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Microscopic Modeling of Supernova Matter
Igor Mishustin FIAS, J. W. Goethe University, Frankfurt am Main, Germany
andNational Research Center “Kurchatov Institute”, Moscow, Russia
NEOS2011, FIAS, November 28-30, 20111
Challenging task for nuclear community
Evaluation of nuclear properties in stellar environments, i.e. at finite temperature (T), baryon density (ρ) and fixed electron fraction (Ye): 0<T<10 MeV, 10-5<ρ/ρ0<0.5, 0.1<Ye<0.6.
This can be done by using Wigner-Seitz approximation. Then binding energies and excited states of nuclei can be found in individual cells characterized by Z, N and RC .
The whole “Nuclear Chrt” (1<A<1000, 0<Z<A) should be re-calculated in small steps of T, ρ and Ye. This input is needed to find the Nuclear Statistical Ensemble at given T, ρ and Ye.
Altogether up to 107 new “data” points should be tabulated. Any “reasonable” approach can be used (LDM, HFB, RMF, CEFT, …).
Possible tool: RMF model + electronsT. Buervenich, I. Mishustin and W. Greiner, Phys. Rev. C76 (2007) 034310;C. Ebel, U. Heinzmann, I. Mishustin, S. Schramm, work in progress
First step: constant electron density
Second step: self-consistent calculation
parameter set: NL3
Wigner-Seitz approximation
neutrons+electrons
spherical nucleus
deformed nucleus
spherical cell deformed cell
Requirements on the cells: 1) electroneutrality, 2) non-vanishing particle density at rR
The whole system is subdivided into individual cells each containing one nucleus, free neutrons 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
neutrons+protons
deformed ground state
behind barrier
charge density
240Pu
kF = 0.5 fm-1=100 MeV
2 0.28 0.60
RMF calculations in the Wigner-Saitz cell
Modification of Nuclear Chart due to electrons
with increasing kF theβ-stability line movestowards the neutron drip line,they overlap already at kF=0.1 fm-1=20 MeVfree neutrons appearat higher kF (“neutronization”)
protondripline
neutron dripline
Q-values drop gradually untilcross zero at kF=0.24/fm=48 MeV
Suppression of decay
Life times first decrease and then grow rapidly as Q0
Improvedcalculation
Due to electron screening Q-value drops with kF
2 5/3 5/3 5/31 2( , ) ( )FQ N Z e k Z Z Z
Suppression of spontaneous fission
Fissility parameter
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
Adding neutrons into the WS cell 1
Sn, N=82 Z=108, N=3492
Sn, N=650
Sn, N=1650
Ebel, Buervenich, I. Mishustin et al., work in progress
Adding neutrons into the WS cell 2
1) Dripping neutrons distribute rather uniformly inside and outside the nucleus2) Protons are distributed rather uniformly inside the nucleus 3) With increasing A the surface tension decreases (smaller density gradients)
Adding neutrons into the WS cell 3
1) Neutrons as well as protons develop a hole at the center of the nucleus2) Central proton density drops gradually with increasing nucleus size
Adding nucleons into the WS cell at fixed Ye=Z/A=0.2
Single-particle levels in β-equilibrium
1) All protons are shifted down due to the attractive potential generated by electrons.2) Neutrons have attractive mean field inside and outside the nucleus. 3) Neutron level density in the continuum is very high.
n p e
Conclusions Microscopic (HFB, RMF, CEFT,...) calculations are needed to
obtain information about nuclear properties (binding energies, level densities etc) in dense and hot stellar environments.
Partly such information can be obtained also from experiments studying multifragmentation reactions.
This information is crucial for calculating realistic NEOS and nuclear composition of supernova matter within the Statistical equilibrium approach.
Survival of (hot) nuclei may significantly influence the explosion dynamics through both the energy balance and modified weak reaction rates.
Deformation energy (w.r. to ground state)
Deformation becomes less favourable because of reduced Coulomb energyEnergy of isomeric state (or saddle point) goes up with ne
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