I am reading Quantum Mechanics book by N. Zettili (2nd ed.) and encountered something confusing in the chapter of scattering theory, section 11.5: scattering of identical particles.
This is the problem:
First it is mentioned that for two classical identical particles, whose interaction potential is central the differential scattering cross section is given by (in center of mass frame),
$$ (d \sigma (\theta)/d \Omega )_{cl} = |f(\theta)|^2 + |f(\pi - \theta)|^2 $$
Here $f(\theta)$ is the scattering amplitude, which appears in the scattered wave function. Then after a few lines it is mentioned that for distinguishable particles when $ \theta = \pi/2 $, the differential cross section is $ |f(\pi/2)|^2 $.
I think classical identical particles are always distinguishable. So, it should be $ 2 |f(\pi/2)|^2 $, not $ |f(\pi/2)|^2 $, according to the 1st formula.
What am I missing here ?