Nuclear reactions in the Gamow shell model and solutions of the pairing Hamiltonian based on the rational Gaudin model

Abstract : Moving towards drip lines, or higher in excitation energy, the continuum coupling becomes gradually more important, changing the nature of weakly bound states. In this regime, atomic nuclei are open quantum systems which can be conveniently described using the Gamow shell model (GSM) which offers a fully symmetric treatment of bound, resonance and scattering states. The understanding of specific nuclear properties is often improved by considering exactly solvable models, motivated by a symmetry of the many-body system. In the first part , we have generalized the rational Gaudin pairing model to include the continuous part of the single-particle spectrum, and then derived a reliable algebraic solution which generalizes the exact Richardson solution for bound states. These generalized Richardson solutions have been applied for the description of binding energies and spectra in the long chain of carbon isotopes. In the second part, we have formulated the reaction theory rooted in GSM. For that the GSM is expressed in the basis of reaction channels and generalized for multi-nucleon projectiles. This reaction theory respects the antisymmetrization of target and projectile wave functions, as well as the wave function of the combined system. The application of this theory have been presented for the reaction 14O(p,p’)14O, where the combined system 15F is a proton emitter, and for 40Ca(d,d)40Ca.
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Alexis Mercenne. Nuclear reactions in the Gamow shell model and solutions of the pairing Hamiltonian based on the rational Gaudin model. Nuclear Theory [nucl-th]. Université de Caen Normandie, 2016. English. ⟨tel-01469139⟩

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