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Neutrino Reactions on the Deuteron in Core-Collapse Supernovae

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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

Important relevance to neutrino physics, astrophysics

- Supernova (n-heating, n-emission)
- n-oscillation experiment @ SNO
- Solar fusion (pp-chain)

Well-established method for electroweak processes in few-nucleon systems

AV18, Nijmegen, Bonn, etc.

- Model for Hew
- n-heatingin supernova
- n-emission in supernova

Nuclear current

Impulse approximation (IA) current

★pp-fusion ( ) for solar model , Schiavilla et al. PRC 58 (1998)

- ★Muon capture ( , ) , Marcucciet al., PRC 83 (2011)
- [1] [2] [email protected]
- [3] Theory

[1] Cargnelli et al. (1998)

[2] Bardin et al. NPA 453 (1986)

[3] 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

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)

Sumiyoshi, Röpke, PRC 77, 055804 (2008)

15 M, 150ms after core bounce

Nuclear statistical equilibrium assumed

cf. Arcones et al. PRC 78, 015806 (2008)

CC (absorption)

NC (scattering)

Thermal average

Result

Neutrino-deuteron 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)

S. Nasu, SXN, T. Sato, K. Sumiyoshi, F. Myrer, K. Kubodera

arXiv:1402.0959

New agents

11 dimensional integral !!

Approximation necessary to evaluate Q

Approximation !

3 dimensional integral

- 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

_

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

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

Q (e+n) > Q(e+ d) > Q (NNd)

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)

NN brems

e+e-

_

npdne necan be very important !

Q (NN brem) ≈ Q (npd)

Whenever NN brem is important,

npdcan be also important

Possible important role

in proto-neutron star cooling

Large effect on NN fusion !

- 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

- 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

- Current conservation for one-pion-exchange potential
- VND coupling is fitted to np dg data

Exchange currents contribute about 10 %

Kubodera, Delorme, Rho, PRL 40 (1978)

Soft pion theorem + PCAC

r(x) [fm-1]

const.