1. Neutrino Reactions on the Deuteron in Core-Collapse Supernovae Satoshi Nakamura Osaka University Collaborators: S. Nasu, T. Sato (Osaka U.), K. Sumiyoshi (Numazu Coll. Tech.) F. Myhrer, K. Kubodera (U. of South Carolina) arXiv:1402.0959, PRC 80, 035802 (2009)

2. Neutrino reactions on the deuteron Important relevance to neutrino physics, astrophysics Supernova (  heating,  emission)  oscillation experiment @ SNO Solar fusion (pp-chain) Introduction

3. Calculational method Well-established method for electroweak processes in few-nucleon systems AV18, Nijmegen, Bonn, etc.

4. Contents Model for H ew  heating in supernova  emission in supernova

5. MODEL

7. Nuclear current

8. Impulse approximation (IA) current

9. Exchange axial-vector current

10. Most recent applications of the model to weak processes ★ Muon capture (, ), Marcucci et al., PRC 83 (2011) [1] [2] Theory MuSun@PSI [3] Theory ★ pp-fusion ( ) for solar model, Schiavilla et al. PRC 58 (1998) ★ d-reactions (, ) for SNO experiment SN et al. PRC 63 (2000) ; NPA707 (2002)  evidence of -oscillation, solar problem resolved [1] Cargnelli et al. (1998) [2] Bardin et al. NPA 453 (1986) [3] Ackerbauer et al. PLB 417 (1998)

11. SXN, K. Sumiyoshi, T. Sato, PRC 80, 035802 (2009) 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) Neutrino-deuteron reaction as heating mechanism in Supernova

13. Abundance of light elements in supernova Sumiyoshi, Röpke, PRC 77, 055804 (2008) 15 M , 150 ms after core bounce Nuclear statistical equilibrium assumed cf. Arcones et al. PRC 78, 015806 (2008)

14. Energy transfer cross section CC (absorption) NC (scattering) Thermal average

15. Neutrino-deuteron cross sections Result

16. Thermal average of energy transfer cross sections 3 H (  Arcones et al. PRC 78 (2008) 4 He(  : Haxton PRL 60 (1998) _ 3 He (   O’conner et al. PRC 78 (2007) 4 He (  : Gazit et al. PRL 98 (2007)

17. Thermal average of energy transfer cross sections

18. Electron capture on deuteron & NN fusion as neutrino emission mechanism S. Nasu, SXN, T. Sato, K. Sumiyoshi, F. Myrer, K. Kubodera arXiv:1402.0959

19. -emission previously considered (A≤2) New agents

20. Emissivity (Q)

21. 11 dimensional integral !! Approximation necessary to evaluate Q

22. Emissivity (Q) Approximation ! 3 dimensional integral

23. Previous common approximation to evaluate Q NN-brem One-pion-exchange potential, Born approximation Low-energy theorem Neglect momentum transfer ( )  also angular correlation between and Nuclear matrix element  long wave length limit  constant _

24. Supernova profile Sumiyoshi, Röpke, PRC 77, 055804 (2008) 150 ms after core bounce Nuclear statistical equilibrium assumed

25. 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)

26.  electron capture NN fusion e - p, e + e - : Bruenn, ApJS 58 (1985) NN brem: Friman et al, ApJ 232 (1979) Q (e - p) > Q(e - d) > Q (NN  d) Deuterons exit at the cost of the proton abundance +  (e - p) >  (e - d)  Effectively reduced e  emissivity  less  flux, -heating, slower deleptonization & evolution of proto-neutron star  Need careful estimate of light element abundance & emissivity e -emissivity

27.  positron capture NN fusion e -emissivity _ Q (e + n) > Q(e + d) > Q (NN  d)

28. Change of e emissivity due to deuteron Q(N+d) / Q(N) e e _ Mass fraction d p Deuterons exit at the cost of the proton abundance +  (e - p) >  (e - d)  Effectively reduced e  emissivity p (w.o. d fraction)

29. e -emissivity _ (inner region proto-neutron star) np  d e  e  can be very important ! _ e+e-e+e- NN brems

30.  -emissivity Q (NN brem) ≈ Q (np  d) Whenever NN brem is important, np  d can be also important  Possible important role in proto-neutron star cooling

31. Meson exchange current effect on Q Large effect on NN fusion !

32. 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

33. Deuteron breakup ( -heating) & formation ( -emission) in SN Framework : NN wave functions based on high-precision NN potential + 1 & 2-body nuclear weak currents (tested by data) -heating: Substantial abundance of light elements (NSE model) for deuteron : much larger than those for 3 H, 3 He, 4 He 25-44% of for the nucleon Summary

34. -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 e emissivity  Need careful estimate of light element abundance & emissivity NN fusions  np  d  can be very important for e &  emissivites  play a role comparable to NN bremsstrahlung & modified Urca _ _ Summary

35. 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

36. Backups

37. Compilation I : Shen EoS, N, 4 He, a heavy nucleus Compilation II : light elements abundance from Sumiyoshi & Röpke (2008) Both have the same density, temperature, electron fraction Emissivites from direct Urca, e + e - annihilation, NN brems  compilation I Emissivites from election captures on d & NN fusion  compilation II

38. Exchange vector current ★ Current conservation for one-pion-exchange potential ★ VN  coupling is fitted to np  d  data

39. Comparison with np  d  data Exchange currents contribute about 10 %

40. Exchange axial charge Kubodera, Delorme, Rho, PRL 40 (1978) Soft pion theorem + PCAC

41.  ( x ) [fm -1 ] const.

43. Neutrino spectrum

44. Supernova profile densitytemperature Sumiyoshi, Röpke, PRC 77, 055804 (2008)