This project deals with the theoretical description and explanation of the phenomenology of geometries manifested in the shapes of exotic nuclei. The phenomenology concerns low-energy states of a nucleus under study and transitions between them. The project consists of two parts. Part I will provide theoretical descriptions of experimental data, chiefly taken in GANIL with Radioactive-Ion Beams, related with shape coexistence (objective GN1), pear-shaped nuclei (GN2) and shape/phase transitions (GN3). The theoretical models to be used are the Geometric Collective Model (GCM) and the Shell Model (SM). Part II will introduce conformal symmetry in nuclear structure as a means to explain the occurrence of nuclear shapes.
It will be introduced in the SM (GN4) to investigate the emergence of the GCM from complex many-body calculations. This will be achieved by extending the SU(3) model of quadrupole deformation and a related description of octupole deformation through algebraic methods used in classical Yang-Mills theories. Conformal symmetry will also be introduced in the GCM (GN5) as a means to import higher symmetries in the GCM and investigate their relation with single-particle effects. This will be achieved based on a geometric method using formal correspondences with cosmological models, recently explored by the candidate. These correspondences will be extended to methods used in the gravitational multipole moments with the aim to propose the conformal symmetry of space as a fundamental symmetry of the nuclear multipole moments. In parallel, patterns of conformal symmetry in nuclear structure will be investigated numerically within the Interacting Boson Model. The theoretical results of Part II will be examined in shape coexistence, pear shaped nuclei and shape/phase transitions.
During this entire project precious transfer of knowledge will occur between the candidate, the supervisor and the experimental groups in GANIL.
Funding SchemeMSCA-IF-EF-ST - Standard EF
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