We conducted a theoretical study on the process \(\Sigma ^{+} p \rightarrow \Lambda a_0^{+} p\) based on an effective Lagrangian approach. This model encompasses the excitation of intermediate resonance leading to the production of \(\Delta (1920)\) through \(\pi ^{+}\) and \(K^{+}\) meson exchanges between the initial \(\Sigma ^{+}\) and p baryons, as well as the generation of \(\Delta (1940)\) via \(\pi ^{+}\) and \(\rho ^{+}\) meson exchanges. We provide predictions for the total and differential cross sections and discuss the potential impacts of cut-off parameters, off-shell effects, and branching ratios of the \(\Delta (1920) \rightarrow a_0 p\) and \(\Delta (1940) \rightarrow a_0 p\) decays. Given the dominance of \(\Delta (1940)\) in the region close to the reaction threshold, this reaction is considered an ideal platform for exploring the features of the \(\Delta (1940)\) resonance.
