1. Modeling of Clusterized Nuclear Matter under Stellar Conditions Igor Mishustin with T. Buervenich, C. Ebel, U Heinzmann, S. Schramm, W. Greiner FIAS, J. W. Goethe University, Frankfurt am Main, Germany and National Research Center “Kurchatov Institute”, Moscow, Russia NUFRA2015, Kemer, October 4-11, 2015

2. Contents Introduction: Macro- and Micro-Superovae Uncertainties in Nuclear Statistical Ensemble Nuclear structure calculations in stellar environments Pasta phases with realistic electrostatic potentials Conclusions

3. A.S. Botvina, I.N. Mishustin, Phys. Lett. B584, 233 (2004); Phys. Rev. C72, 048801 (2005}; Nucl. Phys. A 843, 98-132 (2010); A. Botvina and I. Mishustin, Phys. Rev. C72 (2005) 048801; Th. Buervenich, I.N. Mishustin, W. Greiner, Phys. Rev. C 76, 034310 (2007)‏; + Ebel, paper in preparation 3} N. Buyukcizmecl, A.S. Botvina, I.N. Mishustin, R.Ogul, M. Hempel, J. Schaffner-Bielich, F.K. Thielemann, S.Furusawa, K.Sumiyoshi, S. Yamada, H. Suzuki, Nucl. Phys. A (2013) N. Buyukcizmecl, A.S. Botvina, I.N. Mishustin, Astrophys.J. 789 (2014) 33 Claudio Ebel, Igor Mishustin, Walter Greiner, J.Phys. G42 (2015) 10, 105201 U. Heinzmann, I. Mishustin, S. Schramm, paper in preparation Relevant publications

4. Macro-Supernovae: Numerical simulations 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 laboratory T Heating : T~10 MeV  <  0, P~0 slow expansion t>100 fm/c Peripheral AA collision (ALADIN) Multifragmentation – creation of micro-supernovae in laboratory, Power-law mass distributions: (liquid-gas phase tr.) Can be well understood within the equilibrium statistical approach developed in 80s (following ideas of N. Bohr and E. Fermi): Randrup&Koonin, D.H.E. Gross et al, Bondorf-Mishustin-Botvina, Hahn&Stoecker,... Expanding equilibrated source made of hot nuclei P or T spectator t=0 fm/c P

6. Similarity of conditions in nuclear reactions and supernova explosions I. Thermal multifragmentation of nuclei: Production of hot fragments at T≈ 3-8 MeV  ≈ (0.1 -0.3)  0 A chance to investigate properties of hot fragments in dense environment, which may differ from their ground state properties. II. Collapse of massive stars leading to Supernova II explosions: Production of hot nuclei in stellar matter at T≈ 1-10 MeV   0.3  0 Characteristic times (milliseconds) are very long for nuclear statistical equilibrium to be established. Properties of hot clustered nuclear matter may influence essentially the dynamics of collapse and explosions. Multifragmentation reactions and properties of hot stellar matter at sub-nuclear densities Botvina&Mishustin, PRC72 (2005) 048801

7. Statistical description of stellar matter calculations are done in a box containing 1000 baryons, density of individual fragments is fixed at

8. Nuclear statitical ensembles Grand Canonical version of SMM: Botvina, Mishustin et al., Sov. J. Nucl. Phys. 42 (1985) 712) <1

9. Mass distributions : SMSM, FYSS and HS (  /  0 =10 -1 ) (from talk of Nihal Buyukcizmeci) Various versions of the statistical model using “reasonable” assumptions on nuclear properties give very different results!

10. Isotopic distributions : 26 Fe

11. Evaluation of nuclear properties in stellar environments, i.e. at finite temperature (T), baryon density (ρ) and electron or lepton fraction (Y): 0<T<10 MeV, 10 -5 <ρ/ρ 0 <0.5, 0.1<Y<0.6. One should evaluate a) binding energies, b) excited states, c) decay probabilities of huge numbers of nuclei (1<A<1000, 0<Z<A), i. e. construct a “Nuclear Chart” for each set (T, ρ, Y). Existing nuclei represent only a very small subset at (0,0,0). Altogether up to 10 8 new “data” points should be calculated using any “reasonable” approach (LDM, HFB, RMF, CEFT, …) Such data are needed as inputs for a Statistical Model to find the most probable Nuclear Statistical Ensemble (NSE) in a specific stellar environment. Challenging task for nuclear community

12. This slide is borrowed from Valery Zagrebaev Nuclear Chart is not fully explored even at laboratory conditions

13. Wigner-Seitz approximation neutrons+electrons spherical nucleus deformed nucleus spherical celldeformed cell Requirements on the cells: 1) electroneutrality, 2) fixed average barion density and Z/A 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

14. Possible tool: R MF model + electrons First step: constant electron density Second step: self-consistent calculation parameter set: NL3 T. Buervenich, I. Mishustin and W. Greiner, Phys. Rev. C76 (2007) 034310; C. Ebel, U. Heinzmann, I. Mishustin, S. Schramm, work in progress

15. deformed ground state behind barrier charge density 240 Pu k F = 0.5 fm -1 =100 MeV 0.280.60 Nuclear structure calculations in uniform electron background

16. Nuclear chart in SN environments 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

17. Energy‏ of ellipsoidal deformation 1) Deformation becomes less favourable because of reduced Coulomb energy 2) Energy of isomeric state (or saddle point) goes up with n e

18. 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

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

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

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

22. 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.

23. Electrostatic properties of clustered matter Proton density parameterized by Woods-Saxon distribution, neutrons neglected, electrons treated “exactly” Claudio Ebel, Igor Mishustin, Walter Greiner, J.Phys. G42 (2015) 10, 105201

24. Modeling pasta phases in WZ approximation Spherical cell Cylindrical cell Cartesian cell 2) all cells have equal average baryon density and proton fraction 3) each cell has zero net charge, i. e. the number of protons (dark) is equal to the number of electrons (bright), i. e. Ye=Yp, and vice versa for inverse sapes 4) any interaction between the cells is neglected 1) The whole system is divided into cells of different geometry

25. R ealistic electron distributions Poisson equation for electrostatic potential Thomas-Fermi approximation Chemical potential from the normalization Boundary conditions

26. Results for droplet (left) and tube (right) Over the cell electron density changes up to 30  !

27. Results of numerical calculations Energy density – bulk contr.Optimum cell radius Standard sequence of shapes: droplets (d), rods (r), plates (p), tubes (t), bubbles ( b, uniform (u) Using realistic electron densities leads to lowering energies and shifting boundaries between different shapes d r p t b u Ye=0.3

28. Electron chemical potential Using realistic electron densities leads to lowering electron chemical potential up to 5 MeV!

29. 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. Using “exact” electron distributions may lead to a significant change of electron fraction (δμ~5 MeV)and shift of the inner crust boundary to deeper layers.