Lifetimes of excited states of the ground-state rotational band in the ${}^{136}\mathrm{Sm}$ nucleus have been measured up to $I^{\pi }={20}^{+}$ using the Doppler-shift attenuation method. The states were populated in the reaction ${}^{107}\mathrm{Ag}$(${}^{32}\mathrm{S}$, $1p2n$) at 145-MeV beam energy and the $\gamma$ rays emitted from the excited states were detected using the Indian National Gamma Array at the Tata Institute of Fundamental Research, Mumbai. The extracted transitional quadrupole moments indicate a reduction of collectivity with increasing spin after the band crossing. The results have been compared with the predictions of the cranked shell model as well as the triaxial projected shell-model calculations and indicate that the nucleus evolves from prolate $\gamma$-soft to a stable triaxially deformed shape after the first and the second crossing involving $\pi h_{11/2}^2$ and $\pi h_{11/2}^2\otimes \nu h_{11/2}^2$ configurations, respectively.

A pair of nearly degenerate positive-parity bands were observed in ${}^{82}\mathrm{Br}$ for the first time using the ${}^{82}\mathrm{Se}(\alpha ,p3n)$ reaction. The positive-parity doublet bands are proposed to be chiral doublet bands based on the triaxial particle rotor model and the potential energy surface calculations. The root-mean-square values of the angular momentum components and their probability distributions are discussed in detail to exhibit the chiral geometry and its evolution in ${}^{82}\mathrm{Br}$.

Background: The neutron-deficient lead region provides a range of nuclear phenomena, including isomerism at low energies. This phenomenon can be studied by $\alpha$ decay because the degree of hindrance of $\alpha$ decay provides information on the change in nuclear structure of connected states.

Purpose: The aim of this work was to investigate the $\alpha$-decay properties of ${}^{200,202}\mathrm{Fr}$ and daughter products.

Method: Neutron-deficient francium nuclei are produced at ISOLDE-CERN bombarding a ${\mathrm{UC}}_x$ target with 1.4 GeV protons. Surface ionization and mass-separation techniques were employed to provide a pure radioactive ion beam at a radiation-detection setup.

Results: Due to the very high statistics and the high beam purity, improved decay data for ${}^{202}\mathrm{Fr}$ and its daughters were obtained. In particular, this data set allowed us to identify many fine-structure $\alpha$ lines with a relative reduced $\alpha$-decay width up to five orders of magnitude lower as the strongest ground-to-ground state or isomeric-to-isomeric state $\alpha$-decay transition. In addition, several half-life values were extracted with similar or better precision as compared with the literature.

Conclusions: The observation of crossover transitions positioned the isomeric high-spin level of ${}^{198}\mathrm{At}$ at an excitation energy of 265(3) keV. Half-life values of 4.47(5) s and 1.28(10) s were extracted for the ground state and isomeric state of ${}^{198}\mathrm{At}$ and 52(3) ms for the ground-state decay of ${}^{200}\mathrm{Fr}$. Furthermore, $\alpha$-decay schemes for ${}^{202}\mathrm{Fr}$ and its daughter ${}^{198}\mathrm{At}$ could be constructed.

The rapidity-odd component of directed flow ($v_1$) of identified hadrons (${\pi }^{\pm }$, $K^{\pm }$, $K_S^0$, $p$, $\overline{p}$, $\varphi$, $\mathrm{\Xi }$, $\overline{\mathrm{\Xi }}$, $\mathrm{\Lambda }$, $\overline{\mathrm{\Lambda }}$) and partons ($u$, $\overline{u}$, $d$, $\overline{d}$, $s$, $\overline{s}$) in $\mathrm{Au}+\mathrm{Au}$ collisions at various beam energies ($\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, 200 GeV) is analyzed using a multiphase transport model. A data driven approach (inspired from the experimental analysis) is performed here to distinguish the transported and produced quarks which are found to have different directed flow values at various collision beam energies. The coalescence sum rule (number of constituent quark scaling) violation is observed at lower energies where hadronic matters dominate. The strange quark ($s$) and $\varphi$ meson slope ($d{v}_1/dy$) show a double sign change around 14.5 GeV unlike other partons and hadrons. It suggests that the strange quark is more sensitive to the softening of the equation of state.

Quadrupole moments and charge radii in cadmium isotopes are studied from a microscopic perspective. The results obtained from self-consistent deformed Hartree-Fock$+\mathrm{BCS}$ calculations with Skyrme forces are compared with isomer and isotope shifts measured from high-resolution laser spectroscopy experiments. The microscopic calculations reproduce fairly well the main features observed in those isotopes that include the linear increase with the neutron number of the quadrupole moments of the $11/2^{-}$ isomers, as well as the parabolic behavior of the mean-square charge radii difference between isomers and ground states.

