Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Luminosity (a.u.)
1e+13
8e+12
6e+12
4e+12
2e+12
0 20 40 60 80
Neutrino Energy (MeV)
Figure 3.3: Neutrino fluxes at the neutrinosphere: the curves show the Fermi-
Dirac distributions used for electron neutrinos with Tνe= 3.2 MeV (solid), electron
anti-neutrinos T¯νe= 4.8 MeV (dashed) and for the other flavors Tνx= 7.6
MeV (with νx = νµ, ντ, ¯νµ, ¯ντ) (dotted line).
Reaction Rates
As seen earlier, the dominant reactions that control the n/p ratio is the capture
reactions on free nucleons
νe + n ⇋ p + e − , (3.24)
and
¯νe + p ⇋ n + e + . (3.25)
In our calculation [26] (see chapter 5) we took a simplified formula 9 for the
reaction cross sections, namely [100]
and
σνe(Eνe) ≈ 9.6 × 10 −44
σ ¯νe(E ¯νe) ≈ 9.6 × 10 −44
2 Eνe + ∆np
cm
MeV
2 , (3.26)
2 E¯νe − ∆np
cm
MeV
2 , (3.27)
where ∆np ≈ 1.293 MeV is the neutron proton mass difference. The associated
rates can be written as [67]
dLν
λ = σ(E)ν dEν. (3.28)
dEν
9 Such cross sections can also be computed numerically exactly. For simplicity we ignored
weak magnetism and recoil corrections, which may be important [76].
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