Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
The main problem is to know by how much the νµ and ντ fluxes are different
at the neutrino sphere. Unfortunately, a realistic numerical simulation that
gives an estimate of the difference has never been performed so far.
6.3 Numerical results
The main goal of this section is to investigate numerically the effects that can
arise when the factorization Eq.(6.8) is not satisfied, by varying δ ∈ [0 ◦ , 180 ◦ ]
while we show results for δ = 180 ◦ when at such value the effects are maximal.
Following section 6.2, the results that we present here correspond to the following
possibilities:
a) Hνν = 0 and Vµτ = 0 with the condition Lνµ = Lντ;
b) Hνν = 0 and Vµτ = 0 with the condition Lνµ = Lντ;
c) Hνν = 0 and Vµτ = 0 with the condition Lνµ = Lντ .
The evolution equation
We decided to use the wave functions formalism in our numerical code since such
a code had been developed for the MSW case (Chapter 4). Note that, in such a
formalism, the writing of the neutrino-neutrino interaction Hamiltonian is more
complicated. As we know the ν − ν interaction Hamiltonian consists of diagonal
terms but also of terms that are off-diagonal, which are mainly responsible for
the new conversion behaviours,
We can rewrite Hνν as
⎛
Hνν = ⎝
Hνeνe Hνeνµ Hνeντ
Hνµνe Hνµνµ Hνµντ
Hντνe Hντνµ Hντντ
Hνν = D(r/Rν) Nνe + Nνµ + Nντ dq ′
⎞
⎠. (6.14)
(6.15)
The different terms Nνα in the Hamiltonian Hνν correspond to different initial
conditions since in the supernova, all neutrino flavours are created initially and
115