Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
where we introduced the total proton loss rate λp = λ¯νe + λe− and the total
neutron loss rate λn = λνe + λe +. It has been shown that when the rates of
these processes are rapid as compared to the outflow rate a “weak chemical
equilibrium” is established [99]. The weak freeze-out radius is defined to be
where the neutron-to-proton conversion rate is less than the outflow rate of the
material. If the plasma reaches a weak equilibrium stage then Ye is no longer
changing: dYe/dt = 0. From Eq.(3.35) one can write the equilibrium value of the
electron fraction
+ 1 λp − λn
Xα. (3.36)
2
Ye = λn
λp + λn
λp + λn
At high temperatures alpha particles are absent and the second term in Eq.(3.36)
can be dropped10 . In the region just below where the alpha particles are formed
approximately one second after the bounce, the temperature is less then ∼ 1
MeV. Here both the electron and positron capture rates are very small and Ye
can be approximated as
Y (0)
e =
Using Eq. (3.32), we rewrite Eq. (3.37):
Y (0)
e (r) =
1 +
∞
0
∞
0
1
. (3.37)
1 + λ¯νe/λνe
σ¯νe(E) dL¯νe(r,E)
dE dE
σνe(E) dLνe(r,E)
dE dE
−1
. (3.38)
This is the formula we use in our numerical simulations (see chapters 4 and
6). Neutrino oscillations, since they can swap energies of different flavors, can
affect the energy-dependent rates in Eqs.(3.37) and (3.38), changing the electron
fraction. In the next chapter, we will show how CP-violation effects may impact
the electron neutrino and anti-neutrino fluxes, and consequently the electron
fraction.
10 At lower temperature the alpha particle mass fraction increases. Consequently free nucleons
get bound in alphas and cease interacting with neutrinos, because of the large binding energy
of the alpha particle. This phenomenon is called ”alpha effect”, it can increases the value of Ye
which implies fewer free neutrons, and therefore negatively impacts r-process nucleosynthesis
[118]. We do not consider the alpha effect in our numerical simulation, a future work should
include it.
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