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A microscopic treatment of correlated nucleons : collective properties in stable and exotic nuclei

Abstract : This Ph.D. work falls within the scope of theoretical techniques tailored to the solution of the nuclear many-body problem. It was motivated by the perspective of using beyond-mean-field methods to improve the description of excitation spectra of stable and exotic nuclei, especially the low-energy states and the giant resonances. The chosen path in this direction is the development of models based on the second random-phase approximation (SRPA) used with a subtraction procedure. These developments aim to extend the range of applicability of the initial model and to include correlations in the ground state.A first part consists in applying the SRPA used with a subtraction method to the study of the dipole and quadrupole response in medium to heavy-mass nuclei, including the electric dipole polarizability. We verify that the subtracted SRPA corrects the problems observed with the standard SRPA model and improves the description of excitation spectra compared to the random-phase approximation (RPA). We also study beyond-mean-field effects that arise in the subtracted SRPA by exploiting the relation between the axial breathing modes in nuclei and the effective mass in nuclear matter.A second part is dedicated to extensions.As a first step, we extend the initial numerical tools by employing the equal-filling approximation (EFA), to enable the applications to nuclei with partially-occupied orbitals. We next propose a method to estimate part of the pairing effects using correlated occupation numbers.A study of possible ways to renormalize the subtracted SRPA is carried out by employing a model which goes beyond the quasiboson approximation. This extension also relies on the use of occupation numbers as a means to include ground state correlations. We show that correlations obtained from the computation of occupation numbers in iterative RPA calculations are not sufficient to address the standard SRPA drawbacks.
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Olivier Vasseur. A microscopic treatment of correlated nucleons : collective properties in stable and exotic nuclei. Nuclear Theory [nucl-th]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLS223⟩. ⟨tel-02361379⟩

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