Unitary limit in heavy nuclei

The unitary limit refers to a scattering problem at infinite scattering length where a scattering state becomes bound. Such a limit is experimentally accessible in systems of cold atoms at the vicinity of Feshbach resonances. In nuclear physics, a physical manifestation of the unitary limit is of interest both from the experimental challenge to measure such a limit in nuclei and from the theoretical aspects that accompany that limit such as conformal symmetry, a quantum critical point and the BCS-BEC crossover. In this talk the application of a symmetry-based approach to the unitary limit in collective states of heavy, even-even nuclei is presented that is performed by means of the Interacting Boson Model of nuclear structure in conjunction with the Feshbach formalism of nuclear reactions. The results of this application start from the determination of what is to be measured in the experiment for the examination of the unitary limit in collective nuclear states. That is the fluctuations of the cross-section of the A+2n compound nucleus. The primary theoretical result concerns the representations of conformal symmetry in A+2n compound nuclei via the fluctuations of cross sections.