Neutrinos are tiny, have no charge and are extremely weakly interactive. Detecting neutrinos relies upon the extremely unlikely event of a neutrino striking the nucleus of an atom directly resulting in the emission of light.
In crystals atoms are arranged in patterns. When we look through models of crystals we notice that at certain angles whole rows of atoms may be hidden from view because they are obscured by the first atom in the row. If a neutrino was to pass through the crystal at this angle it would be extremely unlikely that it would strike a nucleus.
However, we can also imagine that if we alter the angle that we are looking at the crystal by the very smallest amount then the atoms behind the first in the row gradually come into view. Thus, it must be true, that if a neutrino where to pass through a crystal there are certain angles of incidence that would result in a greater chance that it strike a nucleus.
If we could grow crystals of an appropriate material (ice?) large and ordered enough, then perhaps we could arrange them in such a way so as to maximize the potential for a collision along one particular angle of incidence at the expense of the rest and thus build a neutrino detector that could be pointed at potential sources of the particle.
It seems to me that you do not understand how the propagation and interaction of an elementary particle works. The scattering probability is not in fact a purely geometric problem. It is described in terms of "crossections" only to give us some tools similar to those we use on gas dynamics. Due to the uncertainty relation the of the particle is a line only form the general point of view. You can say that it can pass just through the nucleus without any interaction.
The probability of interaction of neutrino (as well as muon, electron and any other particle) depends not on the area of the surface but on density of material and the total length of such material. In case of neutrino the probability of interaction is better for light atoms, therefore the best candidate for target volume is water, which is used in the most spectacular experiments like Super-Kamiokande or Ice Cube.
Christopher,
there is a simple consideration: the energy of 1 electronvolt is the equivalent of about 11000 K. Even relic neutrinos have energy of few eV, and real neutrinos that one intended to measure form stars usually have energy about few MeV (a typical energy for nuclear reactions). From the point of view of neutrino, any temperature you can obtain on the Earth is about zero, so it does not make any difference.
The other point is a low temperature for your detecting equipment. It is well known that many background signals are lower for lower temperatures. So if you need to get very "clear" signal it sometimes necessary to lower the temperature of equipment.
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