A phenomenological investigation of the shower particle pseudorapidity fluctuations in hadron-nucleus collisions

From the experimental matrix $\text{?(N}{}_{\mathrm{<mtext>g</mtext>}}\text{; n}{}_{\mathrm{<mtext>s</mtext>}}\text{, Δη}{}_{\mathrm{i}}\text{)}$ (the number of events with a given number N_g of particles with velocity 0.3c<v<0.7c, and n_s, the number of shower particles (v > 0.7c) in a pseudo-rapidity interval Δη_i) obtained from the Heidelberg-Igel hadron-nucleus experiment at CERN, we extract the shower particle multiplicity distributions as a function of ν, the number of nucleons that interacted with the projectile. We use a theoretically justified statistical correlation between ν and N_g (recoil protons) and the assumption that the correlation between n_s and N_g is given merely through ν. The data used are for incoming energies 50 and 150 GeV with a proton or pion as the projectile and Cu or Pb as the target. We find that the shower particle multiplicity distributions are of a Poissonian character in each η bin and for each value of ν. The average multiplicities $\text{〈n}{}_{\mathrm{<mtext>s</mtext>}}\text{〉(ν)}\text{Δη}{}_{\mathrm{i}}$ are approximately the same for the two targets and for the different projectile, possibly with a small excess for the pion projectile.The results are compared to a rather general theoretical model of the soft interaction type. The predictions from this model for the shower particle pseudorapidity distributions are very close to the derived values.