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

PhD. Progress report2 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 report3 Supernova II Supernova II - The death of a massive star Crab Nebula

PhD. Progress report4 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… ~1 sec ~100 msec

PhD. Progress report5 Schematic structure Proto-Neutron Star e  e Neutrinosphere T~4MeV  ~ g / cc shock “Hot Bubble” T~1-2MeV  ~ g / cc Envelope layers: Si, O, C, He … ~ 10% A=3, 4 nuclei ~70% A= 4 nuclei nucleosynthesis

PhD. Progress report6 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: ~ 10 MeV ~ 15 MeV ~ 20 MeV

PhD. Progress report7 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 report8 Nuclei below the shock The Hot Bubble: –Low density, high temperature. –Favors the creation of 4 He: “Alpha effect” Inelastic - 4 He reactions can diminish the effect. –Composition: 4 He, nucleons and electrons. –Haxton [1988]: Inelastic -nuclei reactions release a substantial amount of energy. Sufficient amount of  have enough energy to dissociate 4 He (~20 MeV). Near the newly born star, the temperature and density increases.

PhD. Progress report9 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, 3 He, . 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 report10 Equilibrium n,p,t, 3 He,  Abundances

PhD. Progress report11 Neutrino nucleosynthesis in the Helium layer Neutrino inelastic interactions with nuclei above the shock is a seed to nucleosynthesis. These neutrinos dissociate 4 He in the He layer. The A=3 nuclei fuse with 4 He to create 7 Li, through the chain of reactions: and Only neutral current reactions with 4 He are important, because of 4 He binding energy. Current knowledge of the neutrino sector indicates 1-3 neutrino flavor oscillations in the O/C layers. –Increases e energy, and increases nucleosynthesis through charged reactions. Energy dependent, accurate cross- sections are needed.

PhD. Progress report12 Calculating the cross-section

PhD. Progress report13 Neutrino-nucleus interaction lepton current Nuclear current

PhD. Progress report14 Nuclear Neutral Current Isovector Axial Vector Isoscalar Vector

PhD. Progress report15 Nuclear Charged Current Isovector Axial Vector

PhD. Progress report16 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 report17 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  – the theory cutoff. ( MeV) Write all the possible operators which agree with the symmetries of the underlying theory (QCD). Derivatives or pion masses nucleons order of interaction

PhD. Progress report18 Chiral Lagrangian (NLO)  -N basic interaction  Lagrangian  N of order 3 2N contact terms Calibrated using 3 H life time

PhD. Progress report19 Currents inside the nucleus The chiral Lagrangian has SU(2) axial and vector symmetries. The Nuclear Axial (vector) Current: Resulting one body operators – Same as in standard nuclear physics approach

PhD. Progress report20 Leading 1-body transition operators The closed shell character of 4 He, 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 report21 MEC – back to configuration space Usually we would use Fourier transform. But, operators are valid only up to a certain cutoff . We use the same approach as Park et al: Gaussian cutoff function

PhD. Progress report22 Remarks This approach gives the same scattering operators as in Park et. al. (PRC 67(2003), ). We are left with one unknown parameter: d r. This parameter is calibrated using the experimental triton half life.  Transition operators – done.

PhD. Progress report23 Advantages No free parameters.  dependence gives error estimation due to higher degrees of freedom.

PhD. Progress report24 Disadvantages In order to correctly describe light nuclei spectra, one has to expand the Hamiltonian at least to N 3 LO. The phenomenological Hamiltonians of SNPA are successful in doing so. Thus, MEEFT… [Rho 2006]

PhD. Progress report25 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, (2003)

PhD. Progress report26 –realistic NN potential: AV8’ or AV18. –realistic NNN potential: UIX (combined with AV18) The Nuclear Hamiltonian

PhD. Progress report27 Cross-section calculation Where the response functions, The initial and final states should be calculated using a model for the 4 He nucleus.

PhD. Progress report28 We define the LIT of R(  ) as LIT method

PhD. Progress report29 The LIT method substituting: using closure: where:

PhD. Progress report30 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 report31 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, (2001); Nucl. Phys. A, 693 (2001) 565.

