Born approximation: the scattering rate is proportional to the square of the matrix element of the interaction potential

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Born approximation: the scattering rate is proportional to the
square of the matrix element of the interaction potential between
the initial and final states. These two colliding particles
interact with one another through a contact potential V = λδ3 (r1 −
r2) = λδ(x1 − x2)δ(y1 − y2)δ(z1 − z2). Determine the scattering
rate when the two colliding particles are indistinguishable
spin-1/2 particles with total spin 1. Explain your result in terms
of the probability that the particles are found at the same point
in space. The two particles have initial and final momenta of pi,
-pi and pf, -pf respectively.