Someone argues: "the baryon has isospin and spin

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Particle Physics, Ch Isospin: a symmetry used as bookkeeping

Problem

Someone argues: "the

\Delta^{++}

baryon has isospin

I=3/2

and spin

J=3/2

. Since isospin obeys the same half-integer counting rule as ordinary angular momentum, the two quantum numbers must combine, so the

\Delta^{++}

's true total angular momentum is

J+I=3

." ((a)) Is this reasoning correct? If not, identify the flaw. ((b)) State the actual, measured spin of the

\Delta^{++}

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