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.)

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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

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)


Neutrino reactions on the deuteron

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

Calculational method

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

AV18, Nijmegen, Bonn, etc.


Contents

Contents

  • Model for Hew

  • n-heatingin supernova

  • n-emission in supernova


Model

MODEL


Neutrino reactions on the deuteron in core collapse supernovae

Nuclear current


Neutrino reactions on the deuteron in core collapse supernovae

Impulse approximation (IA) current


Exchange axial vector current

Exchange axial-vector current


Most recent applications of the model to weak processes

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)

  • [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


Neutrino deuteron reaction as heating mechanism in supernova

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

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

Energy transfer cross section

CC (absorption)

NC (scattering)

Thermal average


Neutrino reactions on the deuteron in core collapse supernovae

Result

Neutrino-deuteron cross sections


Thermal average of energy transfer 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)


Thermal average of energy transfer cross sections1

Thermal average of energy transfer cross sections


Electron capture on deuteron nn fusion as neutrino emission mechanism

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

n-emission previously considered (A≤2)

New agents


Emissivity q

Emissivity (Q)


Emissivity q1

Emissivity (Q)

11 dimensional integral !!

Approximation necessary to evaluate Q


Emissivity q2

Emissivity (Q)

Approximation !

3 dimensional integral


Previous common approximation to evaluate q nn brem

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

Supernova profile

Sumiyoshi, Röpke, PRC 77, 055804 (2008)

150 ms after core bounce

Nuclear statistical equilibrium assumed


Neutrino reactions on the deuteron in core collapse supernovae

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

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 (NNd)


Positron capture nn fusion

_

ne-emissivity

positron capture NN fusion

Q (e+n) > Q(e+ d) > Q (NNd)


Change of n e emissivity due to deuteron

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


N e emissivity

_

(inner region

proto-neutron star)

ne-emissivity

NN brems

e+e-

_

npdne necan be very important !


N m emissivity

nm-emissivity

Q (NN brem) ≈ Q (npd)

Whenever NN brem is important,

npdcan be also important

Possible important role

in proto-neutron star cooling


Meson exchange current effect on q

Meson exchange current effect on Q

Large effect on NN fusion !


Why so large meson exchange current effect

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


Neutrino reactions on the deuteron in core collapse supernovae

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


Neutrino reactions on the deuteron in core collapse supernovae

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dnncan be very important for ne & nmemissivites

 play a role comparable to NN bremsstrahlung & modified Urca


Future work

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

Backups


Neutrino reactions on the deuteron in core collapse supernovae

Emissivites from direct Urca, e+e- annihilation, NNbremscompilation 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

Exchange vector current

  • Current conservation for one-pion-exchange potential

  • VND coupling is fitted to np dg data


Comparison with np d g data

Comparison with np dg data

Exchange currents contribute about 10 %


Exchange axial charge

Exchange axial charge

Kubodera, Delorme, Rho, PRL 40 (1978)

Soft pion theorem + PCAC


Neutrino reactions on the deuteron in core collapse supernovae

r(x) [fm-1]

const.


Neutrino spectrum

Neutrino spectrum


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