What nuclear multifragmentation reactions imply for modifications of the symmetry and surface energy in stellar matter Nihal Buyukcizmeci 1,2, A. Ergun 1, R. Ogul 1, A.S. Botvina 2,3, I.N. Mishustin 2,4 1 Selçuk University, Department of Physics, 42079, Konya Turkey 2 Frankfurt Institute for Advanced Studies, J.W. Goethe University, D Frankfurt am Main, Germany 3 Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia 4 Kurchatov Institute, Russian Research Center, Moscow, Russia NUFRA2015, October , Kemer, Antalya,Turkey CONTENT 1.Introduction 2.Statistical Model for Supernova Matter (SMSM) description 3.Discussion of the symmetry and surface energy terms for stellar matter 4.Conclusions

fragmentation of nuclear matter in nuclear reactions and astrophysical processes Thermal multifragmentation of nuclei: Production of hot fragments at T≈ 3-8 MeV  ≈ 0.1  0  0 =0.15 fm -3 = g cm -3 Interpretation: liquid-gas type phase transition in finite nuclei. A chance to investigate properties of hot fragments in dense environment of other nuclei and nucleons, which can be different from their ground state properties. Collapse of massive stars leading to Supernova II explosions: We expect production of hot fragments in nuclear matter at T≈ 1-10 MeV   0.3  0 Characteristic times of the processes are very large (miliseconds), nuclear equilibrium is expected. Properties of hot fragments influence processes during the collapse and explosions. This figure is taken from N. Buyukcizmeci et al, NPA 907 (2013)13-54.

3 Statisticle ensemble with fix T,  B, Y e Calculations in a box containing 1000 baryons, density of fragments is fixed at  0 =0.15 fm -3 All system is divided to Wigner-Seitz cells containing one nucleus, neutrons and electrons. 1  A   Z  A Statistical approach for supernova matter, SMSM:A.S. Botvina, I.N. Mishustin, NPA 843, 98 (2010) nuclear species (A,Z): electrons e - : neutrinos : Protons : Neutrons: Baryon number conservation:: Electrical neutrality: Lepton number conservation: trapped : free :

The total free energy density: The nucleon thermal wavelength: Excluded volume correction: Internal free energy of species (A,Z) ( A>4 ) : Bulk energy: Surface energy: Coulomb energy: Symmetry energy: Nucleons and light fragments Statistical approach for supernova matter, SMSM:A.S. Botvina, I.N. Mishustin, NPA 843, 98 (2010)

In the supernova environment, as compared to the nuclear reactions, several new important ingredients should be taken into consideration. 1.The matter at stellar scales must be electrically neutral and therefore electrons should be included to balance positive nuclear charge. 2.Energetic photons present in hot matter may change nuclear composition via photonuclear reactions. 3.The matter is irradiated by a strong neutrino wind from the protoneutron star. Using SMSM model, one can investigate the following conditions: (1) fixed lepton fraction Y L corresponding to a  -equilibrium with trapped neutrinos inside the neutrinosphere (early stage); (2) fixed electron fraction Ye but without  -equilibrium inside a hot bubble (early and intermediate times); Buyukcizmeci, Botvina, Mishustin, APJ 789 (2014) 33. (3) full  -equilibrium without neutrino (late times, after cooling and neutrino escape). Corresponding SMSM tables are under preparation.

SMSM EOS Table Buyukcizmeci, Botvina, Mishustin, APJ 789 (2014) fixed electron fraction Ye but without  -equilibrium inside a hot bubble (early and intermediate times)

SMSM HS FYSS 1  A  3311  A  1000 N. Buyukcizmeci, A.S. Botvina, I.N. Mishustin, R. Ogul, M. Hempel, J. Schaffner-Bielich, F.-K. Thielemann, S. Furusawa, K. Sumiyoshi, S. Yamada, H. Suzuki, NPA 907 (2013) SMSM:Statistical Model for Supernova Matter: A.S. Botvina, I.N. Mishustin, PLB 584 (2004)233,NPA 843, (2010) 98., Buyukcizmeci, Botvina, Mishutin, APJ 789 (2014)33. HS: M. Hempel and J.Schaffner-Bielich, NPA 837 (2010) 210. FYSS: S. Furusawa, S. Yamada, K. Sumiyoshi, H. Suzuki, APJ, 738 (2011) 178. The basic thermodynamical properties of stellar matter for T ≈ MeV, Ye ≈ and  /  0 ≈ have more or less similar behavior except higher  and lower T.

mass distributions : SMSM, FYSS and HS  /  0 =10 -1 significant differences between mass distributions of SMSM, HS and FYSS models especially at low electron fractions, low temperatures and high densities

Comparison of isotopic distributions : 8 O

10 1AGeV A γ=25 γ=15 Z/A The symmetry energy coefficient  was investigated in several independent experiments, which use both the isoscaling phenomenon and isotope distributions of fragments. G.Souliotis et al., PRC75 (2007) A.S.Botvina et al., PRC 72 (2005) Investigation of the symmetry energy term ALADIN: A. Le Fevre et al., Phys. Rev. Lett. 94, (2005).  =25  = 15 MeV

