states in ${}^{99}\mathrm{Y},{}^{101}\mathrm{Y},{}^{101}\mathrm{Nb},{}^{103}\mathrm{Nb}$, and ${}^{105}\mathrm{Nb}$ were measured in an experiment using the recoil distance Doppler shift method at GANIL (Grand Accélérateur National d'Ions Lourds). The neutron-rich nuclei were produced in fission reactions between a ${}^{238}\mathrm{U}$ beam and a ${}^9\mathrm{Be}$ target. Prompt $\gamma$ rays were measured with the EXOGAM array and correlated with fission fragments that were identified in mass and atomic number with the VAMOS++ spectrometer. The measured lifetimes, together with branching ratios, provide $B\left(M1\right)$ and $B\left(E2\right)$ values for the strongly coupled rotational bands built on the $\left[422\right]5/2^{+}$ ground state in the Y and Nb nuclei with neutron number $N\ge 60$. The comparison of the experimental results with triaxial particle-rotor calculations provides information about the evolution of the nuclear shape in this mass region.

The Pauli exclusion principle induces a repulsion between composite systems of identical fermions such as colliding atomic nuclei. Our goal is to study how heavy-ion fusion is impacted by this “Pauli repulsion.” We propose a new microscopic approach, the density-constrained frozen Hartree-Fock method, to compute the bare potential including the Pauli exclusion principle exactly. Pauli repulsion is shown to be important inside the barrier radius and increases with the charge product of the nuclei. Its main effect is to reduce tunneling probability. Pauli repulsion is part of the solution to the long-standing deep sub-barrier fusion hindrance problem.

The present experimental study illustrates how large deformations attained by nuclei due to cluster formation are perceived through the giant dipole resonance (GDR) strength function. The high energy GDR $\gamma$ rays have been measured from ${}^{32}\mathrm{S}$ at different angular momenta ($J$) but similar temperatures in the reactions ${}^4\mathrm{He}(E_{\text{lab}}=45\mathrm{MeV})+{}^{28}\mathrm{Si}$ and ${}^{20}\mathrm{Ne}(E_{\text{lab}}=145\mathrm{MeV})+{}^{12}\mathrm{C}$. The experimental data at lower $J$ ($\sim 10\hslash$) suggests a normal deformation, similar to the ground state value, showing no potential signature of clustering. However, it is found that the GDR lineshape is fragmented into two prominent peaks at high $J$ ($\sim 20\hslash$) providing a direct measurement of the large deformation developed in the nucleus. The observed lineshape is also completely different from the ones seen for Jacobi shape transition at high $J$ pointing towards the formation of cluster structure in superdeformed states of ${}^{32}\mathrm{S}$ at such high spin. Thus, the GDR can be regarded as a unique tool to study cluster formation at high excitation energies and angular momenta.

In this study, the role of bombarding energy in analyzing the interaction potentials and describing the densities of interacting nuclei during fusion is investigated. For this purpose, the fusion cross sections of the ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}, {}^{16}\mathrm{O}+{}^{92}\mathrm{Zr}$, and ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$ systems are calculated by the use of potentials derived from the semiclassical Skyrme energy density functional and the coupled-channel formalism. The comparisons drawn between the theoretical fusion data and the experimental ones demonstrate the energy-dependence behavior of the potentials employed in the calculations. Considering this dependence, we also show the variations of the density parameters of the colliding nuclei with the bombarding energy. The obtained results indicate that with increasing energy, the fusion barrier heights increase, while the diffuseness parameters of the densities decrease.

Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of ab initio many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.

For the first time the astrophysical factor of the ${}^{10}\mathrm{B}(p,{\alpha }_0){}^7\mathrm{Be}$ reaction has been measured over a wide energy range, from 5 keV to 1.5 MeV, via the Trojan horse method (THM) applied to the quasifree ${}^2\mathrm{H}({}^{10}\mathrm{B},\alpha {}^7\mathrm{Be})n$ reaction. Therefore, the $S\left(E\right)$ factor has been recast into absolute units by scaling in the energy range 200 keV–1.2 MeV to a recent measurement using the activation method, leading to a normalization uncertainty of $4\%$. An $R$-matrix fit of the THM data was performed, to parametrize the $S$ factor, obtain spectroscopic information on the populated resonances, and compare with other recent experiments. Finally, a new determination of the screening potential $U_e$ has been obtained, $U_e=240\pm 50$ eV, with a much smaller error than our previous measurement.

