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

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

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

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

AV18, Nijmegen, Bonn, etc.


Contents

  • Model for Hew

  • n-heatingin 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

★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

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

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

CC (absorption)

NC (scattering)

Thermal average


Result

Neutrino-deuteron 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 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 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)


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)


_

ne-emissivity

positron capture NN fusion

Q (e+n) > Q(e+ d) > Q (NNd)


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


_

(inner region

proto-neutron star)

ne-emissivity

NN brems

e+e-

_

npdne necan be very important !


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

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


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

  • 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


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

  • Current conservation for one-pion-exchange potential

  • VND coupling is fitted to np dg data


Comparison with np dg 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


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