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