| We study both fluctuation properties and average properties of nuclei in the framework of the interacting shell model. The thesis is divided accordingly into two parts. In the first part of the thesis, fluctuation properties of nuclear levels and electromagnetic transition intensities are studied and quantified using a random matrix model. These fluctuation properties provide useful information about isospin symmetry breaking in N ∼ Z nuclei. The strength of isospin breaking is characterized by a dimensionless parameter in the random matrix model. We determine this parameter in the nucleus 30P for three isospin-nonconserving interactions by comparing the random matrix model and shell model results. We find consistent values across different statistical measures. In the second part of the thesis, shell model Monte Carlo methods are applied to calculate average properties of nuclei at finite temperature. In particular, we extend the Monte Carlo techniques to calculate expectation values of three-body and four-body observables by introducing source terms in the imaginary-time propagation. We use these methods to calculate invariants of quadrupole moments and determine the effective quadrupole deformation in a series of even iron isotopes. As the neutron number increases across the shell, the effective shape of the nucleus changes from prolate-like to oblate-like. The oblate isotopes are found to be less rigid. The Monte Carlo methods are extended to also include the calculation of moments of strength functions. |
