### Conveners

#### Symmetries and quantum phase transitions in nuclei

- Jose Arias
- Amiram Leviatan

#### Symmetries and quantum phase transitions in nuclei

- Amiram Leviatan
- Jose Arias

In a partial dynamical symmetry (PDS), the stringent conditions imposed by an exact dynamical symmetry are relaxed, so that solvability and/or good quantum numbers are retained by only a subset of states. Detailed studies have shown that PDSs account quite well for a wealth of spectroscopic data in various nuclei. In all these phenomenological studies, an Hamiltonian with a prescribed PDS is...

For any fermionic system, seniority, ν, is defined as the number of particles not in pairs coupled to angular momentum J=0. It is a conserved quantum number for a system with n identical particles, each with angular momentum j, interacting through a pairing force [1]. Nuclei such as 9444Ru50 with valence particles situated in the upper half of the N/Z=28-50 major shell are influenced by the...

While we often use group symmetries in nuclear structure, they are seldom perfect and are often mixed. After demonstrating an efficient way to decompose a wave function into group irreps, I show how one can adapt the similarity renormalization group to 'unmix' symmetries.

A quantum simulation of the Agassi model from nuclear physics is proposed so as to be implemented within a trapped-ion quantum platform. Numerical simulations and analytical estimations illustrate the feasibility of this simple proposal with current technology, while our approach is fully scalable to a larger number of sites. The use of a quantum correlation function is studied as a signature...

Differences between excitation energies of analogue states in mirror nuclei depend on the variations of the nuclear radius as a function of the spin. These mirror energy differences (MED) can be reproduced by shell model calculations where the evolution of the radius can be accounted for through the occupation of low-l orbits, that present larger radius than the large-l ones in a main shall....

Nuclei with a closed-shell configuration for neutrons and protons exhibit low-energy excitations with angular momentum J=3 and negative parity. Such excitations are associated with nuclear shapes that break reflection symmetry and, in particular, with pear-like or octupole shapes. In this talk the symmetry structure of octupole excitations is discussed and the question of their phonon-like...

The sextic oscillator V(r) = Ar^2 + Br^4 +Cr^6 + D/r^2 offers a flexible shape that can be used in

the Bohr Hamiltonian to model transition between spherical and deformed shape phases in the

r=beta variable. The general form of the sextic oscillator is not solvable, however, the A, B and C

coefficients can be parametrized in terms of two independent parameters (a, b) such that the...

Symmetry methods have been of crucial importance to physics. Group theory and conservation laws have become a fundamental language, all the way from quantum mechanical phenomena to general relativity. However, these ideas have had less impact in the biological domain. In this talk I present a view of self organized biological systems as characterized by and evolving towards critical points,...