Consider two hypothetical nuclei \( X_1 \) and \( X_2 \) undergoing \( \beta \) decay, resulting in nuclei \( Y_1 \) and \( Y_2 \), respectively. The decay scheme and the corresponding \( J^P \) values of the nuclei are given in the figure. Which of the following option(s) is/are correct? (\( J \) is the total angular momentum and \( P \) is parity)
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For \( \beta \)-decay, a Fermi transition preserves both the spin and parity, while a Gamow-Teller transition involves a change in spin but no change in parity.
\( X_1 \to Y_1 \) is Fermi transition and \( X_2 \to Y_2 \) is Fermi transition
\( X_1 \to Y_1 \) is Fermi transition and \( X_2 \to Y_2 \) is Gamow-Teller transition
\( X_1 \to Y_1 \) is Gamow-Teller transition and \( X_2 \to Y_2 \) is Fermi transition
\( X_1 \to Y_1 \) is Gamow-Teller transition and \( X_2 \to Y_2 \) is Gamow-Teller transition
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The Correct Option isB
Solution and Explanation
1. Fermi transition:
A Fermi transition occurs when the total angular momentum \( J \) and parity \( P \) of the nucleus do not change during the decay. This type of transition happens when \( \Delta J = 0 \) and \( \Delta P = 0 \), meaning the spin and parity are preserved in the decay.
2. Gamow-Teller transition:
A Gamow-Teller transition involves a change in the total angular momentum (\( \Delta J \neq 0 \)), but the parity remains unchanged (\( \Delta P = 0 \)).
3. Analyzing the given system:
In the first decay \( X_1 \to Y_1 \), both the initial and final nuclear states have the same parity (\( P = 0^+ \) to \( P = 0^+ \)), and there is no change in the total angular momentum (\( J = 0 \to J = 0 \)), indicating a Fermi transition.
In the second decay \( X_2 \to Y_2 \), the initial state is \( J^P = 0^+ \) and the final state is \( J^P = 1^+ \), indicating a change in the total angular momentum (\( \Delta J = 1 \)) while the parity remains unchanged (\( P = 0^+ \) to \( P = 1^+ \)), which is characteristic of a Gamow-Teller transition.
