In a nuclear reactor, delayed neutrons play a critical role in sustaining a controllable chain reaction. Delayed neutron’s relative yields and decay constants are very important for modeling reactivity control and have been studied for decades. Researchers have tried different experimental and numerical methods to assess these delayed neutron parameters. The reported parameter values vary widely, much more than the small statistical errors reported with these parameters. Interestingly, the reported parameters fit their individual measurement data well in spite of these differences. This dissertation focuses on evaluation of the errors and methods of delayed neutron relative yields and decay constants for thermal fission of U-235. Various numerical methods used to extract the delayed neutron parameter from the measured data, including Matrix Inverse, Levenberg-Marquardt, and Quasi-Newton methods, were studied extensively using simulated delayed neutron data. This simulated data was Poisson distributed around Keepin’s theoretical data. The extraction methods produced totally different results for the same data set, and some of the above numerical methods could not even find solutions for some data sets. Further investigation found that ill-conditioned matrices in the objective function were the reason for the inconsistent results. To find a reasonable solution with small variation, a regularization parameter was introduced using a numerical method called Ridge Regression. The results from the Ridge Regression method, in terms of goodness of fit to the data, were good and often better than the other methods. Due to the introduction of a regularization number in the algorithm, the fitted result contains a small additional bias, but this method can guarantee convergence no matter how large the coefficient matrix condition number. Both saturation and pulse modes were simulated to focus on different groups. Some of the factors that affect the solution stability were investigated including initial count rate, sample flight time, initial guess values. Finally, because comparing reported delayed neutron parameters among different experiments is useless to determine if their data actually differs, methods are proposed that can be used to compare the delayed neutron data sets.

Muon decay is a unique process involving only the four leptons of the first two generations. This makes it an ideal framework to study the weak interaction. The momentum-angle spectrum of the decay positron can be studied using a general 4-fermion interaction model. Only four parameters are needed in this model to entirely describe the spectrum. The measurement of these four muon decay parameters, rho, eta, delta and Pmu xi, provide a direct test of the Standard Model and its extensions. This thesis presents the final results from the blind analysis of the decay parameter delta using the TWIST (TRIUMF Weak Interaction Symmetry Test) spectrometer. The new precision on the parameter delta is a factor of 11.5 better than the last experimental result prior to TWIST achieving the goal of the TWIST collaboration of an order of magnitude improvement. The challenging parameter eta is also measured from the momentum-angle spectrum for the first time since 1969 with a precision improved by a factor of 7.4. The results are included in a global analysis to obtain stringent limits on some of the coupling constants of the 4-fermion interaction. The result of the measurement of delta are used to evaluate the possibility for a non-local tensor interaction.