quantum phase transitions in nuclei
DESCRIPTION
Broad perspective on structural evolutionTRANSCRIPT
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 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 evolutionof 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 + Nnpairing 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 RegionTransitional RegionRotational Region
Critical Point New analytical solutions, E(5) and X(5) Few valence
nucleons Many valence Nucleons X(5) Critical Point Symmetries
E
First Order Phase Transition Phase Coexistence E 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+ { U(5)
0SU(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 + Nnpairing