The work started with the comparison with the experimental data of the shape coexistence scenarios that had been developed during the first postdoc of the Fellow at the Racah Institute of Physics, Hebrew University, Israel and constitute the first study of shape coexistence in the Geometric Collective Model using a computationally tractable version of the latter the so called Algebraic Collective Model. After elaborating on the initial scenarios, the elements in the Ar-Si-S series and especially 44-46Ar were identified as candidate nuclei of spherical-gamma-unstable coexistence. However, more experimental data are needed for a detailed comparison especially in the population of higher excited states. The initial scenarios were also extended to the investigation of coexistence between spherical and axially symmetric shapes through two internship theses from graduate students that were supervised by the Fellow. We report the first case where the ACM does not manifest convergence in an axially symmetric shape that coexists with a spherical shape.
In pear-shaped nuclei the work started by the theoretical investigation of the empirical rules for the correlations between the energies of the 2+ and the 3- states in neutron deficient xenons around 100Sn. Our results do not reproduce an unusual, enhanced B(E3) transition in 114-112Xe and follow the empirical rules which however do not conform to a symmetry pattern for those isotopes. The training through research was realized in microscopic calculations in the Shell Model using realistic interactions for the reproduction of monopole, quadrupole and the octupole degrees of freedom through boson mappings. The results finally led to the formulation of a semi-empirical binding energy formula for proton emitters around 100Sn with specific predictions of proton separation energies and their half-lives.
The transition to the second part is guided by the conformal invariance implied by the symmetry of quantum critical points in Shape/Phase transitions. To that aspect, the interdisciplinary aspects of the project were focused on the physics of trapped cold atoms that manifest the unitary limit – which supports a quantum critical point - in the vicinity of Feshbach resonances. The application of these methods in the Interacting Boson Model of nuclear structure led to the major achievement of the project. This is the regularity pattern of fluctuations of cross sections in A+2n (two neutrons) compound nuclei that represents conformal symmetry in nuclear structure. The energies and the widths of such fluctuations are calculated, and a new type of a two-neutron transfer reaction is proposed for the examination of the unitary limit in A+2n compound and exotic nuclei. These fluctuations tune the scattering length that reaches the unitary limit when the incident two neutrons are captured as an intermediate boson in the A+2n compound nucleus. As a result, a novel theoretical understanding emerges for the A+2n compound nucleus as a cold and dilute gas of nucleons (in formal analogy with a cold and dilute atomic gas) where paired nucleons form IBM bosons (in formal analogy with the formation of diatomic molecules in Feshbach resonances between cold atoms) at low temperatures.
The first theoretical implication of the unitary limit is the manifestation of the BCS-BEC crossover in nuclear physics. The second is the underlying quantum critical point that appears through the maximization of the fluctuations of cross sections. Finally, we discuss the relation of symmetries of collective nuclear states with the large N limit of the SU(N) gauge group through the introduction of elements of algebras with an infinite number of generators that classify the reaction channels of A+2n compound nuclei.
