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Neutrino Reactions on the Deuteron in Core-Collapse Supernovae . arXiv: 1402.0959, PRC 80, 035802 (2009 ). Satoshi Nakamura Osaka University. Collaborators: S. Nasu , T. Sato (Osaka U.), K. Sumiyoshi (Numazu Coll. Tech.)
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Neutrino Reactions on the Deuteron in Core-Collapse Supernovae arXiv:1402.0959, PRC 80, 035802 (2009) Satoshi Nakamura Osaka University Collaborators: S. Nasu, T. Sato (Osaka U.), K. Sumiyoshi (Numazu Coll. Tech.) F. Myhrer, K. Kubodera (U. of South Carolina)
Introduction Neutrino reactions on the deuteron Important relevance to neutrino physics, astrophysics • Supernova (n-heating, n-emission) • n-oscillation experiment @ SNO • Solar fusion (pp-chain)
Calculational method Well-established method for electroweak processes in few-nucleon systems AV18, Nijmegen, Bonn, etc.
Contents • Model for Hew • n-heatingin supernova • n-emission in supernova
Most recent applications of the model to weak processes ★pp-fusion ( ) for solar model , Schiavilla et al. PRC 58 (1998) • ★Muon capture ( , ) , Marcucciet al., PRC 83 (2011) •   TheoryMuSun@PSI •  Theory  Cargnelli et al. (1998)  Bardin et al. NPA 453 (1986)  Ackerbauer et al. PLB 417 (1998) • nd-reactions ( , ) for SNO experiment • SN et al. PRC 63 (2000) ; NPA707 (2002) • evidence ofn-oscillation, solar nproblem resolved
Neutrino-deuteron reaction as heating mechanism in Supernova In many simulations, supernova doesn’t explode ! extra assistance needed for re-accelerating shock-wave ★neutrino absorption on nucleon (main) ★neutrino scattering or absorption on nuclei (extra agent) SXN, K. Sumiyoshi, T. Sato, PRC 80, 035802 (2009)
Abundance of light elements in supernova Sumiyoshi, Röpke, PRC 77, 055804 (2008) 15 M, 150ms after core bounce Nuclear statistical equilibrium assumed cf. Arcones et al. PRC 78, 015806 (2008)
Energy transfer cross section CC (absorption) NC (scattering) Thermal average
Result Neutrino-deuteron cross sections
Thermal average of energy transfer cross sections _ 3H (n) : Arcones et al. PRC 78 (2008) 4He(n) : Haxton PRL 60 (1998) 3He (n): O’conner et al. PRC 78 (2007) 4He (n) : Gazit et al. PRL 98 (2007)
Electron capture on deuteron & NN fusion as neutrino emission mechanism S. Nasu, SXN, T. Sato, K. Sumiyoshi, F. Myrer, K. Kubodera arXiv:1402.0959
n-emission previously considered (A≤2) New agents
Emissivity (Q) 11 dimensional integral !! Approximation necessary to evaluate Q
Emissivity (Q) Approximation ! 3 dimensional integral
Previous common approximation to evaluate QNN-brem • One-pion-exchange potential, Born approximation Low-energy theorem • Neglect momentum transfer ( ) • also angular correlation between n and n • Nuclear matrix element long wave length limit constant _
Supernova profile Sumiyoshi, Röpke, PRC 77, 055804 (2008) 150 ms after core bounce Nuclear statistical equilibrium assumed
Result • Surface region of proto-neutron star • Inner region of proto-neutron star • Deuteron can be largely modified, or even doesn’t exist • ”deuteron” as two-nucleon correlation in matter • More elaborate approach based on thermodynamic Green’s function • (S. Nasu, PhD work in progress)
ne-emissivity electron capture NN fusion Deuterons exit at the cost of the proton abundance + s(e- p) > s(e- d) Effectively reduced neemissivity less n-flux, n-heating, slower deleptonization & evolution of proto-neutron star Need careful estimate of light element abundance & emissivity e-p, e+e-: Bruenn, ApJS 58 (1985) NN brem: Frimanet al, ApJ 232 (1979) Q (e- p) > Q(e- d) > Q (NNd)
_ ne-emissivity positron capture NN fusion Q (e+n) > Q(e+ d) > Q (NNd)
Change of ne emissivity due to deuteron Q(N+d) / Q(N) Mass fraction _ ne p (w.o. d fraction) p ne d Deuterons exit at the cost of the proton abundance + s(e- p) > s(e- d) Effectively reduced neemissivity
_ (inner region proto-neutron star) ne-emissivity NN brems e+e- _ npdne necan be very important !
nm-emissivity Q (NN brem) ≈ Q (npd) Whenever NN brem is important, npdcan be also important Possible important role in proto-neutron star cooling
Meson exchange current effect on Q Large effect on NN fusion !
Why so large meson exchange current effect ? • Higher NN kinetic energy causes large exchange current effect • Axial exchange current & higher partial waves are important ; uncertainty
Summary Deuteron breakup (n-heating) & formation (n-emission) in SN Framework : NN wave functions based on high-precision NN potential + 1 & 2-body nuclear weak currents (tested by data) n-heating: Substantial abundance of light elements (NSE model) for deuteron : much larger than those for 3H, 3He, 4He 25-44% of for the nucleon
Summary n-emission: New agents other than direct & modified Urca, NN bremsstrahlung Emissivities Rigorous evaluation of nuclear matrix elements No long wave length limit, no Born approximation Electron captures effectively reduced ne emissivity Need careful estimate of light element abundance & emissivity _ _ NN fusions npdnncan be very important for ne & nmemissivites play a role comparable to NN bremsstrahlung & modified Urca
Future work • Similar calculations of emissivites for modified Urca • NN bremsstrahlung • rigorous few-body calculation is still lacking SN et al. in progress • Elaborate treatment for nuclear medium effects • Thermodynamic Green’s function approach (S. Nasu, PhD work in progress) Useful information for supernova and neutron star cooling simulations
Emissivites from direct Urca, e+e- annihilation, NNbremscompilation I Emissivites from election captures on d & NN fusion compilation II • Compilation I : ShenEoS, N, 4He, a heavy nucleus • Compilation II : light elements abundance from Sumiyoshi & Röpke (2008) Both have the same density, temperature, electron fraction
Exchange vector current • Current conservation for one-pion-exchange potential • VND coupling is fitted to np dg data
Comparison with np dg data Exchange currents contribute about 10 %
Exchange axial charge Kubodera, Delorme, Rho, PRL 40 (1978) Soft pion theorem + PCAC
r(x) [fm-1] const.