Energy dependence of the ${}^{12}C$ (p, $π^{+}$ $)^{13}$ $C^{/ e m p h >}$ reaction in the region of the $Δ_{1232}$ resonance

Differential cross sections for the

{}^{12}C

(p,

π^{+}

)^{13}

C^{*}

reaction at

T_{p = 250}

, 354, and 489 MeV are presented and compared with previously published data taken at other energies in the

Δ_{1232}

resonance region. At fixed four momentum transfers greater than 0.4

{GeV}^{2}

c^{2}

, the differential cross sections exhibit a maximum near the invariant mass of the

Δ_{1232}

. This energy dependence is similar to that shown by the pp→d

π^{+}

reaction at equivalent energy, and provides strong evidence of a NN→NN

π^{+}

process in the (p,

π^{+}

) reaction mechanism. The total cross section for each transition exhibits a maximum at an energy about 100 MeV lower than that expected from the

Δ_{1232}

invariant mass. This energy dependence could be the result of an interplay between the increase in cross section due to the role of the

Δ_{1232}

in the (p,

π^{+}

) reaction mechanism, and the decrease in cross section due to the large momentum transfers that the reaction is restricted to at higher energies.

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Energy dependence of theC12(p,π+)13C/emph>reaction in the region of theΔ1232resonance