dimensionless said:
That's a whole lot of empty space. Does this not happen with electrons because their electrical charge changes the direction of their path?
It's funny, but physics has a whole lot of ways of answering this question that are valid. The reason is that there are many different ways of making the calculation and many different ways of interpreting it.
One way of describing it is that electric charge is carried by a particle, the photon, that is massless. Since it is massless, it obeys an inverse square law.
Neutrinos have no electric charge, they can only interact weakly. Now electrons interact weakly too, but it is very weak compared to their electric charge interactions.
When I say that the interactions are "weak" I really don't mean that, technically, their coupling constants are all that different. Instead, the weak force is weak only because the carrier for it, the W and Z particles are not massless, and in fact have pretty high masses.
Because they have masses, the weak force is unlikely to travel very far. The reason for it being "unlikely" is because the energy to create such a massive particle has to be borrowed and under the Heisenberg uncertainty principle, a high amount of energy is likely to be be borrowed for only a very short amount of time, and therefore is unlikely to travel very far.
Now that all said, if it were the case that a neutrino was very energetic, then it would be a lot easier to borrow the energy for that W or Z particle, and then the neutrino would be a lot more likely to interact. Because of this, the neutrino "cross section", or apparent size, increases as the energy of the neutrino increases.
In fact, with some of the very high energy particle accelerators that are planned, there is a possibility that the neutrinos themselves could cause enough radiation that this radiation would be dangerous to human life. Part of the reason for the high radiation levels is because the higher energy neutrinos are more likely to collide, and part of the reason is because when they do collide, being high energy, they cause a bigger particle shower.
For this reason, the designers of these bigger particle accelerators are taking this into account in designing these machines:
http://www.arxiv.org/abs/physics/9908017
The above article also talks about how neutrino cross sections increase with energy.
Carl