(Solved): 8. In a nucleus described by the rotational model, the second excited state is always a 4+state ...

8. In a nucleus described by the rotational model, the second excited state is always a $$4^{+}$$state. This state decays by E2 radiation to the $$2^{+}$$state. Justify this observation by calculating, using the Weisskopf estimates, the ratio between the E2 decay probability and (a) the octupole $$(L=3)$$ and hexadecapole $$(L=4)$$ decays to the $$2^{+}$$ state and (b) the hexadecapole state to the ground state. (Note: These are collective rotational states, for which the Weisskopf estimates should not be taken too seriously).