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

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






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


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)



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 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


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


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 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



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


r(x) [fm-1]

const.



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