= Isospin-invariant two-body decay amplitude
{title2=$A_{M_1M_2;M}=a\langle I_1M_1,I_2M_2\mid IM\rangle$}
An <isospin>-invariant <decay amplitude> is an intertwining map from the initial <isospin multiplet> into the final tensor product. The <Clebsch-Gordan decomposition for SU2> contains each allowed final isospin once. Commutation with the third generator and the <quadratic Casimir operator> places the image in the matching coupled state. Commutation with the <ladder operators> makes its scalar coefficient independent of the magnetic component. Orthogonality of the <Clebsch-Gordan coefficients> then gives a summed squared amplitude $|a|^2$. A physical <decay rate> additionally includes phase space and spin sums, which can be absorbed into a common reduced coefficient when exact isospin symmetry makes them identical between channels.
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