Implementation of $ab$ $initio$ perturbed angular correlation observables for analysis of fluctuating quadrupole interactions

A review about the nuclear properties, namely the nuclear moments (magnetic dipole moment and electric quadrupole moment) and their interaction with electromagnetic fields external to the nucleus (hyperfine interactions), as well as the angular distribution of radiation produced by $\gamma$-decay, is presented. A detailed description about the theory of Perturbed Angular Correlations was done, including the comparison between $\gamma-\gamma$- correlations and $e^{-}- \gamma$ correlations. For dynamic nuclear interactions, an introduction to the theory of stochastic states in PAC was performed. We focused on ab-initio implementation of observables for analyzing fluctuating quadrupole hyperfine interactions on time dependent perturbed angular correlations experiments. The development of computacional codes solving the full problem, adapted to fit data obtained on single crystals or polycrystals for two-state transient fields with any axial symmetry and orientation was the main purpose of this work. The final part was the application of a first test case: $^{181}$Hf$\;/^{181}$Ta : GaN(n) and $^{181}$Hf$\;/ ^{181}$Ta : GaN (Mg).