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