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