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)

Question

cdquestions Admin · Accepted Answer

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. Thus, the correct answer is (B).

Answer

$ X_1 \to Y_1 $ is Fermi transition and $ X_2 \to Y_2 $ is Fermi transition

Answer

$ X_1 \to Y_1 $ is Fermi transition and $ X_2 \to Y_2 $ is Gamow-Teller transition

Answer

$ X_1 \to Y_1 $ is Gamow-Teller transition and $ X_2 \to Y_2 $ is Fermi transition

Answer

$ 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 is B

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