11 N. Buyukcizmeci, R. Ogul and A. S. Botvina, EPJ A 25, 57(2005). A.S. Botvina, N. Buyukcizmeci, et al., Phys. Rev. C 74, (2006) Influence of the symmetry energy in nuclear reactions N. Buyukcizmeci, H. Imal, R. Ogul, A. S. Botvina, I.N. Mishustin J. Phys. G: Nucl. Part. Phys. 39 (2012) MSU-:T.X. Liu, et al., Phys. Rev. C 69, (2004). CTM:C.B. Das, S. Das Gupta, W. Lynch, A. Mekjian and B. Tsang, Phys. Rep. 406, 1 (2005). Au

12 The data can be described only with the symmetry energy coefficient  ≈14 MeV. Isocaling : Yield ratio of neutron rich and neutron poor systems is given by: Here  and  are the isoscaling coeffficients The comparison with the experimental data of  (red line) shows that the symmetry term coefficient  should be  15 MeV. R. Ogul et al., Jour. Phys. G: Nucl.Part. Phys. 36, (2009) Theoretical and experimental data in nuclear multifragmentation reactions (symmetry energy coefficient  ) R. Ogul et al., Phys. Rev. C 83, (2011)

13 Influence of the symmetry energy term for stellar matter Buyukcizmeci N., A. S. Botvina, I. N. Mishustin, R. Ogul, Jour. Phys. Con. Ser. 202 (2010) N. Buyukcizmeci, R. Ogul and A. S. Botvina, EPJ A 25, 57(2005). A.S. Botvina, N. Buyukcizmeci, et al., Phys. Rev. C 74, (2006) Influence of the symmetry energy term on mass distributions nuclear reactions stellar matter For the stellar matter, with smaller symmetry energy (  =14) much more heavy nuclei may be formed, since they can accumulate more neutrons at lower temperatures and Ye. practically no influence

Considerable difference for  and 14 MeV at higher density fractions. Influence of the symmetry energy term on Xn, Xp, Xalpha and Xheavy in stellar matter

Properties of hot fragments: the surface energy term B 0 Z -τ analysis of IMF yields A.S.Botvina et al., PRC74(2006) projectiles with different isospin ALADIN SMM for single isolated nuclei: C -- Cameron mass formula (1957) MS -- Myers-Swiatecki mass formula (1966) (include separate volume and surface contributions to the symmetry energy) We obtain an evolution of the surface energy of hot fragments toward region of full multifragmentation

Influence of the surface energy term on mass distributions nuclear reactions stellar matter Even small variations of the surface energy coefficient B0 lead to considered changing in fragment production Similarty ! A.S.Botvina et al., PRC74(2006) This study

Even small variations of the surface energy coefficient B0 (from 18 to 20 MeV) lead to considered changing in fragment production at T=4 MeV. Variations of the surface energy coefficient B0 (from 16 to 20 MeV) lead to practically no effect Influence of the surface energy term on Xn, Xp, Xalpha and Xheavy in stellar matter

mass fractions of neutrons: SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

mass fractions of protons: SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

mass fractions of alphas : SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

mass fractions of heavy fragments(A>4): SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

Average mass numbers of heavier fragments A h (A >4 ):SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

Thermodynamical properties: SMSM, FYSS and HS Symmetry term  =14 MeV surface term B0=16, 20 MeV

It is expected to be fulfilled in certain situations like slow collapse of a massive star, late stages of a supernova explosion or in crusts of neutron stars. The  -equilibrium case can be a useful physical limit for theoretical estimates of the nuclear composition without full knowledge of weak reactions. Buyukcizmeci, Botvina, Mishutin, APJ 789 (2014)33. The SMSM allows for beta-equilibrium case calculations (Botvina &Mishustin 2004, 2010) and the corresponding tables of matter properties at baryon densities ρ = (10 −8 –0.32)ρ 0 and temperatures T = 0.2–25 MeV are under construction  -equilibrium in stellar matter (  e =  n -  p)

Influence of the symmetry and surface energy term in stellar matter  -equilibrium without neutrino (late times, after cooling and neutrino escape)

Lepton conservation calculations: netrinosphere distributions Influence of the symmetry and surface energy term in stellar matter

Symmetry term  =14 MeV surface term B0=16, 20 MeV Influence of the symmetry and surface energy term in stellar matter  -equilibrium without neutrino (late times, after cooling and neutrino escape)

29 1.Similar conditions of nuclear matter are reached in multifragmentation reactions and during the collapse and explosion of massive stars. 2.The statistical models successfully applied for nuclear multifragmentation can be generalized for astrophysical conditions. Nuclear parameters of the models, in particular, the symetry energy can be extracted from multifragmentation experiments. 3.Broad variety of nuclear species including, exotic and neutron rich nuclei, are produced in stellar matter. 4.Modification of liquid drop parameters of nuclei in dense hot medium can be important for rates of electro-weak reactions, and for synthesis of heavy elements. 5.The SMSM allows for beta-equilibrium case calculations and the corresponding tables of matter properties at baryon densities ρ = (10 −8 – 0.32)ρ 0 and temperatures T = 0.2–25 MeV are under construction. Important Results: connection of nuclear multifragmentation with astrophysics