  A detailed study of the elementary p(p,p$'\pi^{+}$)n reaction is presented
using the delta isobar model. In this model, in the first step one of the two
protons in the initial state gets excited to $\Delta $. This, in the second
step, decays into a nucleon and a pion. For the $pp \to N\Delta$ step the
parametrized form of the DWBA t-matrix of Jain and Santra, which reproduces
most of the available data on $pp \to n\Delta^{++}$, is used. The
cross-sections studied include the outgoing proton momentum spectra in
coincidence with the pion, the outgoing pion momentum spectra and the
integrated total cross-section. We find that all the calculated numbers are in
good agreement with the corresponding measured cross sections.
