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 Schrödinger'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 $p+p\to {\pi }^{+}+d$. 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.