Relativistic mean field calculation has been performed for odd mass nuclei with $A\sim 60–70$. The mean field is assumed to be axially symmetric and time-reversal symmetric. Blocked BCS method is used to restore time-reversal symmetry. The total binding energy and the last nucleon binding energy are reproduced with reasonable accuracy. The static quadrupole moments of different nuclei in their ground states are calculated and compared with experiment. In many nuclei, a number of solutions with different shapes but comparable energy values are obtained by blocking different single particle levels. In a few nuclei, the ground state spin is not reproduced.

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum $J$. We show that pairs with spin $J$ are reasonable building blocks for the low-lying states. For systems with only a $J=J_{max}$ pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular, for those with total angular momenta $I⩽2j$. For $I=0$ eigenstates of four fermions in a single-$j$ shell we show that there is only one nonzero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.

We investigate the coexistence of spherical, deformed, and superdeformed states at low spin in ${}^{32}\mathrm{S}$, ${}^{36}\mathrm{Ar}$, ${}^{38}\mathrm{Ar}$, and ${}^{40}\mathrm{Ca}$. The microscopic states are constructed by configuration mixing of BCS states projected on good particle number and angular momentum. The BCS states are themselves obtained from Hartree-Fock BCS calculations using the Skyrme interaction SLy6 for the particle-hole channel and a density-dependent contact force in the pairing channel. The same interaction is used within the generator coordinate method to determine the configuration mixing and calculate the properties of even-spin states with positive parity. Our calculations underestimate moments of inertia. Nevertheless, for the four nuclei, the global structural properties of the states of normal deformation as well as the recently discovered superdeformed bands up to spin 6 are correctly reproduced with regard to both the energies and the transition rates.

The excitation energies of single analog states in even-odd Ti isotopes and double analog states in even-even Ti isotopes are microscopically described in a single $j$-shell formalism. A projection procedure for generalized BCS states has been used. As an alternative description a particle-core formalism is proposed. The latter picture provides a two-parameter expression for excitation energies, which describes fairly well the data in four odd and three even isotopes of Ti.

The cross sections of the single proton knock-out reactions from ${}^{24}\mathrm{F}$, ${}^{25}\mathrm{F}$, and ${}^{26}\mathrm{F}$ on a ${}^{12}\mathrm{C}$ target were measured at energies of about $50\text{MeV}∕\text{nucleon}$. Ground state populations of $6.6\pm 0.9\text{mb}$, $3.8\pm 0.6\text{mb}$ for the reactions ${}^{12}\mathrm{C}\left({}^{24}\mathrm{F},{}^{23}\mathrm{O}\right)$ and ${}^{12}\mathrm{C}\left({}^{25}\mathrm{F},{}^{24}\mathrm{O}\right)$ were extracted, respectively. The data were compared to calculations based on the many-body shell model and the eikonal theory. In the reaction ${}^{12}\mathrm{C}\left({}^{26}\mathrm{F},{}^{25}\mathrm{O}\right)$ the particle instability of ${}^{25}\mathrm{O}$ was confirmed.

The effects of retardation in the Coulomb excitation of radioactive nuclei in intermediate energy collisions $\left(E_{\mathrm{lab}}\sim 100\text{MeV}∕\text{nucleon}\right)$ are investigated. We show that the excitation cross sections of low-lying states in ${}^{11}\mathrm{Be}$, ${}^{38,40,42}\mathrm{S}$, and ${}^{44,46}\mathrm{Ar}$ projectiles incident on gold and lead targets are modified by as much as $20\%$ due to these effects. The angular distributions of decaying $\gamma$ rays are also appreciably modified.

The influence of the in-medium mesons on the effective nucleon mass and in turn on the equation of state of hot∕dense nuclear matter is discussed in the Walecka model. Due to the self-consistent treatment of couplings between nucleons and $\sigma$ and $\omega$ mesons, the temperature and density dependence of the effective hadron masses approaches more towards the Brown-Rho scaling law, and the compression modulus $K$ is reduced from $550\text{MeV}$ in mean field theory to an accepted value $318.2\text{MeV}$.

