The rapid neutron capture process (r-process) is thought to be responsible for the creation of more than half of all elements beyond iron. The scientific challenges to understanding the origin of the heavy elements beyond iron lie in both the uncerta
inties associated with astrophysical conditions that are needed to allow an r-process to occur and a vast lack of knowledge about the properties of nuclei far from stability. There is great global competition to access and measure the most exotic nuclei that existing facilities can reach, while simultaneously building new, more powerful accelerators to make even more exotic nuclei. This work is an attempt to determine the most crucial nuclear masses to measure using an r-process simulation code and several mass models (FRDM, Duflo-Zuker, and HFB-21). The most important nuclear masses to measure are determined by the changes in the resulting r-process abundances. Nuclei around the closed shells near N=50, 82, and 126 have the largest impact on r-process abundances irrespective of the mass models used.
The linear term proportional to $|N-Z|$ in the nuclear symmetry energy (Wigner energy)is obtained in a model that uses isovector pairing on single particle levels from a deformed potential combined with a $vec T^2$ interaction. The pairing correlatio
ns are calculated by numerical diagonalization of the pairing Hamiltonian acting on the six or seven levels nearest the $N=Z$ Fermi surface. The experimental binding energies of nuclei with $Napprox Z$ are well reproduced. The Wigner energy emerges as a consequence of restoring isospin symmetry. We have found the Wigner energy to be insensitive to the presence of moderate isoscalar pair correlations.
A coherent state technique is used to generate an Interacting Boson Model (IBM) Hamiltonian energy surface that simulates a mean field energy surface. The method presented here has some significant advantages over previous work. Specifically, that th
is can be a completely predictive requiring no a priori knowledge of the IBM parameters. The technique allows for the prediction of the low lying energy spectra and electromagnetic transition rates which are of astrophysical interest. Results and comparison with experiment are included for krypton, molybdenum, palladium, cadmium, gadolinium, dysprosium and erbium nuclei.
The influence of the quadrupole shape fluctuations on the dipole vibrations in transitional nuclei is investigated in the framework of the Instantaneous Shape Sampling Model, which combines the Interacting Boson Model for the slow collective quadrupo
le motion with the Random Phase Approximation for the rapid dipole vibrations. Coupling to the complex background configurations is taken into account by folding the results with a Lorentzian with an energy dependent width. The low-energy energy portion of the $gamma$- absorption cross section, which is important for photo-nuclear processes, is studied for the isotopic series of Kr, Xe, Ba, and Sm. The experimental cross sections are well reproduced. The low-energy cross section is determined by the Landau fragmentation of the dipole strength and its redistribution caused by the shape fluctuations. Collisional damping only wipes out fluctuations of the absorption cross section, generating the smooth energy dependence observed in experiment. In the case of semi-magic nuclei, shallow pygmy resonances are found in agreement with experiment.
