Correlation between the sea level muon spectrum and the primary nucleon spectrum using the Cocconi–Koester–Perkins model

Using the recent ISR data of proton–proton interactions on the inclusive production of pions and nucleons, realistic values of the mean pion inelasticity Kπ and the mean nucleon inelasticity KT have been estimated. These values have been used for the derivation of the sea level differential muon spectrum from the primary nucleon spectrum and vice versa using the CKP model as an extension of the work presented in an earlier article. It is found that none of the measured primary nucleon spectra of Ryan, Ormes, and Balasubrahmanyan and Grigorov, Rapoport, and Shestoperov fit any of the precisely measured muon spectra of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley and Allkofer, Carstensen, and Dau in spectral shape or the absolute value. On the other hand good agreement between the derived muon spectra and the spectra of Allkofer et al. and Ayre et al. is found if the primary nucleon spectra of the forms, N(Ep) = (1.38 ± 0.08)Ep−2.59 and N(Ep) = (1.00 ± 0.10)Ep−2.55, respectively, are assumed. The first form is comparable with that obtained by Brooke, Hayman, Kamiya, and Wolfendale following more approximate but similar procedure. It is also not unjustified when compared with the measured primary all nuclei spectrum of Grigorov et al. in the light of suggestions made by Ellsworth, Ito, Macfall, Siohan, Streitmatter, Tonwar, Vishwanath, Yodh, and Balasubrahmanyan. By comparing the pion production spectra derived from the same primary nucleon spectrum but using the CKP and the scaling models, it is concluded that the results are sensitive to the model assumed for the collisions.