GATE 2022 PH – Question 12

Nuclear and Particle Physics · alpha decay, beta-decay, electromagnetic transitions in nuclei · 1 mark · Multiple choice

Match beta-decay order for 1. $X(1/2^+)\to Y(1/2^+)$, 2. $X(1/2^-)\to Y(5/2^+)$, 3. $X(3^+)\to Y(0^+)$, 4. $X(4^-)\to Y(0^+)$. Labels i,ii,iii,iv denote first forbidden, second forbidden, third forbidden, allowed, respectively.

1 – i, 2 – ii, 3 – iii, 4 – iv
1 – iv, 2 – i, 3 – ii, 4 – iii
1 – i, 2 – iii, 3 – ii, 4 – iv
1 – iv, 2 – ii, 3 – iii, 4 – i

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Correct answer: (B) 1 – iv, 2 – i, 3 – ii, 4 – iii

Explanation

The type of a beta decay depends on the change in angular momentum $\Delta J$ and on whether the parity changes.

**Allowed:** $\Delta J=0,1$ with no change of parity.
**First forbidden:** $\Delta J=0,1,2$ with a change of parity.
**Second forbidden:** $\Delta J=2,3$ with no change of parity.
**Third forbidden:** $\Delta J=3,4$ with a change of parity.

Classify the four transitions:
1. $X(\tfrac12^+)\to Y(\tfrac12^+)$: $\Delta J=0$, parity unchanged. **Allowed (iv).**
2. $X(\tfrac12^-)\to Y(\tfrac52^+)$: $\Delta J=2$, parity changes. **First forbidden (i).**
3. $X(3^+)\to Y(0^+)$: $\Delta J=3$, parity unchanged. **Second forbidden (ii).**
4. $X(4^-)\to Y(0^+)$: $\Delta J=4$, parity changes. **Third forbidden (iii).**

Match: **1-iv, 2-i, 3-ii, 4-iii** (option B).