Does anyone know how energetic the annihilation of neutrinos and antineutrinos is?

 

 

When bombarded with neutrons aluminum produces Al28 which decomposes via negative beta decay with a half life of 2.24mins. When bombarded with neutrons potassium produces K40 which decomposes via positive beta decay with a half life of 1.3 billion years, If one were to alloy aluminum with potassium(some element with a shorter half life on the beta source would probably be better) in a vacuum and bombard the alloy with a powerful neutron beam what is the probability of the neutrinos and antineutrinos produced during beta decay of the two elements colliding(not to mention the electrons and positrons produced in the same process)?

Take a look at this:

 

http://en.wikipedia.org/wiki/Double_beta_decay

 

It is not quite the same but almost. The Neutrinoless double-beta-decay experiments are trying to show the neutrino is its own antiparticle, but the rate for your experiment would be comparable to the rates they will get if their hypothesis is correct.