= Alpha-decay angular-momentum and parity selection rule
{title2=$J_X=0,\ \pi_X=+1\ \Longrightarrow\ J_Y=L,\ \pi_Y=(-1)^L$}
The <ground state> of an <even-even nucleus> has $J^P=0^+$, and the emitted <alpha particle> also has $0^+$. In an <alpha decay> to daughter <spin> $J_Y$, <addition of angular momentum> permits total zero only when the relative <orbital angular momentum> is $L=J_Y$. <Parity conservation> gives $+1=\pi_Y(-1)^L$, hence the daughter has <natural parity>, $0^+,1^-,2^+,3^-,\ldots$. This rule does not itself restrict $J_Y$ to even integers. An even-$J$ sequence such as $0^+,2^+,4^+$ requires additional nuclear structure, for example a positive-parity ground-state <nuclear rotational band>.
Back to article page
