The momentum dependence, at fixed pion angles of 180 and 155°, of inclusive pion production reactions has been obtained for 600 MeV protons and 175 MeV/nucleon $\alpha$ particles and deuterons on ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, C, Co, and Ta. The spectra obtained all fall off exponentially with increasing pion momentum, the slope being about 30 MeV/c independent of either target or projectile nature. The data are examined from the point of view of quasi-two-body scaling, a reaction description discussed recently which suggests that $q_{min}$, the minimum nuclear recoil momentum possible kinematically, is the proper scaling variable. When plotted versus $q_{min}$, all data presented here keep their exponential shape, but the slope becomes 70 MeV/c, i.e., nearly the same as obtained for proton production by the same selection of beam projectiles and energies. It is concluded that the same functional of the target momentum space wave function is revealed by quasi-two-body scaling in inclusive pion production experiments, as in inclusive proton and light-fragment production experiments. Finally, the results of a Monte Carlo calculation of pion spectra based on a single $\mathrm{NN}\to \pi \mathrm{NN}$ interaction and taking into account the internal motion of the nucleons in target and projectile are presented. The shape and cross sections are accounted for when effective momentum densities of exponential forms are used; the slope constants necessary are compatible with the ones obtained in quasi-two-body scaling. Using the ground state momentum density of an independent particle shell model produces pion spectra which fall off too rapidly. Furthermore, the Monte Carlo calculation reveals kinematical features of the reaction, which help explain why quasi-two-body scaling works for pion production.

NUCLEAR REACTIONS $\mathrm{C}(p, \pi )$, $E_p=600\mathrm{}$ MeV, ($d, \pi$), $E_d=350\mathrm{}$ MeV, ($\alpha , \pi$) $E_{\alpha }=700\mathrm{}$ MeV; ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, Co, and $\mathrm{Ta}(d, \pi )$, $E_d=350\mathrm{}$ MeV, ($\alpha , \pi$), $E_{\alpha }=700\mathrm{}$ MeV; measured $\sigma (E_{\pi }, {\ominus }_{\pi })$ at 155 and 180°; magnetic spectrometer; compared with quasi-two-body scaling and Monte Carlo, single interaction calculation; discuss relation to internal motion in target and projectile.

• Received 26 April 1978

DOI:https://doi.org/10.1103/PhysRevC.18.1764