Discussion
In the nuclear shell model, orbitals are filled in the following order \({}^{1}s_{1/2}\), \({}^{1}p_{3/2}\), \({}^{1}p_{1/2}\), \({}^{1}d_{5/2}\), \({}^{2}s_{1/2}\), \({}^{1}d_{3/2}\), .......... etc. The splitting between the \(p_{3/2}\) and \(p_{1/2}\) orbitals is caused by :
Answer: C
The splitting is caused by spin-orbit coupling.
Maria Goeppert Mayer and Hans Jensen (1949) showed that a strong spin-orbit term in the nuclear potential, proportional to \(\vec{l}\cdot\vec{s}\), splits each level of orbital angular momentum l into two with \(j = l \pm \frac{1}{2}\). For nuclei the \(j = l + \frac{1}{2}\) level lies lower, which is why \(p_{3/2}\) fills before \(p_{1/2}\) and why the model reproduces the magic numbers 2, 8, 20, 28, 50, 82 and 126.
Orbital angular momentum alone, or spin alone, cannot split the \(p_{3/2}\) and \(p_{1/2}\) levels, which have the same l and the same s; the splitting comes from their coupling, which is what 'spin-orbit' names and what the general phrase 'angular momentum and spin' leaves out.
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