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Properties of nuclear matter in Properties of nuclear matter in supenova explosionssupenova explosions
Igor Mishustin
Frankfurt Institute for Advanced Studies Johann Wolfgang Goethe University
Frankfurt am Main, Germanyand
Kurchatov Institute, Russian Research Center Moscow, Russia
in collaboration with A. Botvina, Th. Buervenich, W. Greiner, ...
INPC2007, Tokyo, June 3-8, 2007INPC2007, Tokyo, June 3-8, 2007
ContentsContents
● Introduction ● Micro- and Micro-Supernovae ● Statistical description of stellar matter● Nuclear structure in supernova environments● Conclusions
Recent publications: A.S. Botvina, I.N. Mishustin, Phys. Lett. B584, 233, 2004; Phys. Rev. C72, 048801, 2005;Th. Buervenich, I.N. Mishustin, W. Greiner, paper in preparation
Creation of chemical elements in the Creation of chemical elements in the UniverseUniverse
Crab nebula
Macro-explosions occur Macro-explosions occur after collapse of massive starsafter collapse of massive stars
supernovae
stars
Big Bang
Numerical simulations of supernova Numerical simulations of supernova explosionsexplosions
H.-T. Janka, K. Kifonidis, M. Rampp Lect.Notes Phys.578:333-363,2001
t~230 ms
~70 km~300km
~150km
Sketch of the post-collapse stellar core during the neutrino heating and shock revival phase
hot bubble
Creation of micro-supernovae in the Creation of micro-supernovae in the laboratorylaboratory
HeatingP~0
slow expansion
t>100 fm/ct0 fm/c
PeripheralAA collision
Multifragmentation – nucleosynthesis in expanding nuclear matter,Power-law mass distributions: (liquid-gas p. t.) Can be well understood within the equilibrium statistical approach
Randrup&Koonin, D.H.E. Gross et al, Bondorf-Mishustin-Botvina, Hahn&Stoecker,...
Expanding equilibrated source
( ) , 2Y A A
inin proton-nucleus and nucleus-nucleus collisionsproton-nucleus and nucleus-nucleus collisions
Similarity of physical conditions in Similarity of physical conditions in nuclear reactions and supernova nuclear reactions and supernova
explosionsexplosionsNuclear reactions leading to multifragmentation of nuclei:
temperature baryon densityno leptonsvolumetime scales
The only available tool to investigate properties of hot nuclear fragments in dense environments
Collapse of massive stars leading tosupernova (type II) explosions:
temperature baryon densitylepton fractionvolumetime scales
Presence of hot nuclei is importantfor the equation of state, dynamical evolution and weak reaction rates
3 8 MeVT 0(0.1 0.3)B
3(10 fm)V 3(100 km)V exp 100 fm/c
exp 100 ms
(0.1 10) MeVT 6
0(10 1.0)B 0.2 0.45eY
This information can be used as input for SN simulations
The shock gets stronger when less initial (Fe) nuclei are destroyed
Previous studies of stellar nuclear Previous studies of stellar nuclear mattermatter
Nuclear structure and pasta phases:G. Baym, H.A. Bethe, C. Pethick, Nucl. Phys. A175 (1971) 225;
J.W. Negele and D. Vautherin, Nucl. Phys. A207(1973) 278;
D.G. Ravenhall, C.J. Pethick, and J.R. Wilson,, Phys. Rev. Lett. 50 (1983) 2066;
T. Moruyama, , T. Tatsumi, D. Voskresensky, T. Tanigawa, S. Chiba, Phys. Rev. C72 (2005) 015802;
C.J. Horowitz,Eur. Phys. J. A30 (2006) 303.
Nuclear Statistical Ensemble and Equation of state:J.M. Lattimer, C.J. Pethick, D.G. Ravenhall, and D.Q. Lamb, Nucl. Phys. A432 (1985)646;
J.M. Lattimer and F.D. Swesty, Nucl. Phys. A535 (1991) 331;
H. Shen, H. Toki, K. Oyamatsu, and K. Samiyoshi, Nucl. Phys. A637 (1998) 435;
C. Ishizuka, A. Ohnishi, and K. SSamiyoshi, , Nucl. Phys. A723 (2003) 517.
Our approach is based on the Statistical Multifragmentation Model (SMM) which
previously was very successfully used for description of the multifragmentation reactions
See review: J. P. Bondorf, A.S. Botvina, A.S. Iljinov, I.N. Mishustin, and K. Sneppen, Phys. Rep. 257 (1995) 133.
