Equation of State for nuclear matter: research at CHARMS PART I: Generalities about the Equation of State (EOS) for ordinary matter and for nuclear matter PART II: Our research with the FRS connected to EOS

PART I: Equation of State for ordinary matter and for nuclear matter Fundamental interactions and residual forces e.m. interactionresidual e.m. interaction (e.g. covalent bond) residual e.m. interaction (molecular force) ordinary matter strong interactionresidual strong interaction (nucleon-nucleon force) nuclear matter ATOM MOLECULE LIQUID NUCLEON NUCLEUS

Range dependence of the residual force u r u r molecule-molecule (Lennard-Jones) nucleon-nucleon (Skyrme) Nuclear matter in normal condition (nuclei) behaves as a liquid! The scales are very different: Ordinary matter Nuclear matter Density: 1 g/cm g/cm 3 Typical distance: m m How do microscopic properties translate into macroscopic properties?

EOS for the ordinary matter How does molecular force change when we have a great number of molecules? How strong is the molecular bond? Macroscopic quantities that are observable when I heat a liquid: - volume, V - pressure, P - temperature, T Relation among V, P, T: the equation of state IDEAL GAS:. REAL GAS (Van der Waals):. strenght intramolecular force volume molecule

Solution of the EOS (van der Waals) for a given material (a and b given) V P Isothermes spinodal region liquid gas coexistence  measuring P, V, T  a and b  intramolecular force high T low T 2 nd virial coefficient

How can I explore experimentally the P,V diagram? 1) I increase T at constant pressure V P Isothermes gas coexistence liquid 100°C  1 atm T E P constant V increasing Caloric curve (liquid-gas phase transition) liquid-gas coexistence

How can I explore experimentally the P,V diagram? 2) I increase P at constant temperature  increase  (compression) V P Isothermes gas coexistence liquid  heat bath compressibility EOS

Study of the EOS for the nuclear matter “Exploring the nuclear-matter phase-diagram and identifying the different phases of nuclear matter is one of the main challenges of modern nuclear physics.” NUPECC 1)Measuring the phase transitions 2)Measuring the compressibility How can I explore experimentally the P,V diagram? projectile targetspectator participant „fireball“ Nucleus-nucleus collisions at relativistic energies 2) this part is compressed 1) these parts get excitation energy E*

Liquid-gas phase transition Liquid phase Fragmentation Transition (coexistence) Multifragmentation Gas phase Vaporisation

Phase transition superfluid  liquid superfluid liquid coexistence gas E/MeV A  T/MeV Superfluid phase revealed by structural effects e.g. even-odd staggering

Liquid-gas phase transition 1)What is T? How to measure T? 2)What is E*? How to measure E*? 3)What is P? Is it constant? 4)What is V? Is it measurable?

Classical Temperature Temperature is a macroscopic observable that rules the exchange of energy between bodies. Correlation between the temperature and the energy of the molecules of the ideal gas AT EQUILIBRIUM = = = 1/2 k T T high T low

Nuclear Temperature: zero temperature The nucleus is: a mesoscopic system a fermionic quantum system  the nucleons inside the nucleus do not have the same degrees of freedom: they have increasing energy

E TOT = a T 2 a  A E/A  T 2 Nuclear Temperature: non-zero temperature

Thermometers SLOPE THERMOMETER: Energy spectrum for nucleons from evaporation ISOMER THERMOMETER: Nuclei in a heat bath at T>0. The energy of different isomers will be different ISOTOPE THERMOMETER: Nuclei in a heat bath at T>0. The mass (or binding energy) of different isomers will be different

Excitation energy Excitation energy : quantity related to the individual energy of the nucleons Pressure and Volume Pressure : pressure done by the nucleons Volume: volume occupied by the nucleons ?????