Effective values of the axial-vector coupling constant $g_{\mathrm{A}}$ have lately attracted much attention due to the prominent role of $g_{\mathrm{A}}$ in determining the half-lives of double $\beta$ decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of $g_{\mathrm{A}}$. The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured $\beta$ electron spectra of forbidden nonunique $\beta$ decays yields information on the magnitude of $g_{\mathrm{A}}$. In parallel, we investigate the impact of the next-to-leading-order terms of the $\beta$-decay shape function and the radiative corrections on the half-life method and the SSM by analyzing the fourfold forbidden decays of ${}^{113}\mathrm{Cd}$ and ${}^{115}\mathrm{In}$ by using three nuclear-structure theory frameworks; namely, the nuclear shell model, the microscopic interacting boson-fermion model, and the microscopic quasiparticle-phonon model. The three models yield a consistent result, $g_{\mathrm{A}}\approx 0.92$, when the SSM is applied to the decay of ${}^{113}\mathrm{Cd}$ for which $\beta$-spectrum data are available. At the same time the half-life method yields results which are in tension with each other and the SSM result.

The properties of excited states in the neutron-rich nucleus ${}^{194}\mathrm{Os}$ have been investigated using the ${}^{192}\mathrm{Os}\left({}^{18}\mathrm{O},{}^{16}\mathrm{O}\right){}^{194}\mathrm{Os}$ reaction with an 80 MeV beam provided by the IFIN-HH Laboratory, Bucharest. Discrete $\gamma$-ray decays from excited states have been measured using the hybrid HPGe-${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ array RoSPHERE. The current work identifies a number of previously unreported low-lying nonyrast states in ${}^{194}\mathrm{Os}$ as well as the first measurement of the half-life of the yrast $2^{+}$ state of 302(50) ps. This is equivalent to a $B(E2:2^{+}\to 0^{+})=45\left(16\right)$ W.u. and intrinsic quadrupole deformation of ${\beta }_{\mathrm{eff}}=0.14\left(1\right)$. The experimental results are compared with Hartree-Fock-Bogoliubov–interacting-boson-model calculations and are consistent with a reduction in a quadrupole collectivity in Os isotopes with increasing neutron number.

Background: The nature of oscillations or excitations around the equilibrium deformed nuclear shape remains an open question in nuclear structure. The ${}^{162}\mathrm{Dy}$ nucleus is one of the most extensively studied nuclei with the $\left(n,\gamma \right)$, $\left(n,e^{-}\right)$, $\left(\alpha ,2n\right)$ reactions and most recently the $\left(p,t\right)$ pickup reaction adding 11 $0^{+}$ states to an excitation energy of 2.8 MeV to an already-well-developed level scheme. However, a major shortfall for a better understanding of the nature of the plethora of bands and levels in this nucleus has been the lack of lifetime measurements.

Purpose: To determine the character of the low-lying excited bands in this ${}^{162}\mathrm{Dy}$ nucleus, we set out to measure the level lifetimes.

Method: Lifetimes were measured in the ${}^{162}\mathrm{Dy}$ nucleus following neutron capture using the Gamma-Ray-Induced Doppler (GRID) broadening technique at the Institut Laue-Langevin in Grenoble, France.

Results: In total, we have measured the lifetimes of 12 levels belonging to a number of excited positive- and negative-parity bands in the low-lying spectrum of the ${}^{162}\mathrm{Dy}$ nucleus. The lifetime of the $K^{\pi }=2^{+}$ bandhead at 888.16 keV was previously measured. We confirm this value and measure lifetimes of the $3^{+}$ and $4^{+}$ members of this band yielding $B\left(E2\right)$ values that are consistent with a single $\gamma$-vibrational phonon of several Weisskopf units. The first excited $K^{\pi }=4^{+}$ band, with a bandhead at 1535.66 keV, is strongly connected to the $K^{\pi }=2^{+}$ band with enhanced collective $B\left(E2\right)$ values and it is consistent with a double phonon vibrational $\left(\gamma \gamma \right)$ excitation. Lifetime of $K^{\pi }=0^{+}$ band members have also been measured, including the $4_{K^{\pi }=0_2^{+}}^{+}$ state at 1574.29 keV and the $2_{K^{\pi }=0_3^{+}}^{+}$ state at 1728.31 keV. This latter state also displays the characteristics of a double phonon excitation built on the $K^{\pi }=2^{+}$ band.