We describe bound states, resonances, and elastic scattering of light ions using a $\delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems $d+\alpha$, ${}^3\mathrm{H}+\alpha$, ${}^3\mathrm{He}+\alpha$, $\alpha +\alpha$, and $p+{}^{16}\mathrm{O}$. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of ${}^{17}\mathrm{F}$.

The formalism developed for hadron quasifree scattering to infer relativistic single-nucleon responses is extended to data for hadronic charge exchange for a wide range of beams and nuclear samples. Scaling tests of the first, second, and third kinds are applied to the results.

Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some well-known shortcomings, one of which is insufficient dissipation of collective motion. The stochastic mean-field approach (SMF), where a set of MF trajectories with random initial conditions are considered, is a good candidate to include dissipative effects beyond mean field. In this approach, the one-body density matrix elements are treated initially as a set of stochastic Gaussian c numbers that are adjusted to reproduce first and second moments of collective one-body observables. It is shown that the predictive power of the SMF approach can be further improved by relaxing the Gaussian assumption for the initial probabilities. More precisely, using Gaussian or uniform distributions for the matrix elements generally leads to overdamping for long times, whereas distributions with smaller kurtosis lead to much better reproduction of the long time evolution.

I have used parameters previously determined from a simple mixing analysis of 0 ↔ 2 transition strengths in several nuclei to compute $E2$ transition matrix elements for the $2_2$ (or $2_3$, as determined by the experimenters) $\to 2_1$ transition. Agreement with experimental $E2$ transition matrix elements is reasonable.

The cross sections of complete fusion and incomplete fusion for the ${}^9\mathrm{Be}+{}^{197}\mathrm{Au}$ system, at energies not too much above the Coulomb barrier, were measured for the first time. The online activation followed by an offline $\gamma$-ray spectroscopy method was used for the derivation of the cross sections. A slightly higher value of the incomplete fusion to total fusion ratio has been observed, compared to other systems reported in the literature with a ${}^9\mathrm{Be}$ beam. The experimental data were compared with coupled channel calculations without taking into account the coupling of the breakup channel, and experimental data of other reaction systems with weakly bound projectiles. A complete fusion suppression of about 40% was found for the ${}^9\mathrm{Be}+{}^{197}\mathrm{Au}$ system, at energies above the barrier, whereas the total fusion cross sections are in agreement with the calculations.

Relativistic quantum molecular dynamics with scalar and vector interactions based on the relativistic mean meson field theory, RQMD.RMF, is developed. It is implemented into the microscopic transport code jam, which includes both hadron resonances from the PDG book and string degrees of freedom. The sensitivity of the directed and of the elliptic proton flow in high energy heavy-ion collisions on the stiffness of the RMF equation of state (EoS) is examined. These new calculations are compared to high statistics experimental data at mid-central Au $+$ Au collisions in the beam energy range $2.5<\sqrt{s_{NN}}<20$ GeV. This new RQMD model with the relativistic mean-field scalar and vector meson interactions does describe consistently, with one RMF parameter set, the beam energy dependence of both the directed flow and the elliptic flow, from SIS18 to AGS and RHIC BES-II energies, $\sqrt{s_{NN}}<10$ GeV. This is interesting, as there are different sensitivities of these different kinds of flow to the EoS: elliptic flow is most sensitive to the nuclear incompressibility constant, at the moderate beam energies $\sqrt{s_{NN}}<3$ GeV, whereas the directed flow is most sensitive to the effective baryon mass at saturation density at $3<\sqrt{s_{NN}}<5$ GeV. This self-consistent relativistic $N$-body hadronic transport approach describes well the experimental flow data up to higher beam energies, $\sqrt{s_{NN}}<10$ GeV, by a stiff, monotonous EoS. Matters abruptly change in the next higher energy range, $\sqrt{s_{NN}}\gtrsim 10$–20 GeV: the directed flow data show a double change of sign of the slope of $v_1$, inverting twice in this energy range, in sudden contradiction to the RQMD.RMF calculation for a monotonous, stiff EoS. This surprising oscillating behavior, a double change of sign of the $v_1$ slope, points to the appearance of a hitherto unknown first-order phase transition in excited QCD matter at high baryon densities in mid-central Au $+$ Au collisions.

Using a model for the equation of state and composition of dense matter and the magnitude of singlet proton superconductivity and triplet neutron superfluidity, we perform the first simultaneous fit of neutron star masses and radii determined from observations of quiescent low-mass x-ray binaries and luminosities and ages determined from observations of isolated neutron stars. We find that the Vela pulsar strongly determines the values inferred for the superfluid/superconducting gaps and the neutron star radius. We find, regardless of whether or not the Vela pulsar is included in the analysis, that the threshold density for the direct Urca process lies between the central density of 1.7 and 2 solar mass neutron stars. We also find that two solar mass stars are unlikely to cool principally by the direct Urca process because of the suppression by neutron triplet superfluidity.

