Simple Nonrelativistic Model for Single Meson Production

Single pseudoscalar meson production is assumed to be described by a transition matrix element taken between initial and final two-nucleon wave functions defined as solutions to Schr\"odinger's equation with a phenomenological potential included. The effective interaction is a linear combination of the two possible nonrelativistic invariants. The angular distribution and energy dependence is considered in detail for the reaction p+p→π⁺+d. Using the Jastrow potential to define the proton wave functions, the large anisotropy can be explained by including the D state of the deuteron. Results become less satisfactory at increasing energies. The predicted energy dependence of the total cross section for proton beam energies from 311 Mev to 515 Mev agrees well with experiment. The strong dependence of the cross section on the incident proton momentum contributes to the agreement.An order of magnitude estimate of the alternate reaction, p+p→π⁺+n+p, predicts, at 340 Mev (laboratory system), a branching ratio slightly greater than one.Finally, the absorption rate of π^- mesons by deuterons from a K-shell orbit, i.e., π^-+d→2n, is calculated. This gives an estimate of the strength of the S meson wave part of the interaction and is consistent with the restrictions imposed by the results obtained for the reaction p+p→π⁺+d.