b(i) Transitions between energy levels in the nucleus can be mediated by photons
(gamma rays). The photon carries away angular momentum, L, where L can
take a range of values. What are the three possible values of L for the transition
between the $j_i = 3$ and $j_f = 1$ states? Consider such a transition where the parity
does not change: what are the three types of transition that can occur (e.g. E1,
E2, E3, E4,... and/or M1, M2, M3, M4,...)?
(ii) The strong spin-orbit interaction causes splitting of the energy levels in the nu-
cleus. The energy levels are labelled s, p, d, f, g, h, i depending on their orbital
quantum number L. Each of the energy levels with non-zero orbital angular mo-
mentum splits into two subsets of energy levels. Consider the 1f set of energy
levels: how many protons (or neutrons) does it take to fill only the lower of the two
subsets of energy levels?