Mapping DFT to effective Hamiltonians

Abstract: This thesis proposes a new effective Hamiltonian to represent the interactions taking place in the atomic nucleus. This estimated Hamiltonian is analogous to the Pairing-Plus-Quadrupole model and this work is focused exclusively on the quadrupole part, with the aim of describing nuclear structure in a computationally efficient way. We have compared the accuracy of our proposed expression with the one proposed by K. Kumar and B. Sørensen [Nucl. Phys. A146 (1970) 1] studying the root-mean-squared error between those estimates and the exact formula. We also compare the spectra yielded by the different expressions. After this study, we conclude that the derived approximations appear to be more precise than the one proposed by Kumar and Sørensen.