Question

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

• A. \( \dfrac{1}{2}^- \, \dfrac{5}{2}^+ \)
• B. \( \dfrac{1}{2}^+ \, \dfrac{5}{2}^+ \)
• C. \( \dfrac{1}{2}^- \, \dfrac{1}{2}^- \)
• D. \( \dfrac{1}{2}^+ \, \dfrac{1}{2}^- \)

Hint:

In first forbidden transitions, the spin-parity changes significantly, leading to specific spin values for the initial and final states.

Answer 1

The Correct Option is A

Step 1: In \( \beta^+ \) decay, the spin-parity values of the initial and final states are determined by the selection rules and the spin-parity coupling during the decay process.

Step 2: The first forbidden \( \beta^+ \) decay results in a change in both the parity and the spin. In this case, the only valid transition that satisfies the spin-parity conservation and the selection rules is from \( \dfrac{1}{2}^- \) to \( \dfrac{5}{2}^+ \).
Thus, the correct answer is (A).