Conclusions: We discuss our findings in terms of the presence or absence of collective quadrupole and octupole vibrational excitations. We find two positive-parity excited bands at 1535.66 keV $\left(K^{\pi }=4^{+}\right)$ and the 1728.312-keV $2^{+}$ state of a $K^{\pi }=0^{+}$ band at 1666 keV connected with sizably collective $B\left(E2\right)$ values to the $\left(K^{\pi }=2^{+}\right)\gamma$ band at 888 keV.

The cross sections of the ${}^{70}\mathrm{Zn}\left(n,\gamma \right){}^{71}\mathrm{Zn}^{\mathrm{m}}\left(T_{1/2}=3.96\pm 0.05\text{−}\mathrm{h}\right)$ reaction have been measured relative to the ${}^{197}\mathrm{Au}\left(n,\gamma \right){}^{198}\mathrm{Au}$ cross sections at 0.96 and 1.69 MeV using a ${}^7\mathrm{Li}\left(p,n\right){}^7\mathrm{Be}$ neutron source and activation technique. The cross section of this reaction has been measured for the first time in the MeV region. The new experimental cross sections have been compared with the theoretical prediction by talys-1.6 with various level-density models and $\gamma$-ray strength functions as well as the tendl-2015 library. The talys-1.6 calculation with the generalized superfluid level-density model and Kopecky-Uhl generalized Lorentzian $\gamma$-ray strength function predicted the new experimental cross sections at both incident energies. The ${}^{70}\mathrm{Zn}\left(n,\gamma \right){}^{71}\mathrm{Zn}^{\mathrm{g}+\mathrm{m}}$ total capture cross sections have also been derived by applying the evaluated isomeric ratios in the tendl-2015 library to the measured partial capture cross sections. The spectrum averaged total capture cross sections derived in the present paper agree well with the jendl-4.0 library at 0.96 MeV, whereas it lies between the tendl-2015 and the jendl-4.0 libraries at 1.69 MeV.

For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, I establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, I first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, I examine my scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave function from the Lippmann-Schwinger equation coincides with that from the Schrödinger equation for an energy-independent interaction. Of special interest is that the two-body wave function from the scattering amplitude is automatically scaled; the norm of the two-body wave function, to which I refer as the compositeness, is unity for an energy-independent interaction, while the compositeness deviates from unity for an energy-dependent interaction, which can be interpreted to implement missing-channel contributions. I also discuss general properties of the two-body wave function and compositeness for bound states with the schematic models.

A beyond-mean-field approach consisting of angular momentum projection techniques and generator coordinate method based on Skyrme–Hartree-Fock calculations is employed to investigate single- and double-$\mathrm{\Lambda }$ hypernuclear systems. The density-dependent $N\mathrm{\Lambda }$ interactions derived from the Nijmegen soft-core potentials are used. Rotational energy spectra and electric-quadrupole transition strengths $B\left(E2\right)$ of the hypernuclei ${}_{\mathrm{\Lambda }}{}^{13}\mathrm{C},{}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^{14}\mathrm{C},{}_{\mathrm{\Lambda }}{}^{21}\mathrm{Ne}$, and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^{22}\mathrm{Ne}$ are presented and compared with those of the corresponding core nuclei ${}^{12}\mathrm{C}$ and ${}^{20}\mathrm{Ne}$. The shrinkage effect of the $\mathrm{\Lambda }\mathrm{s}$ is demonstrated by the $B\left(E2\right)$ values, the charge radii, and the shape deformation $\beta$ of the nuclear core. It is found that the reduction of the $B\left(E2\right)$ values in ${}_{\mathrm{\Lambda }}{}^{13}\mathrm{C}$ and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^{14}\mathrm{C}$ is mainly caused by the shrinkage of the charge radii of the nuclear cores, while the reduced shape deformations also play important roles; but the contrary is the case in ${}_{\mathrm{\Lambda }}{}^{21}\mathrm{Ne}$ and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^{22}\mathrm{Ne}$. Comparison between this and other theoretical models are made, and the differences between them are illuminated.

