Development of a Liquid Scintillator and of Data ... - Borexino - Infn
Development of a Liquid Scintillator and of Data ... - Borexino - Infn
Development of a Liquid Scintillator and of Data ... - Borexino - Infn
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1 Solar Neutrinos<br />
Using the unitarity <strong>of</strong> the mixing matrix this can be written as<br />
Ø <br />
¬<br />
Í«Í ¬ Ø ¬ <br />
The transition amplitude « ¬ Ø is<br />
« ¬ Ø ¬ Ø <br />
<strong>and</strong> the transition probability<br />
È « ¬ Ø « ¬ Ø <br />
<br />
Í«Í ¬ Ø <br />
¬ <br />
<br />
Í«Í ¬ Ø<br />
For the case <strong>of</strong> relativistic neutrinos (Ô Ñ) we can use the approximation<br />
<br />
<strong>and</strong> write the transition probability as<br />
È « ¬ Ø <br />
¬<br />
Õ Ô Ñ Ô Ñ <br />
Ô<br />
¬ Æ«¬<br />
<br />
<br />
Í«Í ¬<br />
Ñ <br />
<br />
ÜÔ ¡Ñ Ä<br />
<br />
It is clear that flavour transitions can occur only if neutrino mixing exists (Í Á), <strong>and</strong> if at<br />
least one ¡Ñ .<br />
Oscillations in the Two-Neutrino Case<br />
In the simplest case <strong>of</strong> mixing only between two neutrino flavours the mixing matrix can be<br />
written as<br />
<br />
Ó× <br />
Í <br />
×Ò <br />
<br />
×Ò <br />
Ó× <br />
<strong>and</strong> the transition probability is given by<br />
<br />
Ä<br />
È « ¬ Ø ×Ò Ó× <br />
where ÄÓ× is the oscillation length<br />
ÄÓ× <br />
¡Ñ<br />
Î<br />
¡<br />
ÅÎ ¡Ñ<br />
Therefore the transition probability is a periodic function <strong>of</strong> Ä. This phenomenon is called<br />
neutrino oscillations. The oscillations can be observed if the oscillation length is not much<br />
larger than the distance source - detector<br />
12<br />
Ä ÄÓ× <br />
ÄÓ×<br />
Ñ <br />
<br />
¬<br />
¬ <br />
¬ ¬¬¬¬
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