Neutrino Reactions on the Deuteron
in Core-Collapse Supernovae
Satoshi NakamuraOsaka 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)
Neutrino reactions on the deuteron
Important relevance to neutrino physics, astrophysics
• Supernova ( -n heating, -n emission)
• -n oscillation experiment @ SNO
• Solar fusion (pp-chain)
Introduction
Calculational method
Well-established method for electroweak processes in few-nucleon systems
AV18, Nijmegen, Bonn, etc.
Contents
• Model for Hew
• -n heating in supernova
• -n emission in supernova
MODEL
Nuclear current
Impulse approximation (IA) current
Exchange axial-vector current
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)
★ nd-reactions ( , ) for SNO experiment SN et al. PRC 63 (2000) ; NPA707 (2002)
evidence of n-oscillation, solar n problem resolved
[1] Cargnelli et al. (1998)[2] Bardin et al. NPA 453 (1986)[3] Ackerbauer et al. PLB 417 (1998)
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
Abundance of light elements in supernovaSumiyoshi, Röpke, PRC 77, 055804 (2008)
15 M , 150 ms 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
Neutrino-deuteron cross sections
Result
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)
Thermal average of energy transfer cross sections
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)
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 profileSumiyoshi, 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)
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 (NNd)
Deuterons exit at the cost of the proton abundance + s (e- p) > s(e- d)
Effectively reduced ne emissivity less -n flux, n-heating, slower deleptonization & evolution of proto-neutron star
Need careful estimate of light element abundance & emissivity
ne-emissivity
positron capture NN fusion
ne-emissivity_
Q (e+ n) > Q(e+ d) > Q (NNd)
Change of ne emissivity due to deuteron
Q(N+d) / Q(N)
ne
ne
_
Mass fraction
d
p
Deuterons exit at the cost of the proton abundance + s (e- p) > s(e- d)
Effectively reduced ne emissivity
p (w.o. d fraction)
ne-emissivity_
(inner region proto-neutron star)
np dne ne can be very important !_
e+e-NN brems
nm-emissivity
Q (NN brem) ≈ Q (npd)
Whenever NN brem is important, npd can 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
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 np d nn can be very important for ne & nm emissivites
play a role comparable to NN bremsstrahlung & modified Urca
_ _
Summary
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
Backups
• Compilation I : Shen EoS, N, 4He, 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
Exchange vector current
★ Current conservation for one-pion-exchange potential
★ VN D coupling is fitted to np d g data
Comparison with np d g data
Exchange currents contribute about 10 %
Exchange axial charge
Kubodera, Delorme, Rho, PRL 40 (1978)
Soft pion theorem + PCAC
r(x) [fm-1] const.
Neutrino spectrum