PhD. Progress report32 4-body system with MT-V nucleon-nucleon potential MT-V nucleon-nucleon potential EIHH BARE Binding Energy Matter Radius

PhD. Progress report33 E exp = MeV

PhD. Progress report34 General remarks about the nuclear calculation The calculation is ab-initio: non-relativistic QM –frame work of non-relativistic QM. A Nucleons –explicit degrees of freedom: A Nucleons. nuclear potential excitation operators –only inputs are the nuclear potential and the excitation operators. As a check: –We reproduce d r (  ) from Park et. al. –We reproduce half-life calculations for 6 He, with AV18. EIHH LITThe combination of EIHH and LIT methods had been used to for calculating photo-disintegration and electron scattering processes for A=3,4,6,7.

PhD. Progress report35 Photoabsorption on 4 He 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 report36 Berman et al. ( ,n) 1980 Feldman et al. ( ,p) 1990 Wells et al Nilsson et al Shima et al He total photoabsorption cross-section with the realistic forces AV18+UIX. Gazit et. al., PRL 96, (2006) Gazit et. al., PRC 74, R (2006)

PhD. Progress report37 Neutrino scattering on A=3,4 nuclei Neutrino scattering on A=3,4 nuclei Results

PhD. Progress report38 Convergence of the calculation

PhD. Progress report39 MEC contribution Has quantitative effect only for GT (E 1 A ) due to symmetry relations. 4 He: –GT is suppressed due to closed shell character of . –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 report40 Inelastic neutral neutrino reactions on 4 He Woosley et. al, ApJ 356, 272 (1990) Haxton, PRL 60, 1999 (1988)

PhD. Progress report41 Energy transfer in reaction on 4 He and A=3

PhD. Progress report42 Energy transfer near the neutrinosphere

PhD. Progress report43 Conclusions A complete microscopic calculation of the neutral and charged neutrino scattering on 4 He, 3 H, 3 He was 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 4 He is the most abundant nuclei.

PhD. Progress report44 Publication summary (refereed journals) PRL, 96 (2006) “Photoabsorption on 4 He with a realistic nuclear force”, Doron Gazit, Sonia Bacca, Nir Barnea, Winfried Leidemann, Giuseppina Orlandini, PRL, 96 (2006) ”, PRC 74 (2006) “Photonuclear sum-rules and the tetrahedral configuration of 4 He”, Doron Gazit, Nir Barnea, Sonia Bacca, Winfried Leidemann, Giuseppina Orlandini, PRC 74 (2006) PRC 70 (2004) “Neutrino neutral reaction on 4 He, effects of final state interaction and realistic NN force “, Doron Gazit, Nir Barnea, PRC 70 (2004) “Low energy neutrino reactions on 4 He”, Doron Gazit, Nir Barnea, January 2007, PRL (Submitted for publication). 5.“Few-body calculation of neutrino neutral inelastic scattering on 4 He “, Doron Gazit, Nir Barnea, October 2007, Nucl. Phys. A (Submitted for publication). 6.“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). 7.“Low energy inelastic neutrino reactions on light nuclei”, Doron Gazit, Nir Barnea, in preparation.

PhD. Progress report45 storage

PhD. Progress report46 Cutoff dependence of 3 H cross-section

PhD. Progress report47 Choose  ( MeV) to calibrate the half life. calculations in this method experimentally AV18 + UIX Get d r (  ). Use d r (  ) to calculate MEC contribution in other reactions. 3 H half life

PhD. Progress report48 Effective Interaction in the Hyperspherical Harmonics method 1 st step: remove center of mass 2 nd step: introduce hyperspherical coordinates: 3 rd step: rewrite KE in hyperspherical coordinates:

PhD. Progress report49 Effective Interaction in the Hyperspherical Harmonics method HH functions are eigen-functions of the hyperspherical angular momentum operator K 2 4 th step: transform the HH basis into (anti) symmetric basis Expand WF in HH In many situations this expansion converges very slow. 5 th step: replace bare potential with an effective one, through the Lee-Suzuki similarity transformation: