# Orbital angular momentum of nucleus?

For nuclei, I know that it is the $J^{\pi}$ that is usually measured/calculated, which is the spin-parity. I don't see "orbital angular momentum" of a nucleus very often. Now my notion of spin vs. orbital angular momentum is that spin is entirely instrisic, while orbital angular momentum is more of a classical characteristic (by movement/orbit in a bit more of a literal sense).

Do nuclei even have orbital angular momentum? Is their magnetic moment-like properties only derived from its spin-parity, or am I mistaken? What's really throwing me off is that spin is always in half-integer units, whereas orbital angular momentum is 'always' in whole-integer units.

• Couldn't it be that you confuse orbital angular momentum of the whole nucleus, with the orbital angular momentum of nucleons within the shell-model of nucleus? – Sofia Mar 9 '15 at 18:38
• That is very possible. – Arturo don Juan Mar 9 '15 at 23:11
• Could you explain what you mean by that? – Arturo don Juan Mar 9 '15 at 23:12
• See Bill N's answer. – Sofia Mar 9 '15 at 23:14
• Oh no I mean like how does one determine the orbital angular momentum of an entire nucleus going around, let's say, another entire nucleus? – Arturo don Juan Mar 9 '15 at 23:16

For a famous example of a nucleus with internal orbital angular momentum, consider the deuteron. Considerations of exchange symmetry, spin, and isospin demand that the deuteron have unit spin, rather than zero spin. However the pion-nucleon interaction, gleaned from neutron-proton scattering and deuteron formation, suggests that about 4% of the deuteron wavefunction is $D$-wave, with orbital angular momentum $L=2$. (The $P$-wave component, with $L=1$, would have negative parity, $(-1)^L$; the deuteron's parity is positive.)
The success of the nuclear shell model strongly supports that each nucleon has a spin-orbit ($\vec{j}$) angular momentum which it contributes, and like particles combine first. Each $j$ quantum number will be a half-integer, with like $|lj>$ pairs combining (in the energy ground state) to give zero spin contribution. All nuclei with even proton count (Z) and even neutron count (N=A-Z) have $0^+$ spin and parity in the ground state, the protons combining to zero and the neutrons combining to zero. All even-odds and odd-evens (referring to Z and N) have odd-half integer spin with a parity determined by the $l$ of the extra (odd) nucleon. Odd-odd nuclei have integer, usually non-zero, spin. The two half integer quantum numbers (from the odd proton and the odd neutron) combine for an integer.