Statistical description of stellar matterStatistical description of stellar matteri i B i Q i LB Q L
AZFor nuclear species ( , ) : B QA Z A Z
-eelectrons : Q L e
e
neutrinos : L
( , )
( , )
Baryon number conservation :
fixed
Electric neutrality
0
B AZA Z
Q AZ eA Z
BA n
V
QZ n n
V
B
e
Lepton number conservatio
(trapped ) (free )
n
or = eL e
B B
n n nLY Y
B
Q
( )
Statistical ensemble
with fixed , ,B L eT Y
calculations done in a box containing 1000 baryons,nuclear density fixed at
30 0.16 fm
Nuclear equilibrium ensembleNuclear equilibrium ensembleGrand Canonical version of SMM (Botvina et al., Sov. J. Nucl. Phys. 42 (1985) 712)
3/2
fAZ 3
Number density of nuclear species ( , ) :
V A 1=g exp -
V TAZ AZ AZT
A Z
n F
nuc
( , )
Pressure = electrons
nuc AZA Z
P P
P T n
5 / 42 22 2B 2 / 3AZ 0 0 2 2
0
Internal free energy of species ( , ) for 4
( 2 )F
liquid drop parametrizat
( ) , ,
Reduced Coulomb energy
ion
d
B S sym CAZ AZ AZ AZ AZ
S symcAZ AZ
c
A Z A
F F F F F
T TT A ZT w A F A F
AT T
1/ 32
1/ 30 00
ue to the electron screening
3 ( ) 3 1( ) ( ) , ( ) 1
5 2 2C e eAZ e e e
p p
n neZF n c n c n
n nr A
L, , found by iterative procedure
B Q
<1
Nuclear composition of supernova Nuclear composition of supernova mattermatter
Superheavy nuclei
Nuclear mass distributions are non-
Gaussian
Significant amounts of heavy and superheavy nuclei can be
produced
Nuclear composition IINuclear composition II
A>4
Very strong variation of mass distribution with T: Very strong variation of mass distribution with T: 1 MeV - U-shaped, 2 MeV - power law, 3 MeV - exponential1 MeV - U-shaped, 2 MeV - power law, 3 MeV - exponential
Evolution of mass distributions along Evolution of mass distributions along isentropesisentropes
Power-law mass distribution occurs Power-law mass distribution occurs at c. p. of the liquid-gas phase transition at c. p. of the liquid-gas phase transition
Nuclear structure calculations in stellar environmentsNuclear structure calculations in stellar environments
The framework: The framework: RMFRMF model + electron gas model + electron gas
constant electron density (allowing axially deformed charge distributions)
parameter set: NL3
Wigner-Seitz approximationWigner-Seitz approximation
electrons
spherical nucleus
deformed nucleus
spherical cell deformed cell
Requirements on the cells: 1) electroneutrality, 2) zero quadrupole moment
The whole system is subdivided into individual cells each containing one nucleus and electron cloud
Nuclear Coulomb energy is reduced due to the electron screening:
1/32( )3 3 1( ) ( ), ( ) 1 15 2 2p pA
eC ee e eAZ
nneZF n c n c nR nn
3
23F
ek
n
3,23
F ppk
n
protons
Deformation energy (w.r. to Deformation energy (w.r. to ground state)ground state)
Deformation becomes less favourable because of reduced Coulomb energyEnergy of isomeric state (or saddle point) goes up with kF
deformed ground state
behind barrier
charge density240240PuPu
kF = 0.5 fm-1=100 MeV
2 0.28 0.60
RMFRMF calculations in Wigner-Saitz cell calculations in Wigner-Saitz cell
Neutron and proton driplinesNeutron and proton driplineswith increasing kF theβ-stability line movestowards the neutron
drip line,they overlap already at kF=0.1 fm-1=20 MeVfree neutrons appear
at higher kF (“neutronization”)
protondripline
neutron dripline
Q-values drop gradually untilcross zero at kF=0.24/fm=48 MeV
Suppression of Suppression of decaydecay
Life times first decrease and then grow rapidly as Q0
ImprovedImproved
calculationcalculation
Due to electron screening Q-value drops with kDue to electron screening Q-value drops with kFF
2 5/3 5/3 5/31 2( , ) ( )FQ N Z e k Z Z Z
Suppression of spontaneous Suppression of spontaneous fissionfission
Fissility parameter
Z2
2 2 48
( )S
C F
aZ
A a c k
increases with kF due to reduced Coulomb energy
At kF=0.25 fm-1 =50 MeV
280Z
A
Decreasing Q-values disfavor fission mode
--
ConclusionsConclusions● Statistical equilibrium approach is very useful for describing
equation of state and composition of supernova matter..
● Survival of (hot) nuclei may significantly influence the explosion dynamics through both the energy balance and modified weak reaction rates.
● Statistical mechanism may provide “seed” nuclei for further nuclear transformations in r-, rp- and s- processes.
● Alpha-decay and spontaneous fission of neutron-rich heavy and superheavy nuclei are suppressed in supernova environments (electron screening of nuclear Coulomb interaction).