We study the regularization and renormalization of a finite-range inverse-cube potential in the two- and three-body sectors. Specifically, we compare and contrast three different regulation schemes frequently used to study few-body systems as well as the associated renormalization group (RG) flows. We also calculate bound-state and scattering observables over a wide range of cutoffs, demonstrating the sufficiency of a two-body contact interaction to renormalize two- and three-body observables. We supplement these plots with quantified analyses of the observables' residual cutoff dependences.

A method of the quasiparticle random-phase approximation (QRPA) calculation using the Skyrme energy density functional (EDF) in three-dimensional wave-number space is presented. This method allows one to perform the QRPA calculation for weakly bound nuclei in much smaller mesh space than that in three-dimensional Cartesian mesh. With this code, I discuss $K^{\pi }=0^{+}$ isoscalar quadruple excitations in neutron-rich Mg isotopes. The large low-lying transition strengths are induced by the strong pairing fluctuation due to the coherent contribution of nonresonant continuum states around the neutron drip line. This could be an experimental probe of novel pairing correlations such as dineutron correlation.

The empirical proton-neutron interaction $\delta V_{pn}$ for even-even Ra isotopes is analyzed by using the covariant density functional theory and the quadrupole-octupole collective Hamiltonian approach. It is shown that the static deformation and collective fluctuation are crucial ingredients for good reproduction of the data. Particularly, the introduction of octupole deformation ${\beta }_3$ dramatically changes the $\delta V_{pn}$ with $N=134,136,140$. The collective fluctuation smoothly corrects the $\delta V_{pn}$ with good trend. Taking ${}^{224}\mathrm{Ra}$ as an example, the detailed contributions from the static deformation and the collective fluctuation are analyzed, and the microscopic single-particle levels, the octupole driving pairs, and the enhancement of proton-neutron interaction are discussed.

We explore the thermodynamic properties of homogeneous cold (zero-temperature) nuclear matter including nucleons and $\alpha$-particle condensation at low densities by using a generalized nonlinear relativistic mean-field (gNL-RMF) model. In the gNL-RMF model, the $\alpha$ particle is included as an explicit degree of freedom and treated as a pointlike particle with its interaction described by meson exchanges, and the in-medium effects on the $\alpha$ binding energy are described by density- and temperature-dependent energy shift with the parameters obtained by fitting the experimental Mott density. We find that below the dropping density $n_{\mathrm{drop}}$ ($\approx 3\times {10}^{-3}{\mathrm{fm}}^{-3}$), the zero-temperature symmetric nuclear matter is in the state of pure Bose-Einstein condensate (BEC) of $\alpha$ particles while the neutron-rich nuclear matter is composed of $\alpha$-BEC and neutrons. Above the $n_{\mathrm{drop}}$, the fraction of $\alpha$-BEC decreases with density and vanishes at the transition density $n_t$ ($\approx 8\times {10}^{-3}{\mathrm{fm}}^{-3}$). Above the $n_t$, the nuclear matter becomes pure nucleonic matter. Our results indicate that the empirical parabolic law for the isospin asymmetry dependence of the nuclear matter equation of state is heavily violated by the $\alpha$-particle condensation in the zero-temperature dilute nuclear matter, making the conventional definition of the symmetry energy meaningless. We investigate the symmetry energy defined under parabolic approximation for the zero-temperature dilute nuclear matter with $\alpha$-particle condensation and find it is significantly enhanced compared to the case without clusters and becomes saturated at about $7\mathrm{MeV}$ at very low densities ($\lesssim {10}^{-3}{\mathrm{fm}}^{-3}$). The critical temperature for $\alpha$ condensation in homogeneous dilute nuclear matter is also discussed.

We discuss limiting fragmentation within a few currently popular phenomenological models. We show that popular Glauber-inspired models of particle production in heavy ion collisions, such as the two-component model, generally fail to reproduce limiting fragmentation when all energies and system sizes experimentally available are considered. This is due to the energy dependence of number of participants and number of collisions. We quantify this violation in terms of the model parameters. We also make the same calculation within a color glass condensate scenario and show that the dependence of the saturation scale on the number of participants generally leads to violation of limiting fragmentation. We further argue that wounded parton models, provided the nucleon size and parton density vary predominantly with Bjorken $x$, could in principle reproduce both multiplicity dependence with energy and limiting fragmentation. We suggest, therefore, that an experimental measurement of deviation from limiting fragmentation in heavy ion collisions, for different system sizes and including the experimentally available range of energies, is a powerful test of initial-state models.

We study the short-distance part of the intrinsic three-nucleon interaction in a constituent quark model with color-spin interaction. For that purpose, we first calculate the transformation coefficient between the tribaryon configuration and their corresponding three-baryon basis. Using a formula for the intrinsic three-body interaction in terms of a tribaryon configuration, we find that after subtracting the corresponding two-baryon contributions, the intrinsic three-body interaction vanishes in flavor SU(3) symmetric limit for all quantum numbers for the three nucleon states. We further find that the intrinsic three-body interaction also vanishes for flavor-spin type of quark interaction.