To start off, if this write-up doesn't make much sense, it's not completely my fault.
Isospin is a sufficiently
abstract concept that most of the people I've met who study its effects for a living weren't able to explain it to me until I'd had three years of college-level
physics. (and I'm still not too sure whether I understand it or have just gotten used to hearing about it.)
Here's a try, though.
Neutrons and
protons are basically a lot more alike than they are different. Roughly the same
mass, similar interaction via the
weak nuclear force, etc. The major difference is in charge.
So at some point, some
genius thought to himself (I would add or herself, but it being early 1900s physics it was most likely a he), "What if they're really the same
particle in two different states?" When it turned out that
several other families of particles like this existed and that treating them this way led to some neat physics, isospin was born.
Thus, isospin is basically just a totally abstract concept to distinguish between
nucleons or other sets of particles in a given family. For nucleons, they decided it would be easiest to treat one state as +1/2 and the other as -1/2.
Establishing a convention for which was which, however, was a bit tricky. Usually arguments like this go on between physicists and
non-conformist chemists; this time, though, it was a sub-disciplinary battle. The particle physicists all thought that naturally, the positive
charge should get the positive isospin. In nuclear physics, however, it was more convenient the other way around -- to get the total isospin of a nucleus, it's necessary to add the isospins of all the neutrons to those of all the protons. Since nuclei usually have more neutrons, the total comes out positive if the neutrons get the +1/2.
These days, it seems that the
particle physicists won.
The major importance of isospin is that it leads to a new
symmetry (or
conservation law).
For reactions that take place primarily by
strong force mechanisms, the total isospin of the stuff pre-reaction has to equal the total isospin of the stuff post-reaction. (added in the ever-popular
quantum mechanics style, of course, where 1+2 can equal 3,2,or 1)
Some of the neat stuff going on in
nuclear physics these days involves examining what happens when
isospin is not conserved. (i.e.
weak nuclear force reactions)
(note: I'll gladly update this node should I ever reach a deeper insight into the nature of isospin.)