1. Microscopic Modeling of Supernova Matter Igor Mishustin FIAS, J. W. Goethe University, Frankfurt am Main, Germany and National Research Center “Kurchatov Institute”, Moscow, Russia NEOS2011, FIAS, November 28-30, 20111

2. 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/ρ 0 <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 R C. 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 10 7 new “data” points should be tabulated. Any “reasonable” approach can be used (LDM, HFB, RMF, CEFT, …).

3. Possible tool: RMF model + electrons T. 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

4. Wigner-Seitz approximation neutrons+electrons spherical nucleus deformed nucleus spherical celldeformed cell Requirements on the cells: 1) electroneutrality, 2) non-vanishing particle density at r  R 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: neutrons+protons

5. deformed ground state behind barrier charge density 240 Pu k F = 0.5 fm -1 =100 MeV 0.280.60 RMF calculations in the Wigner-Saitz cell

6. Modification of Nuclear Chart due to electrons with increasing kF the β-stability line moves towards the neutron drip line, they overlap already at kF=0.1 fm -1 =20 MeV  free neutrons appear at higher kF (“neutronization”)‏ proton dripline neutron dripline

7. Q-values drop gradually until cross zero at k F =0.24/fm=48 MeV Suppression of  decay Life times first decrease and then grow rapidly as Q  0 Improvedcalculation Due to electron screening Q-value drops with k F

8. Suppression of spontaneous fission Fissility parameter increases with k F due to reduced Coulomb energy At kF=0.25 fm -1 =50 MeV Decreasing Q-values disfavor fission mode

10. Adding neutrons into the WS cell 1 Sn, N=82Z=108, N=3492 Sn, N=650 Sn, N=1650 Ebel, Buervenich, I. Mishustin et al., work in progress

11. Adding neutrons into the WS cell 2 1) Dripping neutrons distribute rather uniformly inside and outside the nucleus 2) Protons are distributed rather uniformly inside the nucleus 3) With increasing A the surface tension decreases (smaller density gradients)‏

12. Adding neutrons into the WS cell 3 1) Neutrons as well as protons develop a hole at the center of the nucleus 2) Central proton density drops gradually with increasing nucleus size

13. Adding nucleons into the WS cell at fixed Ye=Z/A=0.2

14. 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.

15. 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.

16. Deformation energy (w.r. to ground state)‏ Deformation becomes less favourable because of reduced Coulomb energy Energy of isomeric state (or saddle point) goes up with n e