A short-lived particle is produced in the reaction

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Nuclear reactions · Nuclear reactions

The Nucleus Resolved, Ch Reactions: four-vectors, amplitudes and partial waves

Problem

A short-lived particle

X

is produced in the reaction

n + {}^3\mathrm{He} \to p + X

, with measured cross section

0.90\,\mathrm{mb}

, and its inverse

p + X \to n + {}^3\mathrm{He}

has measured cross section

0.80\,\mathrm{mb}

, both at the same centre-of-mass energy. At that energy the centre-of-mass momentum in the

n

{}^3\mathrm{He}

channel is

200\,\mathrm{MeV}/c

and in the

p

X

channel is

150\,\mathrm{MeV}/c

. The neutron,

{}^3\mathrm{He}

and proton all have spin

\tfrac12

. Use detailed balance to determine the spin

J_X

X