Error propagation in nuclear models

Abstract: In this thesis we perform error analysis of a nuclear model based on density-functional theory developed in Lund. The Lund model allows us to perform calculations of nuclear spectra more efficiently by constructing a simple effective Hamiltonian reproducing the quadrupole deformation and pairing interaction strength parameters of a spherical Hartree-Fock reference functional. This constraining of the Hamiltonian allows for more efficient computation. The spectra calculated using Beyond mean-field methods to solve the effective Hamiltonian involve approximations. This work allows us to quantify the uncertainties in the model using statistical methods. In particular, we perform a propagation of errors and covariance analysis to determine the parameters which contribute most to the uncertainties of the calculations of energy spectra E and separation energies T. The covariances calculated indicate that E and T are largely uncorrelated for low spin states, where as spin I=4 shows a larger degree of covariance. Through statistical analysis, we identify that the major contribution to the errors comes from the choice of the pairing parameter, but the magnitude of this contribution decreases for states with larger spin. We speculate that the different parameter sensitivities of states with spin I=2, 4, can be explained by different deformations in spinning states which lead to a breaking of time-reversal symmetry, which leads to a decreased dependence on the pairing parameter g.