Discussion
A nucleus decays from its spin state 5-/2 to spin state 3-/2 by emission of gamma-ray. The gamma-ray decay mode can be classified as :
Answer: B
The possible multipoles are M1, E2, M3, E4.
A gamma ray of multipole order L must satisfy \(|J_{i} - J_{f}| \le L \le J_{i} + J_{f}\) with \(L \ge 1\):
\[ \begin{aligned} L_{min} &= \left|\frac{5}{2} - \frac{3}{2}\right| = 1 \\ L_{max} &= \frac{5}{2} + \frac{3}{2} = 4 \end{aligned} \]
Both states have negative parity, so there is no parity change. Electric multipoles EL change parity by \((-1)^{L}\) and magnetic ones ML by \((-1)^{L + 1}\), so with no change of parity the allowed modes are the even-L electric and odd-L magnetic ones: M1, E2, M3, E4 (in practice M1 and E2 dominate). E1, M2, E3, M4 would require a parity change, and options C and D include orders above 4.
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