A low-energy anti proton beam is introduced into a bubble chamber. Two exposures are made, one with the chamber full of liquid hydrogen (to study the interactions on protons) and one with the chamber full of liquid deuterium (to study the interactions on neutrons). The beam energy is such that the anti protons come to rest in the chamber. We know that the stopped anti protons are captured in an ‘anti proton’ atom and, when they reach an S wave, annihilate. The p̅p and p̅n in S wave are, in spectroscopic notation, the triplet ³S₁ and the singlet ¹S₀. List the possible values of the total angular momentum and parity J^P and iso spin I. Establish what are the eigen states of C and those of G and give the eigen values. What are the quantum numbers of the possible initial states of the process p̅ n → π^– π^– π⁺? Consider the following three groups of processes. 

Compute for each the ratios between the processes:

(a) p̅n → ρ⁰π^-; p̅n → ρ^- π0,

(b) ̅pp(I = 1) → ρ⁺π ^- ; p̅(I = 1) → ρ⁰π⁰; ̅pp(I = 1)+ → ρ^-π⁺,

(c) ̅pp(I = 0) → ρ+π ^- ; p̅p(I = 0) → ρ⁰π⁰; pp̅(I = 0)+ → ρ^-π⁺.