2. Content
Heavy ion reactions started fragmenting nuclei in the 1980’s. Its study taught us that nuclear matter has liquid and gaseous phases, phase changes, critical behavior, and many rich phenomena. Here a summary of theoretical efforts leading to the understanding of the thermodynamics of nuclear matter will be presented, including recent ones that extend the phase diagram in a new direction: isospin.
The nucleus is a liquid
Experimental evidence
Theoretical models
Current efforts
Conclusions

3. The nucleus is a liquid

4. 1980: The nucleus is a liquid
En early 80s the following was well known:
The nuclear density
The nuclear compressibility
The nucleus was a Fermi system
How does the nucleus
behave at higher temperatures?
The rest can be inferred by interpolation
Behaves as a Fermi
gas at low densities
Compressibility: K=n(dp/dn)T (proportional to the slope)
Stable nucleus:
p = 0, density ~ 0.15 fm-3
What were the implication of these facts?

5. 1980: The nucleus is a liquid
Such behavior p – r is similar to that of liquids
Bertsch
Siemens
López
. . .
Could there be a change of phases líquid-gas in the nucleus?
Was there any experimental evidence?

6. Experimental evidence

7. 1980-2010: experimental evidence
Fragmentation exists
Gaseous phase: Separated particles
Larger fragments decrease at higher energies  Evaporation
Liquid phase: continuous medium

8. 1980-2010: experimental Evidence
Evidence of thermalization
Kinetic energy and momentum of fragments follow Maxwell distributions  Thermalization

9. 1980-2010: experimental Evidence
Temperature measurements

10. 1980-2010: experimental Evidence
Temperature
Caloric curve
Temperature does not increase with an increase of energy
 Change of phase

11. 1980-2010: experimental Evidence
Such evidence suggested this reaction mechanism:
Heating compression Change of phaseExpansion

12. Theoretical models

13. 1980-2000: theoretical models Statistical Models SMM Transition State
Sequential Decay
Dynamical Models
Boltzmann, Vlasov, …
Molecular Dynamics
Quantum
Classical

14. 1985: SMM
Bondorf
Schultz
Barz
Donangelo
Sneppen
Botvina
Mishustin
López …
SMM “explores” the phase space during the “freeze-out” to determine the most probable breakups.

15. Data: peripheral collisions with Au
1985: SMM
Theory: SMM
Data: peripheral collisions with Au
Successes:
Reproduced mass distributions
Very good PR
Deficiencies:
Did not use unique parameters
No Kinetic information
No de-excitation of fragments
No inter-fragment interactions
Unrealistic Freeze-out volume
. . .
Multics-NPA650 (1999) 329

16. 1987: transition state treatment
Added inter-fragment interactions
Added de-excitation of fragments
But … it didn’t contain fragment dynamics and the freeze out volume was still a perfect sphere . . .

17. 1988-1990: sequential decay Assumes a sequence of fissions
Uses fission barriers
Conserves energy and momentum
De-excites fragments by evaporation
But Doesn’t explain non-sequential decays

18. > 1990: dynamical Models
Kinetic Theory: Nordheim, Boltzmann, Vlasov
124Sn+124Sn, E/A=50 MeV
Neck fragments
b=7 fm
multifragmentation
b=0 fm
Correct dynamics and geometry
Uses Fermi energy distribution
But . . .

19. >1995: Dynamical Models
Kinetic Theory: Nordheim, Boltzmann, Vlasov
Density evolution
Momentum space
- Use mean fields Use “test particles” instead of real nucleons
- Use Gaussian density distributions Do not produce fragments Fragments are identified by hand
- Fragments do not de-excite by themselves
- Use different parameters in different reactions

20. >1995: Dynamical Models
Quantum Molecular Dynamics
Pauli Potential
Nuclear Force
Coulomb Energy
Kinetic Energy
- Uses Gaussian distributions for p & n
- Uses Mean Field Potentials
- Obeys Fermi Statistics
Uses correct dynamics & geometry
But

21. >1995: Dynamical Models
Quantum Molecular Dynamics
- Does not produce fragments without external help
- Does not de-excite fragments without external help
Does not use a unique set of parameters
But it is widely used (good PR)

22. >1995: Dynamical Models
Classical Molecular Dynamics
- Uses inter-nucleon potentials
- Uses protons & neutrons
Correct dynamics and geometry
- Doesn’t use “test particles”
- Does not use Gaussian distributions of density
- Produces fragments without external help
- De-excites fragments naturally
Uses a unique set of parameters
But it uses classical mechanics and doesn’t obey Fermi statistics

23. >1995: Dynamical Models
Classical Molecular Dynamics
Potential
Solve equation of motion (Verlet)
Recognize clusters (MSE)
Track evolutions in space-time

24. >1995: Dynamical Models
Classical Molecular Dynamics

25. >1995: Dynamical Models
Classical Molecular Dynamics
Determine mass distributions
It has been used to study:
Critical phenomena
Caloric curves
Isoscaling

26. What do we know?

27. We now know much about the equation of state of nuclear matter
What do we know?
We now know much about the equation of state of nuclear matter

28. In a nutshell
Nuclei in reactions are compressed, heated, and expand while going from a liquid phase to a liquid-gas mixture

29. Current efforts

30. Investigating neutron-rich nuclei
Current efforts
Investigating neutron-rich nuclei

31. The study of neutron-rich nuclei
Current efforts
The study of neutron-rich nuclei

32. Current efforts
Isoscaling

33. Infinite nuclear matter
Procedure to study phase diagram of nuclear matter
Create an infinite system
Select density r
Select Temperature
Equilibrate
Measure
Binding energy E(r,T)
Pressure p(r,T)
Compressibility K(r,T)
Obtain equation of state
Study other properties of system

35. System maintains crystalline structure at higher T
Symmetric matter
Binding energy of Pandha medium
Higher T
System maintains crystalline structure at higher T
System produces pasta at r < 0.13 fm-3 at all T

36. Symmetric matter
Low T structures
T=1 MeV
T=0.001 MeV

37. New phases in the nuclear phase diagram!
Symmetric matter
Significance?
New phases in the nuclear phase diagram!

38. Pasta – Crystal: Latent heat needed 1st order phase transition?
Symmetric matter
Significance?
Liquid-Gas - Pasta,
a glass transition?
Liquid-Gas - Crystal,
freezing?
Pasta – Crystal: Latent heat needed
1st order phase transition?

39. Extend what we know into the new dimension: Isospin
Symmetric matter
What’s next?
Extend what we know into the new dimension: Isospin ?

40. Conclusions

41. Extra slides

42. There are more states available than nucleons
Quantum caveats I
There are more states available than nucleons
Pauli blocking is not restrictive

43. Quantum caveats II
Inter particle distance is larger than de Broglie wavelength for all cluster sizes