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).