QB_PH_SEC9_019: Nuclear Models & Decays

In nuclear gamma decay, an electromagnetic transition between states $2^+ \to 0^+$ can proceed via which multipole radiation?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Angular Momentum Conservation**: The photon carries orbital plus intrinsic spin angular momentum $L$: $|J_i - J_f| \le L \le J_i + J_f$ For $J_i = 2$ and $J_f = 0$: $|2 - 0| \le L \le 2 + 0 \implies L = 2$ Single photon emission must have multipolarity $L = 2$ (quadrupole). 2. **Parity Conservation**: $\pi_i = +1, \quad \pi_f = +1 \implies \Delta\pi = \frac{\pi_f}{\pi_i} = +1$ 3. **Multipole Parity Rules**: - Electric multipole ($EL$): $\pi(EL) = (-1)^L$ For $L = 2$: $\pi(E2) = (-1)^2 = +1$ (Matches $\Delta\pi$, ALLOWED) - Magnetic multipole ($ML$): $\pi(ML) = (-1)^{L+1}$ For $L = 2$: $\pi(M2) = (-1)^3 = -1$ (Violates $\Delta\pi$, FORBIDDEN) 4. **Conclusion**: Radiation must be pure Electric Quadrupole ($E2$). Option (A) is correct.