Pion Production in Proton-Proton Collisions

The cut-off form of the Yukawa theory is applied to the reaction $p+p\to {\pi }^{+}+d$. Using the Low-Wick formulation of field theory, an expression is obtained for the appropriate matrix element in terms of the wave functions of a physical deuteron and diproton. Approximations are made for these wave functions and the matrix element is evaluated. The resulting cross section agrees semiquantitatively with that part of the observed cross section due to pions emitted in a $p$-state.