1. Properties of nuclear matter in supenova explosions Igor Mishustin Frankfurt Institute for Advanced Studies Johann Wolfgang Goethe University Frankfurt am Main, Germany and Kurchatov Institute, Russian Research Center Moscow, Russia in collaboration with A. Botvina, Th. Buervenich, W. Greiner,... INPC2007, Tokyo, June 3-8, 2007

2. Contents ● 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

3. Creation of chemical elements in the Universe Crab nebula Macro-explosions occur after collapse of massive stars supernovae stars Big Bang

4. Numerical simulations of supernova explosions 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

5. Creation of micro-supernovae in the laboratory Heating r<r 0 P~0 slow expansion t>100 fm/c t = 0 fm/c Peripheral AA 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 in proton-nucleus and nucleus-nucleus collisions

6. Similarity of physical conditions in nuclear reactions and supernova explosions Nuclear reactions leading to multifragmentation of nuclei: temperature baryon density no leptons volume time scales The only available tool to investigate properties of hot nuclear fragments in dense environments Collapse of massive stars leading to supernova (type II) explosions: temperature baryon density lepton fraction volume time scales Presence of hot nuclei is important for the equation of state, dynamical evolution and weak reaction rates This information can be used as input for SN simulations The shock gets stronger when less initial (Fe) nuclei are destroyed

7. Previous studies of stellar nuclear matter 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.

8. Statistical description of stellar matter calculations done in a box containing 1000 baryons, nuclear density fixed at

9. Nuclear equilibrium ensemble Grand Canonical version of SMM (Botvina et al., Sov. J. Nucl. Phys. 42 (1985) 712) <1

10. Nuclear composition of supernova matter Superheavy nuclei Nuclear mass distributions are non- Gaussian Significant amounts of heavy and superheavy nuclei can be produced

11. Nuclear composition II A>4 Very strong variation of mass distribution with T: 1 MeV - U-shaped, 2 MeV - power law, 3 MeV - exponential

12. Evolution of mass distributions along isentropes Power-law mass distribution occurs at c. p. of the liquid-gas phase transition

13. Nuclear structure calculations in stellar environments The framework: RMF model + electron gas constant electron density (allowing axially deformed charge distributions) parameter set: NL3

14. Wigner-Seitz approximation electrons spherical nucleus deformed nucleus spherical celldeformed 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: protons

15. 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 k F

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

17. Neutron and proton driplines with increasing k F the β-stability line moves towards the neutron drip line, they overlap already at k F =0.1 fm -1 =20 MeV  free neutrons appear at higher k F (“neutronization”) proton dripline neutron dripline

18. 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

19. Suppression of spontaneous fission Fissility parameter Z2 increases with k F due to reduced Coulomb energy At k F =0.25 fm -1 =50 MeV Decreasing Q-values disfavor fission mode --

20. Conclusions ● 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).