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Résumé |
The fundamentals of the \textit{ab-initio} Self-Consistent Gorkov Green's function (SCGGF) [1-2] approach for the investigation of low-lying energy spectrum of the semi-magic even-even nuclei are presented. In the last decade, the SCGGF method
has brought a significant renewal in the realm of ab-initio approaches to nuclear structure, marking a step
forward in the knowledge of bulk nuclear properties of even-even nuclei, such as the ones lying
along the Ar-Cr [3-4] isotopic chains. The access to the one-particle propagator
has allowed the study of ground and excited
states of neighbouring odd-A isotopes [5-6]. Nonetheless, the prediction of excited
energy levels and reduced electric and magnetic multipole transition probabilities calls for the introduction of
the polarization propagator, previously not embedded in the $\mathrm{U}(1)_Z \times \mathrm{U}(1)_N$ symmetry breaking formalism.
In quantum chemistry, present-day approaches for the description of the spectrum of medium-sized
organic molecules [7-8] are based on diagrammatic many-body Green's function theory applied to the
polarization propagator at third order in the \textit{algebraic diagrammatic construction} (ADC) approach [9-13].
Another return of this is study will be provided by the prediction of new shell closures in
neutron-rich even-even nuclei, identified through the local maxima in the energy of the $2_1^+$
state and in the related electric quadrupole transition probability, $B(E2,0_1^+\rightarrow 2_1^+)$ [14].
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