Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Figure B.1: Neutrino energy levels in matter vs electron number density Ne. Dashed
line – in the absence of mixing, solid line – with mixing.
Coherently, if Phop is taken equal to 1, a non adiabatic transition occurs and the
matter eigenstates are mixed. On the contrary, if Phop = 0 the evolution will be
adiabatic. To finish with the behaviour of the considered neutrino, we illustrate
what we derived previously with the figure (B.1). We start at the right end of
the upper branch. We follow the adiabatic evolution of the matter eigenstate
νm2. Arriving at the resonance point, depending on the adiabaticity, either νm2
hops into the other matter eigenstate (Phop = 1) and the neutrino created as
electron neutrino will exit as an electron neutrino (left end of the lower branch)
or νm2 remains in its state (Phop = 0) and exits as a muon neutrino νµ (left
end of the upper branch). note that an adiabatic resonant conversion is the
present explanation of the ”solar neutrino deficit” problem first observed by R.
Davis. This phenomenon is known as the Mikheyev-Smirnov-Wolfenstein effect
(See section 1.2.1).
B.2 The adiabaticity parameter
We have just calculated an analytic oscillation probability formula, and tested it
in the two extreme limits of a completely adiabatic or a completely non-adiabatic
propagation. What would be interesting is to obtain a formula, even with some
approximation, for the more general and more frequent cases, where partial adiabaticity
is taken. As said at the beginning of the previous section, the adiabaticity
measures the difference of the eigenvalues of the effective matter hamiltonian
compared with the difference of the off-diagonal terms. A natural definition for
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