We present a generalized Richardson solution for fermions interacting with the pairing interaction in both discrete and continuum parts of the single-particle (s.p.) spectrum. The pairing Hamiltonian is based on the rational Gaudin model which is formulated in the Berggren ensemble. We show that solutions of the generalized Richardson equations are exact in the two limiting situations: (i) in the pole approximation and (ii) in the s.p. continuum. If the s.p. spectrum contains both discrete and continuum parts, then the generalized Richardson equations provide accurate solutions for the Gamow shell model.

I have investigated the possibility that the near vanishing of the proton strength of the 9.17-MeV state in ${}^{14}\mathrm{N}$ could be due to isospin mixing. If the two levels involved are at 9.17 and 8.98 MeV, the mixing intensity is 0.41(9) with a $T$-mixing matrix element of 94(10) keV. Some consequences of such mixing are examined.

We discuss the formulation of a nonadiabatic approach to study the rotational states in triaxially deformed odd-$A$ nuclei. The rotation-particle coupling is treated microscopically by coupling the triaxial rotor states of the even-even core with the states of the valence particle in order to obtain the matrix elements of the odd-$A$ system. We arrive at a nonadiabatic quasiparticle approach where the rotational states can have contributions from various quasiparticle states near the Fermi level. We bring out the advantages of this approach over the conventional particle rotor model with a fixed or variable moment of inertia. One clear evidence favoring our approach is the rotation alignment phenomenon which is demonstrated in the case of ${}^{137}\mathrm{Pm}$. We discuss our results for ${}^{136}\mathrm{Nd}$ and ${}^{137}\mathrm{Pm}$, and justify that this approach is suitable also for studying nuclei away from stability.

Background: The study of evolution of asymmetric dinuclear systems (DNSs) formed in heavy ion collisions is a topic of intense research. The DNS evolution leads to a variety of reaction channels such as deep inelastic, complete fusion, quasifission, fast fission, fusion-fission, and evaporation of particles. The time evolution of the DNS in the quasifission process and the role of relevant parameters are still not fully understood.

Purpose: The influence of the entrance channel mass asymmetry on the time evolution of an excited and rotating DNS, populated via four reactions with different entrance channel mass asymmetry parameters which all lead to the compound nucleus ${}^{216}\mathrm{Ra}$, is explored.

Method: The driving potential, emission barriers for the binary decay (namely the quasifission and intrinsic fusion barriers), rate of the quasifission channel, and the lifetime of an excited DNS, as well as the fission rate and fission lifetime of the compound nucleus ${}^{216}\mathrm{Ra}$ formed in the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb},{}^{19}\mathrm{F}+{}^{197}\mathrm{Au},{}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$, and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions, are calculated by the dinuclear system approach.

Results: Our results show that the intrinsic fusion barrier values are equal to zero for the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ and ${}^{19}\mathrm{F}+{}^{197}\mathrm{Au}$ reactions. Therefore, the quasifission signature is extremely hindered for these reactions, while the ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ calculated results contain quasifission contributions. Provided the quasifission rate is nonzero, the quasifission rate increases with increasing orbital angular momentum $\ell$ of the composite system for a given excitation energy $E_{CN}^{*}$ of the compound nucleus. On the other hand, the quasifission lifetime decreases moderately with increasing $\ell$. Furthermore, both quasifission and fission rates increase with increasing excitation energy $E_{CN}^{*}$, while the quasifission and fission lifetimes decrease with increasing $E_{CN}^{*}$ for a given $\ell$.

Conclusions: Although these reactions with different entrance channels populate the same compound nucleus ${}^{216}\mathrm{Ra}$ at similar excitation energies, the fused system presents different behaviors for different entrance channel mass asymmetry parameters. In the ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ and ${}^{48}\mathrm{Ca}+{}^{168}\mathrm{Er}$ reactions having smaller entrance channel mass asymmetry, the quasifission signature dominates over the complete fusion process. Because of the small quasifission barrier for these reactions, the lifetime of the DNS is short and its $E_{\mathrm{DNS}}^{*}$ excitation energy is not sufficient to overcome the saddle point along the way to fusion. Instead, in the ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ and ${}^{19}\mathrm{F}+{}^{197}\mathrm{Au}$ reaction systems, at $E_{\mathrm{DNS}}^{*}$ excitation energy higher than the threshold energy, the DNS has sufficient energy and time to reach a compound nucleus. In other words, the model calculations predict that the quasifission rate is negligible for the reactions with higher entrance channel mass asymmetry and complete fusion is a dominant decay channel.