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Electro-Weak Reactions on light nuclei * in supernovae

This progress report discusses the role of neutrino reactions with nuclei in various fields of physics, including astrophysics and particle physics. It explores open questions in astrophysics, such as the core collapse supernovae explosion mechanism, and nucleosynthesis in supernovae.

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Electro-Weak Reactions on light nuclei * in supernovae

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  1. March 2007 Electro-Weak Reactions on light nuclei*in supernovae Electro-Weak Reactions on light nuclei*in supernovae Doron Gazit progress report talk Supervisor: Prof. Nir Barnea.

  2. Neutrino reactions with nuclei play major role in various fields of Physics. Astrophysics,particle physics… Open questions in Astrophysics: Core collapse Supernovae explosion mechanism. Nucleosyntesis in Supernovae. Introduction PhD. Progress report

  3. Supernova II- The death of a massive star Crab Nebula PhD. Progress report

  4. ~1 sec ~100 msec The death of a massive star“the nuclear physicist paradigm” After millions of years of evolving… • Iron peak nuclei don’t burn to heavier nuclei  no support to the core mass. • The core becomes gravitationally unstable collapses. • Nuclear forces halt the collapse, and drive an outgoing shock. • The shock loses energy due to dissociation, neutrino radiation. • The shock stalls… PhD. Progress report

  5. ne nm,t nm,t ne Proto-Neutron Star Schematic structure Envelope layers: Si, O, C, He … n nucleosynthesis “Hot Bubble” T~1-2MeV r~107-109 g/cc Neutrinosphere T~4MeV r~1011-1012 g/cc shock ~70% A= 4 nuclei ~ 10% A=3, 4 nuclei PhD. Progress report

  6. ~ ~ ~ 10 MeV 15 MeV 20 MeV n wind from the newly born PNS • Carry 99% of the explosion energy. • Produced almost in flavor equilibrium inside the hot collapsed core (proto-neutron star). • Due to charged current reactions on electrons: PhD. Progress report

  7. n wind from the newly born PNS • Influence all the important processes: • Deposit energy in matter below the shock, to determine shock radius. • Set neutron richness in the hot bubble, to initiate the r process. It also fragments synthesized heavy nuclei. These processes can be affected by the existence of nuclei in the shocked region PhD. Progress report

  8. Nuclei below the shock • The Hot Bubble: • Low density, high temperature. • Favors the creation of 4He: “Alpha effect” • Inelastic n-4He reactions can diminish the effect. • Composition: 4He, nucleons and electrons. • Haxton [1988]: • Inelastic n-nuclei reactions release a substantial amount of energy. • Sufficient amount of nm,t have enough energy to dissociate 4He (~20 MeV). • Near the newly born star, the temperature and density increases. PhD. Progress report

  9. Abundances of A=3,4 nuclei near the neutrinosphere • The neutrinosphere is too dense to use simple NSE. • Virial expansion extends NSE and includes the inter-particle scatterings. • We wrote a virial EOS which includes: p, n, t, 3He, a. • The abundances are then derived from the EOS. “Neutrino Breakup of A=3 Nuclei in Supernova”, E. O’Connor, D. Gazit, C. J. Horowitz, A. Schwenk, N. Barnea, PRC (submitted for publication). PhD. Progress report

  10. Equilibrium n,p,t,3He,a Abundances PhD. Progress report

  11. Neutrino nucleosynthesis in the Helium layer • Neutrino inelastic interactions with nuclei above the shock is a seed to nucleosynthesis. • These neutrinos dissociate 4He in the He layer. • The A=3 nuclei fuse with 4He to create 7Li, through the chain of reactions: and • Only neutral current reactions with 4He are important, because of 4He binding energy. • Current knowledge of the neutrino sector indicates 1-3 neutrino flavor oscillations in the O/C layers. • Increases ne energy, and increases nucleosynthesis through charged reactions. Energy dependent, accurate cross-sections are needed. PhD. Progress report

  12. Calculating the cross-section PhD. Progress report

  13. Neutrino-nucleus interaction lepton current Nuclear current PhD. Progress report

  14. Isovector Axial Vector Isoscalar Vector Nuclear Neutral Current PhD. Progress report

  15. Isovector Axial Vector Nuclear Charged Current PhD. Progress report

  16. Construction of the nuclear currents • The leading operators are one-body operators. • It is well known that Mesonic degrees of freedom influence the scattering process. • Conservation of Vector currents means that in low momentum transfer the vector one body operators include Meson exchange currents. • Axial MEC should be calculated explicitly. • Effective Field Theory – a modern perturbative way to construct the many body currents. PhD. Progress report

