Assume that 13 N (Z=7) undergoes first-forbidden + decay from its ground state with spin-parity J i i to a final state J f f. The possible values of J i i and J f f, respectively, are

GATE 2021 PH – Question 17

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

Assume that $^{13}\mathrm N$ ($Z=7$) undergoes first-forbidden $\beta^+$ decay from its ground state with spin-parity $J_i^{\pi_i}$ to a final state $J_f^{\pi_f}$. The possible values of $J_i^{\pi_i}$ and $J_f^{\pi_f}$, respectively, are

$\frac12^-,\frac52^+$
$\frac12^+,\frac52^+$
$\frac12^-,\frac12^-$
$\frac12^+,\frac12^-$

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Correct answer: (A) $\frac12^-,\frac52^+$

Explanation

The ground-state unpaired proton of $^{13}$N lies in a p orbital, giving ground-state spin-parity $1/2^-$. First-forbidden beta decay changes parity and can have $\Delta J=0,1,2$. A transition from $1/2^-$ to $5/2^+$ has $\Delta J=2$ and a parity change, so it is first-forbidden. B and D use the wrong initial ground-state parity, and C does not change parity.

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