in-medium properties of nuclear fragments at the liquid-gas phase coexistence

In-medium properties of nuclear fragments at the liquid-gas phase coexistence

International Nuclear Physics ConferenceInternational Nuclear Physics ConferenceINPC2007INPC2007

Tokyo, Japan, June 3-8, 2007Tokyo, Japan, June 3-8, 2007

A.S. Botvina1,2,3

1Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia

2Frankfurt Institute for Advanced Studies, J.W.Göthe University,Frankfurt am Main, Germany

3Gesellschaft für Schwerionenforschung, Darmstadt, Germany

(In collaboration with W.Trautmann, I.Mishustin, N.Buyukcizmeci, R.Ogul)

Experimentally established: 1) few stages of reactions leading to multifragmentation, 2) short time ~100fm/c for primary fragment production, 3) freeze-out density is around 0.1ρ0 , 4) high degree of equilibration at the freeze-out.

Multifragmentation of nuclei takes place in reactions initiated by all high energy particles (hadrons, heavy-ions, photons), where high excitation energy of residual nuclei is reached.

Thermal multifragmentation of nuclei:

Production of hot fragments at temperature T ~ 3---8 MeV and density ρ ~ 0.1 ρ0 (ρ0≈0.15 fm-3)

Interpretation: liquid-gas phase transition in finite nuclei. Investigation of properties of

fragments surrounded by nuclear species.

Statistical Multifragmentation Model (SMM)

IMF

IMF

IMFHR

Ensemble of nucleons and fragmentsin thermal equilibrium characterized by neutron number N

0

proton number Z0 , N

0+Z

0=A

0

excitation energy E*=E0-E

CN

break-up volume V=(1+)V0

All break-up channels are enumerated by the sets of fragment multiplicities or partitions, f={N

AZ}

J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133

np

Statistical distribution of probabilities: Wf ~ exp {S

f (A

0, Z

0, E*,V)}

under conditions of baryon number (A), electric charge (Z) and energy (E*) conservation

Fragments obey Boltzmann statistics, liquid-drop description of individual fragments, Coulomb interaction in the Wigner-Seitz approximation

free energy of channel:

individual fragments:

Probability of channel:

mass and charge conservation

Energy conservation

entropy of channel

ALADIN data

multifragmentation ofrelativistic projectiles

GSI

A.S.Botvina et al.,Nucl.Phys. A584(1995)737

H.Xi et al., Z.Phys. A359(1997)397

comparison withSMM (statistical

multifragmentationmodel)

Statistical equilibriumhas been reached in

these reactions

The surface (B0) and symmetry (γ) energy coefficientsin the multifragmentation scenario

Fsym = γ·(N-Z)2/A

Fsuf = B0f(T)A2/3

Isoscaling and the symmetry coefficient γ

α·T ≈ -4γ (Z12/A1

2-Z22/A2

2)S(N)=Y(124Sn)/Y(112Sn)=C∙exp(N∙α+Z∙β)

ALADIN: 12C+ 112,124Sn A.Le Fevre et al., Phys.Rev.Lett 94(2005)162701

1AGeV

A

25AMeV

γ=25γ=15

Z/A

The symmetry energy coefficient γ and isospin of fragments

G.Souliotis et al., PRC75(2007)011601A.S.Botvina et al., PRC72(2005)048801

Fsuf = B0((Tc2-T2)/(Tc

2+T2))5/4A2/3Fsym = γ·(N-Z)2/A

One can distinguish effects of the surface and symmetry energies since the charge yield of fragments is very sensitive to the surface:

A.S.Botvina et al., PRC74(2006)044609

Properties of hot fragments: the surface energy term B0

Z-τ analysis of IMF yields

A.S.Botvina et al., PRC74(2006)044609

projectiles with different isospin

ALADIN

SMM

We obtain an evolution of the surface energy of hot fragments toward region of full multifragmentation

We analyze all previous observables: distributions of IMF , Zmax , T , ...

vs Zbound , and involve additionally new τ - observables for each

projectile (Xe, Au, U)

for single isolated nuclei:C -- Cameron mass formula (1957)MS -- Myers-Swiatecki mass formula (1966)(include separate volume and surfacecontributions to the symmetry energy)

Conclusions

Multifragmentation reactions can be interpreted as a manifestation of the liquid-gas type phase transition in finite nuclei, and allow for investigating the phase diagram of nuclear matter. One can investigate properties of hot nuclei/fragments surrounded by other nuclear species.

By analyzing experimental data it was found: -- decreasing the symmetry energy of primary hot fragments by ~ 40% when the systems evolve toward full multifragmentation (with increasing excitation energy and decreasing the freeze-out density): ALADIN, FRS, MARS;-- as a result of the same process the surface energy of these fragments becomes independent on their isospin, this means that the difference between surface and volume symmetry energies (as adopted in some mass formulas for isolated nuclei) disappears also: ALADIN.

Important applications in astrophysics:since mass distributions of fragments in stellar matter, and electro-weak reactionsare very sensitive to the symmetry energy

A.Botvina and I.Mishustin, PRC72(2005)048801