Relativistic Theory and Ab Initio Simulations of Electroweak Decay Spectra in Medium-Heavy Nuclei and of Atomic and Molecular Electronic Structure

In this work a novel theoretical and computational method for computing electroweak beta decay spectra of medium and heavy-mass nuclei, as well as the electronic structure of atomic and molecular systems is developed. In particular, starting from the phenomenological electroweak interaction of the Standard Model (SM) of particles, a general expression of the beta decay rate was derived. Relativistic effects are taken into account by solving the many-electron Dirac equation from first-principles. Furthermore, an extension of this approach to include the nucleon-nucleon interaction at the same level of theory of the electronic correlations has been devised. It is shown that post-collisional effects, and to a lesser extent the electronic exchange and correlation, can modify significantly the cross-section only at low energies (<10 keV), while nuclear correlations considerably affect the lineshape of both the absorption and emission spectra particularly in odd-odd nuclear transitions, where the independent particle approximation, on which the nuclear shell model is framed, is more likely to fail. These findings demonstrate the importance of moving beyond the independent particle picture to obtain an accurate description of the experimental data by adding the many-body correlations between the spectator and participator hadrons and leptons involved in the decay. The application of our approach to a number of test cases, such as the modeling of beta decay of 36 Cl, 63 Ni, 129 I, 210 Bi, 241 Pu and of the electron capture of 138 La 3+ , leads to an extremely good agreement with the relevant experimental data. Finally, the extension of this method to atomic and molecular systems by calculating the electronic structures of 138 La 3+ and several isomers (MgCN, MgNC) and molecules (HMgCN, MgCNO, and BrCF 3 ) relevant to astrophysical scenarios is presented. This method, which is capable to deal with both nucleonic and electronic degrees of freedom, has far-reaching implications also in neutrino physics and nuclear astrophysics.