The ${}^{10}\mathrm{B}\left(\vec{p},\gamma \right){}^{11}\mathrm{C}$ reaction was studied by detecting the $\gamma$-rays produced when 100-, 130-, and $160\text{−}\text{keV}$ polarized protons were stopped in a thick ${}^{10}\mathrm{B}$ target. Polarized and unpolarized incident beams were used to measure the cross section and vector analyzing power as a function of angle and energy for capture to the ground $\left(J^{\pi }=3∕2^{-}\right)$, the second $\left(E=4319\mathrm{keV},J^{\pi }=5∕2^{-}\right)$, and the fifth $\left(E=6478\text{keV},J^{\pi }=7∕2^{-}\right)$ excited states of ${}^{11}\mathrm{C}$. The data were analyzed to obtain the amplitudes and phases of the contributing transition-matrix elements at each measured energy for all three transitions. Values of the astrophysical $S$ factors were obtained from the cross section data and are compared to previous results. A direct capture plus resonance model calculation was performed in an attempt to account for all measured quantities. It was found that the large $\left(\sim 32\%\right)$ value of $A_y\left(90°\right)$ observed in the case of capture to the ground state could be accounted for by including the sub-threshold resonance at $8420\text{keV}$.

Calculations based on the relativistic mean field framework have been carried out for the ground state properties of the relevant nuclei appearing in the $\alpha$-emission chain of superheavy element $Z=112$. The calculations compare well with the experiment. The calculated densities along with the energy and the density dependent M3Y effective nucleon-nucleon interaction are used in the double folding model to compute the respective total interaction energies. These, in turn are used to calculate the half-lives of the parent nuclei against the split into an $\alpha$ and the daughter in the WKB approximation. The calculations are repeated for the nuclei appearing in the $4n+2$ $\alpha$ chain for a comparative study. The sensitivity of the calculated half-lives on the input information, especially the $Q$ values are quantitatively investigated.

We address the issue of the degree of equilibrium achieved in a high energy heavy-ion collision. Specifically, we explore the consequences of incomplete strangeness chemical equilibrium. This is achieved over a volume $V$ of the order of the strangeness correlation length and is assumed to be smaller than the freeze-out volume $V_f$. Probability distributions of strange hadrons emanating from the system are computed for varying sizes of $V$ and simple experimental observables based on these are proposed. Measurements of such observables may be used to estimate $V$ and as a result, the degree of strangeness chemical equilibration achieved. This sets a lower bound on the degree of kinetic equilibrium. We also point out that a determination of two-body correlations or second moments of the distributions are not sufficient for this estimation.

Thermal production of $J∕\psi$ within quark gluon plasma is reconsidered. We show that if screening effects are not strong enough, the “in-plasma born” $J∕\psi$’s would show up as a peak in the Feynman momentum distribution at $x_F=0$.

The relation of the recently proposed $E\left(5\right)$ critical point symmetry with the interacting boson model is investigated. The large-$N$ limit of the interacting boson model at the critical point in the transition from U(5) to O(6) is obtained by solving the Richardson equations. It is shown explicitly that this algebraic calculation leads to the same results as the solution of the Bohr differential equation with a ${\beta }^4$ potential.

We propose the cold (neutronless) fission process as a tool for probing mean field properties of exotic neutron rich nuclei. The fissioning state is described as a resonance in the potential well between the emitted fragments. Coupled channels analysis shows that the double fine structure of the binary cold fission is very sensitive to the density distribution. In this way cold fission can be used to investigate the density profile of neutron rich fragments.

Ground-state deformations, binding energies, and potential energy surfaces have been calculated for even-even dysprosium isotopes between ${}^{160}\mathrm{Dy}$ and ${}^{180}\mathrm{Dy}$ in the framework of density-dependent Hartree-Fock calculations with BCS pairing correlations. Further deformed Hartree-Fock with angular-momentum projection and band-mixing calculations explore the yrast spectra of the nuclides approaching the neutron midshell. Predictions of high-$K$ states in the doubly midshell nucleus ${}_{66}{}^{170}{\mathrm{Dy}}_{104}$ are made.

We discuss hadron production in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC). We argue that hadrons at transverse momenta $P_T<5\text{GeV}$ are formed by recombination of partons from the dense parton phase created in central collisions at RHIC. We provide a theoretical description of the recombination process for $P_T>2\text{GeV}$. Below $P_T=2\text{GeV}$ our results smoothly match a purely statistical description. At high transverse momentum hadron production is well described in the language of perturbative QCD by the fragmentation of partons. We give numerical results for a variety of hadron spectra, ratios, and nuclear suppression factors. We also discuss the anisotropic flow $v_2$ and give results based on a flow in the parton phase. Our results are consistent with the existence of a parton phase at RHIC hadronizing at a temperature of $175\text{MeV}$ and a radial flow velocity of $0.55c$.

We calculate the quark distribution function for ${}^3\mathrm{He}∕{}^3\mathrm{H}$ in a relativistic quark model of nuclear structure which adequately reproduces the nucleon approximation, nuclear binding energies, and nuclear sizes for small nuclei. The results show a clear distortion from the quark distribution function for individual nucleons (EMC effect) arising dominantly from a combination of recoil and quark tunneling effects. Antisymmetrization (Pauli) effects are found to be small due to limited spatial overlaps. We compare our predictions with a published parametrization of the nuclear valence quark distributions and find significant agreement.

