1. Phase Transitions & frustration in nuclear physics and astrophysics
workshop ESNT
"Mean Field and Beyond for Nuclear Reactions"
Phase Transitions & frustration in nuclear physics and astrophysics
Karim Hasnaoui(1)
Ph. Chomaz(1), C. Ducoin(1,2), F. Gulminelli(2), P. Napolitani(1)
(1) GANIL (DSM-CEA/IN2P3-CNRS),Blvd. H. Becquerel, F Caen cédex, France
(2) LPC Caen (IN2P3-CNRS/Ensicaen et Université), F Caen cédex, France

2. Nuclear matter and neutron stars
Matter of neutrons, protons, and electrons.
Crust of star Þ r/ r0 Î [~0.1,1].

3. Motivation of the project
Exotic phases. (J.C. Pethick & D.G. Ravenhall).
To understand the phenomenology of phase transitions of nuclear matter.
To study the opalescence of star matter for neutrino propagation. (C. Horowitz & al)

4. Ising analogue to compact star matter
Hinteraction=Hnuclear + HCoulomb
Lattice-gas :
N sites => occupation ni=0,1.
No Isospin =>
Delocalisation of the electron =>

5. Ising analogue to compact star matter
where
&
e=5.5MeV

6. Matrice Cij

7. Result 1 : Equation of state
system uncharged
system charged
Liquid-gas coexistence expands with respect to uncharged nuclear matter => Ttransition > Tc

8. Result 2 : Criticality
The phase transition is not of the second order.
The lengths of correlations do not diverge at the point of transition.

9. Effective interactions
The phase-transition phenomenology depends on the intrinsic interaction => Necessary to use an effective interaction.
to take into account:
Fermionic character of the nuclear system.
Isospin degree of freedom.

10. Fermionic Molecular Dynamics (FMD) (H.Feldmeier & al)
|Y> = Ansatz of Slater =>
Where

11. Fermionic Molecular Dynamics (FMD) (H.Feldmeier & al)
Equation of motion  TDHF

12. Conclusion and perspectives
ISING => Coulomb modifies the phase-transitions phenomenology => suppression of criticality
FMD => to take effective interactions and dynamics into account.
Other exotic phases of the crust.
Neutrino propagation.