undergrad nuclear physics; spin parity rules

grady

Chapter 3 #17 (Krane) The spin-parity of ⁹Be and ⁹B are both 3/2^-. Assuming in both cases that the spin and parity are characteristic only of the odd nucleon, show how it is possible to obtain the observed spin-parity of ¹⁰B(3⁺). What other spin-parity combinations could also appear? (These are observed as excited states of ¹⁰B.)

Here's what I think I know. The parity is (-1)^l. So for ⁹Be and ⁹B, l = 1. It makes sense that these two nuclei have half-integer spin because A = 9 is odd. It makes sense that ¹⁰B has integer spin because A = 10 is even. The fact they're telling me to consider the spin and parity is charactersitic of the odd nucleon is supposed to be hinting at something, but I'm not sure what. I realize ⁹Be has an extra neutron and one less proton than ⁹B, but I don't know if I'm supposed to be getting any useful information from the fact that the unpaired particle is a proton in one case and a neutron in the other. If anyone can fill in any of these blanks for me, I would appreciate it.

Aside from this question, and in general, I'm confused about how nucleons pair off and have their spin cancel out with other nucleons. From what I've heard in class so far even numbers of nucleons should just pair off and leave nuclei with either 0 or 1/2 spin. :(

Tom Mattson

I don't think there's anything to that, since J^P for both p and n are both (1/2)⁺.

That would be true if only the nucleon spin were taken into account. However, the orbital angular momentum of the odd nucleon is seen from the outside as nuclear spin. So, for instance, if an odd proton is spin-up in the p-shell with m_l=1, then the whole nucleus is in a spin-3/2 state.