The thermal neutron cross section and resonance integral of the reaction ${}^{159}\mathrm{Tb}\left(n,\gamma \right){}^{160}\mathrm{Tb}$ in the thermal and $1∕E$ regions, respectively, of a thermal reactor neutron spectrum have been experimentally determined. Literature data on the resonance integral of the reaction show a large scatter ranging from 313 to $780\mathrm{b}$. On the basis of such data it becomes extremely difficult to produce a best value for application. In this work we performed a careful experiment in an effort to produce a precise and accurate measured value, which will be a valuable addition to the literature. The ${}^{159}\mathrm{Tb}\left(n,\gamma \right){}^{160}\mathrm{Tb}$ reaction is studied by irradiating spectrographically pure ${\text{Tb}}_4{\mathrm{O}}_7$ powder samples with thermal and epithermal neutrons in the Pakistan Research Reactor–1 (PARR-1) at PINSTECH. Thermal and epithermal neutron fluence rates were determined with Au and Co activation detectors. The $\alpha$ parameter, which accounts for the deviation of the neutron spectrum shape from the $1∕E$ law in the epithermal neutron region, was obtained with good accuracy by using Au, Co, Mn, and Zn activation detectors and adopting the regression and iterative analysis procedures. The induced activities in the target samples and the activation detectors were measured with a high purity germanium detector system. The cadmium ratio method was used to yield the thermal neutron cross section and resonance integral. The measured thermal neutron cross section at $0.0253\text{eV}$ and resonance integral are $23.6\pm 0.4\mathrm{b}$ and $443\pm 21\mathrm{b}$, respectively. The results are discussed and compared with the literature.

The $\pi N$ interaction is studied within a meson-exchange model and in a coupled-channels approach which includes the channels $\pi N$, $\eta N$, as well as three effective $\pi \pi N$ channels, namely, $\rho N$, $\pi \Delta$, and $\sigma N$. Starting out from an earlier model of the Jülich group systematic improvements in the dynamics and in some technical aspects are introduced. With the new model an excellent quantitative reproduction of the $\pi N$ phase shifts and inelasticity parameters in the energy region up to $1.9\text{GeV}$ and for total angular momenta $J⩽3∕2$ is achieved. Simultaneously, good agreement with data for the total and differential $\pi N\to \eta N$ transition cross sections is obtained. The connection of the $\pi N$ dynamics in the $S_{11}$ partial wave with the reaction $\pi N\to \eta N$ is discussed.

The near-yrast states of ${}^{99,100}\mathrm{Mo}$ have been studied following their population via a binary reaction between a ${}^{136}\mathrm{Xe}$ beam and a thin, self-supporting ${}^{100}\mathrm{Mo}$ target. The yrast sequence in ${}^{100}\mathrm{Mo}$ has been extended to a tentative spin∕parity $\left({20}^{+}\right)$, while the decoupled band built on the $I^{\pi }={\frac{11}{2}}^{-}$ isomeric state in ${}^{99}\mathrm{Mo}$ has been extended through the first alignment up to a tentative spin∕parity of $\left({\frac{43}{2}}^{-}\right)$. The results are compared with self-consistent, cranked-mean-field calculations using a Woods-Saxon potential. The alignment systematics of the intruder $h_{11∕2}$ bands in the $N=57$ isotones from Mo $\left(Z=42\right)$ to Cd $\left(Z=48\right)$ and the yrast sequences in their $N=58$ even-even neighbors are discussed. An overall picture emerges, where the alignment properties evolve from being due to positive-parity neutrons in the ${}_{48}{}^{105}\mathrm{Cd}$ to predominantly ${\left(g_{9∕2}\right)}^2$ proton crossings closer to the $Z=40$ subshell. Qualitatively, this can be explained by an increase in the quadrupole deformation and a simultaneous lowering of the proton Fermi surface in the $g_{9∕2}$ shell with decreasing proton number. These data provide excellent examples of rotational-alignment phenomena in weakly deformed nuclei.

Cold fusion barriers are studied with respect to the change of the charge density within the overlapping region. Charge evolution from separated target and projectile up to the compound nucleus is taken into account by means of a deduced transition formula which depends on geometric parameter variation defining the shape. Macroscopic, shell correction and total deformation energy for fusionlike configurations are calculated for different charge density paths. Minimization along this coordinate produces variations of about $4\text{MeV}$ for light nuclei and up to $8\text{MeV}$ for superheavy synthesis, for the deformation energy in the last part of the process.