  17. EFT systematics • Identify Q – the energy scale of the process. (for SN – few 10’s of MeV) • In view of Q -Identify the relevant degrees of freedom. (I use pions and nucleons). • Choose L – the theory cutoff. (400-800 MeV) • Write all the possible operators which agree with the symmetries of the underlying theory (QCD). nucleons order of interaction Derivatives or pion masses PhD. Progress report

  18. Chiral Lagrangian (NLO) p-N basic interaction p Lagrangian p-N of order 3 2N contact terms Calibrated using 3H life time PhD. Progress report

  19. Leading 1-body transition operators • The closed shell character of 4He, suppresses the usually leading: • Gamow-Teller operator. • Fermi operator. • The leading operators are proportional to the momentum transfer. • Higher multipoles, relativistic corrections, contribute less than 1%. PhD. Progress report

  20. MEC – back to configuration space • Usually we would use Fourier transform. • But, operators are valid only up to a certain cutoff L. • We use the same approach as Park et al: Gaussian cutoff function PhD. Progress report

  21. Remarks • This approach gives the same scattering operators as in Park et. al.(PRC 67(2003), 055206). • We are left with one unknown parameter: dr. • This parameter is calibrated using the experimental triton half life.  Transition operators – done. PhD. Progress report

  22. Advantages • No free parameters. • L dependence gives error estimation due to higher degrees of freedom. PhD. Progress report

  23. Disadvantages • In order to correctly describe light nuclei spectra, one has to expand the Hamiltonian at least to N3LO. • The phenomenological Hamiltonians of SNPA are successful in doing so. • Thus, MEEFT… [Rho 2006] PhD. Progress report

  24. Hybrid EFT-SNPA • We use a hybrid approach: • Nuclear Hamiltonian – phenomenological. • Standard nuclear physics (SNPA) WF. • MEC transition operators – EFT. • This approach was used to calculate:and gave same results as standard nuclear physics. Park et. al., PRC 67, 055206 (2003) PhD. Progress report

  25. The Nuclear Hamiltonian • realistic NN potential: AV8’ or AV18. • realistic NNN potential: UIX (combined with AV18) PhD. Progress report

  26. Cross-section calculation Where the response functions, The initial and final states should be calculated using a model for the 4He nucleus. PhD. Progress report

  27. LIT method We define the LIT of R(w) as PhD. Progress report

  28. The LIT method substituting: using closure: where: PhD. Progress report

  29. Therefore we have to solve the Schroedinger like equations: Few Remarks: • There is no solution to the homogeneous equation. • The boundary conditions are of a bound state. • Assures full final state interaction. HOW DO WE SOLVE FOR WFs? Efros, Leidemann & Orlandini, PLB 408, 1 (1994) PhD. Progress report

  30. Effective Interaction in the Hyperspherical Harmonics method • The HH - eigenfunctions of the kinetic energy operator, with quantum number K. • We expand the WF in (anti) symmetrized HH. • Use Lee-Suzuki transformation to replace the bare potential with an effective one. Barnea, Leidemann, Orlandini, PRC, 63 057002 (2001); Nucl. Phys. A, 693 (2001) 565. PhD. Progress report

  31. Binding Energy EIHH BARE 4-body system with MT-V nucleon-nucleon potential Matter Radius PhD. Progress report

  32. Eexp=28.296 MeV PhD. Progress report

  33. General remarks about the nuclear calculation • The calculation is ab-initio: • frame work of non-relativistic QM. • explicit degrees of freedom: A Nucleons. • only inputs are the nuclear potential and the excitation operators. • As a check: • We reproduce dr(L) from Park et. al. • We reproduce half-life calculations for 6He, with AV18. • The combination of EIHHand LIT methods had been used to for calculating photo-disintegration and electron scattering processes for A=3,4,6,7. PhD. Progress report

  34. Photoabsorption on 4He • The scattering operator at low energy is: • Due to Siegert Theorem, at low energy it includes MEC contribution: • Model independent check of underlying degrees of freedom. • Test of Nuclear Hamiltonian in the continuum. PhD. Progress report

