Quantum Phase Transitions in Nuclei Basic ideas, critical point symmetries, empirical evidence, key signatures, improvements in the descriptions

Broad perspective on structural evolution

Valence proton-neutron interactions -- key to collectivity Proton Magic Valence proton-neutron interactions -- key to collectivity Valence protons

B(E2; 2+  0+ )

From Cakirli 5

Classifying Equilibrium Collective Structure – The Symmetry Triangle Benchmarks – Paradigms Dynamical Symmetries (the IBA) Deformed E(5) Sph. Phase/shape Transitions (Critical Point Symmetries) X(5)

Quantum phase transitions in equilibrium shapes of nuclei with N, Z Potential as function of the ellipsoidal deformation of the nucleus Transitional Rotor E β 1 2 3 4 Increasing valence nucleon number Vibrator For nuclear shape phase transitions the control parameter is nucleon number

Microscopic basis of shape/phase transitions

Different perspectives can yield different insights Onset of deformation Onset of deformation as a phase transition mediated by a change in shell structure Sub-shell changes, induced largely by the monopole p-n interaction, often induce shape transitions by effectively increasing the number of valence nucleons. This can have large effects on binding as one configuration drops below another.

Microscopic origins of phase transitional behavior Potentials involved In Phase transitions Microscopic origins of phase transitional behavior Valence pn interactions Direct experimental evidence

A simple guide to the evolution of structure Which nuclei? A simple guide to the evolution of structure The next slide allows you to estimate the structure of any nucleus by multiplying and dividing two numbers each less than 30 (or, if you prefer, you can get the same result from 10 hours of supercomputer time)

What is the locus of spherical-deformed shape/phase transitional regions? p-n / pairing =  NpNn p – n P Np + Nn pairing P~5

Comparing with the data

Comparison with the data

Signatures of phase transitional behavior (beyond R4/2 which we have already seen)

IBA gives a straight line in 2-neutron separation energies in phase transitional regions Neutron number Z Z-2 S2(N) (MeV) 82 126 30 15 104 Z-1 S2(N) versus N: IBA gives a straight line in normal regions. First order shape phase transitions, discontinuities in Second order transitions, discontinuities in 1st order S2(N) N 2nd order S2(N) N Slide based on Iachello

Neutron Number S (2n) MeV

Empirical evidence of quantum phase transitional behavior in nuclei – a regional perspective

Modeling phase transitional behavior

New analytical solutions, E(5) and X(5) Nuclear Shape Evolution b - nuclear ellipsoidal deformation (b=0 is spherical) Vibrational Region Transitional Region Rotational Region Critical Point New analytical solutions, E(5) and X(5) Few valence nucleons Many valence Nucleons

X(5) Critical Point Symmetries E β  First Order Phase Transition – Phase Coexistence E β 1 2 3 4  Energy surface changes with valence nucleon number Bessel equation Iachello

Parameter- free except for scale

Empirical signature of 1st and 2nd order Energy ratio between 6+ of ground state and first excited 0+ { 1.5 U(5) → 0 SU(3) Vibrator Rotor ~1 at Ph. Tr ~ X(5)

Comparison of relative energies with X(5)

Absolute energy spacings in the 0+2 sequence – effects of a sloped wall Caprio

What is the locus of spherical-deformed shape/phase transitional regions? p-n / pairing =  NpNn p – n P Np + Nn pairing