Bogoliubov Many-Body Perturbation Theory (MBPT) for nuclei: Systematic generation and evaluation of diagrams and first ab initio calculations
The last few decades in nuclear structure theory have seen a rapid expansion of ab initio theories, aiming at describing the properties of nuclei starting from the inter-nucleonic interaction. Such an expansion relied both on the tremendous growth of computing power and novel formal developments.
This work focuses on the development of the recently proposed Bogoliubov Many-Body Perturbation Theory that relies on a particle-number-breaking reference state to tackle singly open-shell nuclei. The formalism is first described in details, and diagrammatic and algebraic contributions are derived up to second order. Its link to standard MBPT is made explicit, as well as its connexion to Bogoliubov Coupled-Cluster theory.
An automated extension to higher orders based on graph theory methods is then detailed, and the ADG numerical program generating and evaluating BMBPT diagrams at arbitrary order is introduced. Such a formal development carries implications that are not restricted to the present work, as the developed methods can be applied to other many-body methods.
Finally, first numerical results obtained for oxygen, calcium and nickel isotopes are presented. They establish BMBPT as a method of interest for large-scale computations of isotopic or isotonic chains in the mid-mass sector of the nuclear chart.