Problems behind the liquid-gas phase transition V P Isothermes gas coexistence liquid 100°C  1 atm 1)Costant pressure? Operational definition of the volume? 2)Quantum system 3)Mesoscopic system 4)Fast heating (no thermalisation – no equilibrium) 5)Mixture of two liquids (proton and neutron subsystems) „Isospin dependence of the EOS“

Compressibility of nuclear matter Nuclear compressibility is directly related to the nuclear force u r (E/A) = Internal energy per nucleon = internal energy stored in compression  /  0 = normalised density  = nuclear compression modulus = curvature at  =  0  large = hard EOS  small = soft EOS

Methods to investigate the compressibility 1)From fireball (Flow, Kaon production) 2)From scattering (Giant resonance) Flow The „squeeze out“ or „flow“ is directly related to the gradiente pressure in the fireball  nuclear compression modulus Kaon production The bulk of K + mesons is produced in secondary or multiple reactions of nucleons in the fireball: N 1 +N 2   N 1 N 2  N 3  K + +  Such secondary reactions occur predominantly at high nuclear density  kaon production yields are sensitive to the compression  nuclear compression modulus

Giant monopole resonance The isoscalar giant monopole resonance (GMR) is a compressional mode of excitation. It is of particular interest because its energy is directly related to compressibility. By measuring the inelastically scattered alpha particles at forward angles, including 0° degrees, one can deduce the energy. Problems behind the compressibility 1)Short time span (dynamical picture  hydrodynamical models) 2)Momentum dependence interaction (MDI) 3)Mesoscopic system (finite size) 4)In-medium effects 5)Mixture of two liquids (proton and neutron subsystems) „Isospin dependence of the EOS“

The study of the EOS at GSI (Germany) ALADIN

KAOS The kaon spectrometer is capable of determining the momentum and charge of the particles, their emission angle, the centrality of the reaction including the total number of participating nucleons, and the orientation of the reaction plane. The momentum is measured via the deflection angle of the particle in the magnetic field and its recorded hit position in the focal plane. The velocity is deduced by reconstructing the flight path and measuring the time of flight. With these quantities known, the rest mass and thus the particle species can be unambiguously determined.

FOPI The charged particles produced by a nickel-nickel collision at an energy of 1.93 GeV per nucleon leave tracks in the central drift chamber. The individual signals in the detector (squares) are automatically connected to form the track. Unambiguous identification of the particle is possible from the curvature of the track and additional information from other sections of the FOPI detector. In the example shown, two strange particles (K 0 and  ) arise simultaneously and decay after a short flight.

PART II: Our research with the FRS connected to EOS 4  detectors  „landscape“ FRS  „a microscope“... a different approach! velocity is calculated from B  : very precise evaluation

Z=26 longitudinal velocity 1 A GeV 238 U on H 2 +Ti Our observables: velocity spectra and cross sections The integral of these spectra gives us the fission cross-section and the fragmentation cross-section

Fission Our observables

Phases 1 - superfluid 2 - liquid 3 - coexistence 4 - gas E/MeV A  T/MeV

Results from e.m.-induced fission of 70 different secondary projectiles (Steinhäuser et al., Nuc. Phys.A 634 (1998) 89 ) Structural properties survive at low energy 1 - Superfluid phase Structural effects are restored in the end products of hot decaying nuclei Z Fissioning nucleus: 226 Th

2 - Liquid phase: an example: 1 GeV p on 238 U proton 1 GeV fission fragments Intra-nuclear Cascade Sequential Evaporation / Fission

2 - Liquid phase: the cross sections of spallation and fragmentation residues "evaporation corridor" or "attractor line" IDEA BEHIND LIMITING FRAGMENTATION

2 - Liquid phase: the velocity of spallation and fragmentation residues Morryssey systematics is found to be valid: 1) for small  A in spallation / fragmentation reactions 2) for compound nuclei which fission

3 - Liquid-gas coexistence: an example: 238 U + Pb fission sequential evaporation 238 U Pb 238 U Pb break-up pre- fragment

3 - Liquid-gas coexistence: an example: 238 U + Pb

3 - Liquid-gas coexistence: indications in the cross sections of "light" residues

238 U 1.59 break-up abrasion evaporation 3 - ISOSPIN THERMOMETER

3 - Liquid-gas coexistence : indications in the cross sections of "light" residues

Liquid-gas coexistence: indications in the velocity of "light" residues

break-up this is due to a dynamical process!

ABRABLA fission sequential evaporation 238 U Pb 238 U Pb break-up pre- fragment break-up

event Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Zbound Zb ALADIN data

ALADIN data Au+Au at 1 A GeV

ABRABLA data Au+Au at 1 A GeV