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A particle A decays into particles B, C and D. The spin of A, B and C particles is 1/2 each. What are the possible spins of particle D?

My attempt is the following:

Since B and C have spin 1/2 each, these can form singlet or a triplet. So the spin of D can only be 1/2 to get a spin of 1/2 for the decayed particle A. But the correct answer which is given is that D can have values like 1/2, 3/2, 5/2, 7/2.... Can any enlightened expert in Physics explain this please. his reaction looks like the decay of a neutron(A) into proton(B), electron(C) and anti-neutrino(D). So I believe my answer to be correct because neutrino has spin=1/2. I would still like confirmation of my reasoning from others.

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I've added the homework tag. In the future, please add this tag yourself on questions that are homework. – Ben Crowell Oct 9 '13 at 5:40
It's not clear in which case 'spin' means 'spin state' (current angular momentum projection) and which case 'spin' means 'property of a particle' (maximum possible angular momentum projection). Also, consider taking into account the orbit spin of the A,B,C system. – Andre Holzner Oct 9 '13 at 8:00

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