Transcript In-medium properties of nuclear fragments at

International Nuclear Physics Conference
INPC2007
Tokyo, Japan,
June 3-8, 2007
In-medium properties of nuclear fragments
at the liquid-gas phase coexistence
A.S. Botvina1,2,3
(In collaboration with W.Trautmann, I.Mishustin, N.Buyukcizmeci, R.Ogul)
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
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.
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.
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)
J.P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, K. Sneppen, Phys. Rep. 257 (1995) 133
IMF
a
n
p
HR
IMF
Ensemble of nucleons and fragments
in thermal equilibrium characterized by
neutron number N0
proton number
Z0 , N0+Z0=A0
excitation energy E*=E0-ECN
break-up volume V=(1+k)V0
IMF
All break-up channels are enumerated by the sets of
fragment multiplicities or partitions, f={NAZ}
Statistical distribution of probabilities: Wf ~ exp {Sf (A0, Z0, E*,V)}
under conditions of baryon number (A), electric charge (Z) and energy
(E*) conservation
Probability of channel:
mass and charge
conservation
Energy conservation
entropy of channel
Fragments obey Boltzmann statistics, liquid-drop description of individual
fragments, Coulomb interaction in the Wigner-Seitz approximation
free energy of channel:
individual fragments:
ALADIN data
GSI
multifragmentation of
relativistic projectiles
A.S.Botvina et al.,
Nucl.Phys. A584(1995)737
H.Xi et al.,
Z.Phys. A359(1997)397
comparison with
SMM (statistical
multifragmentation
model)
Statistical equilibrium
has been reached in
these reactions
The surface (B0) and symmetry (γ) energy coefficients
in the multifragmentation scenario
Fsym = γ·(N-Z)2/A
Fsuf = B0f(T)A2/3
Isoscaling and the symmetry coefficient γ
ALADIN:
12C+ 112,124Sn
A.Le Fevre et al., Phys.Rev.Lett 94(2005)162701
S(N)=Y(124Sn)/Y(112Sn)=C∙exp(N∙α+Z∙β)
α·T ≈ -4γ (Z12/A12-Z22/A22)
The symmetry energy coefficient γ and isospin of fragments
A.S.Botvina et al., PRC72(2005)048801
G.Souliotis et al., PRC75(2007)011601
Z/A
25AMeV
1AGeV
γ=25
γ=15
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
Fsuf = B0((Tc2-T2)/(Tc2+T2))5/4A2/3
Fsym = γ·(N-Z)2/A
Properties of hot fragments: the surface energy term B0
Z-τ analysis of IMF yields
projectiles with different isospin
SMM
ALADIN
A.S.Botvina et al., PRC74(2006)044609
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 surface
contributions to the symmetry energy)
We obtain an evolution of the surface energy of hot
fragments toward region of full multifragmentation
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 reactions
are very sensitive to the symmetry energy
A.Botvina and I.Mishustin, PRC72(2005)048801