  35. 4He total photoabsorption cross-section with the realistic forces AV18+UIX. Berman et al. (g,n) 1980 Feldman et al. (g,p) 1990 Wells et al. 1992 Nilsson et al. 2005 Shima et al. 2005 Gazit et. al., PRL 96, 112301 (2006) PhD. Progress report Gazit et. al., PRC 74, 061001R (2006)

  36. Neutrino scattering on A=3,4 nucleiResults PhD. Progress report

  37. Convergence of the calculation PhD. Progress report

  38. MEC contribution • Has quantitative effect only for GT (E1A) due to symmetry relations. • 4He: • GT is suppressed due to closed shell character of a. • Without MEC, GT contributes less than 1% of CRS in case of AV18+UIX calculation. GT triples due to MEC. • MEC contribution to CRS: 1.5%. • Cutoff dependence of CRS: 0.5% (error estimation). • A=3: • GT contributes 50% for T=1MeV, and decreases quickly to 5% for T=10 MeV. • MEC contribution to CRS: 16% for T=1 MeV. Decreases gradually… • MEC contribution to CRS: 1% for T=10 MeV. • Cutoff dependence of CRS: 1% (error estimation). PhD. Progress report

  39. Inelastic neutral neutrino reactions on 4He Woosley et. al, ApJ 356, 272 (1990) Haxton, PRL 60, 1999 (1988) PhD. Progress report

  40. Energy transfer in n reaction on 4He and A=3 PhD. Progress report

  41. Energy transfer near the neutrinosphere PhD. Progress report

  42. Conclusions • A complete microscopic calculation of the neutral and charged neutrino scattering on 4He, 3H, 3Hewas accomplished: • Full final state interaction (via LIT). • Different realistic potentials were considered, including modern 3NF. • Axial MEC, EFT* based, were included. • The numerical accuracy is less than 1%. • We estimate CRS to be accurate to 5%: • Small cutoff dependence – EW model is accurate to 1%. • Sensitivity to nuclear potential. • We find that A=3 nuclei can be important in the neutrinosphere area. • The work makes an important step towards a more robust and reliable microscopic description of the area below the shock, in which 4He is the most abundant nuclei. PhD. Progress report

  43. Publication summary (refereed journals) • “Photoabsorption on 4He with a realistic nuclear force”, Doron Gazit, Sonia Bacca, Nir Barnea, Winfried Leidemann, Giuseppina Orlandini, PRL, 96 (2006) 112301. • “Photonuclear sum-rules and the tetrahedral configuration of 4He”,Doron Gazit, Nir Barnea, Sonia Bacca, Winfried Leidemann, Giuseppina Orlandini, PRC 74 (2006) 061001. • “Neutrino neutral reaction on 4He, effects of final state interaction and realistic NN force “, Doron Gazit, Nir Barnea, PRC 70 (2004) 048801. • “Low energy neutrino reactions on 4He”, Doron Gazit, Nir Barnea, January 2007, PRL (Submitted for publication). • “Few-body calculation of neutrino neutral inelastic scattering on 4He “,Doron Gazit, Nir Barnea, October 2007, Nucl. Phys. A (Submitted for publication). • “Neutrino Breakup of A=3 Nuclei in Supernova", E. O'Connor, Doron Gazit, C. J. Horowitz, A. Schwenk, N. Barnea, February 2007, PRC (submitted for publication). • “Low energy inelastic neutrino reactions on light nuclei”, Doron Gazit, Nir Barnea, in preparation. PhD. Progress report

  44. storage PhD. Progress report

  45. Cutoff dependence of 3H cross-section PhD. Progress report

  46. calculations in this method 3H half life experimentally AV18 + UIX Choose L (400-700 MeV) to calibrate the half life. Get dr(L). Use dr(L) to calculate MEC contribution in other reactions. PhD. Progress report

  47. Effective Interaction in the Hyperspherical Harmonics method • 1st step: remove center of mass • 2nd step: introduce hyperspherical coordinates: • 3rd step: rewrite KE in hyperspherical coordinates: PhD. Progress report

  48. Effective Interaction in the Hyperspherical Harmonics method HH functions are eigen-functions of the hyperspherical angular momentum operator K2 4th step: transform the HH basis into (anti) symmetric basis Expand WF in HH In many situations this expansion converges very slow. 5th step: replace bare potential with an effective one, through the Lee-Suzuki similarity transformation: PhD. Progress report

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