Stars as Laboratories for Fundamental Physics - MPP Theory Group

Oscillations of Trapped Neutrinos 311
neutrino flavor (say ν e ) scatters with a rate Γ while the other (say ν µ )
does not. An initial ν e will begin to oscillate into ν µ . The probability
for finding it in one of the two flavors evolves as previously discussed
and as shown in Fig. 9.1 (dotted line). However, in each collision the
momentum of the ν e component of the superposition is changed, while
the ν µ component remains unaffected. Thus, after the collision the two
flavors are no longer in the same momentum state and so they can no
longer interfere: each of them begins to evolve separately. This allows
the remaining ν e to develop a new coherent ν µ component which is made
incoherent in the next collision, and so forth. This process will come
into equilibrium only when there are equal numbers of ν e ’s and ν µ ’s.
This decoherence effect is even more obvious when one includes the
possibility of ν e absorption and production by charged-current reactions
ν e n ↔ pe. Because of oscillations an initial ν e is subsequently found
to be a ν µ with an average probability of 1 2 sin2 2θ (mixing angle θ)
and as such cannot be absorbed, or only by the reaction ν µ n ↔ pµ
if it has enough energy. The continuous emission and absorption of
1
ν e ’s spins off a ν µ with an average probability of
2 sin2 2θ in each
collision! Chemical relaxation of the neutrino flavors will occur with
an approximate rate 1 2 sin2 2θ Γ where Γ is a typical weak interaction
rate for the ambient physical conditions. An initial ν e population
turns into an equal mixture of ν e ’s and ν µ ’s as shown schematically
in Fig. 9.1 (solid line).
Fig. 9.1. Neutrino oscillations with collisions (solid line). In the absence
of collisions and for a single momentum one obtains periodic oscillations
(dotted line), while for a mixture of energies the oscillations are washed out
by “dephasing” (dashed line).