Coulomb interaction in the diffraction description of the $^{12}$C(d,p)X reaction

Within the Glauber-Sitenko diffraction multiple-scattering theory, we calculate Coulomb corrections to the invariant cross section for inclusive deuteron breakup in the $^{12}$C(d,p)X reaction at small proton emission angles. Extending our previous analysis of the longitudinal momentum transfer $Q_z$ and the transverse relative momentum of the final $pn$ pair, we include the proton--nucleus electromagnetic interaction, Coulomb-nuclear interference, and the Coulomb correction to double $pn$ rescattering. For a finite nuclear charge distribution, we derive the Coulomb phase and relate its spatial scale to the measured charge radius. Closed and Yukawa-screened expressions for the proton Coulomb term are obtained. The two-dimensional correction to $pn$ rescattering is reduced to a one-dimensional integral without an independent Gaussian approximation to the full transition form factor. Calculations with the $S$-wave components of the K2 and Nijm-I deuteron wave functions show that the Coulomb effect is concentrated near the quasifree peak. Its interference with the strong amplitude increases the peak height but decreases rapidly with relative momentum. It therefore cannot explain the experimental enhancement at $0.3$--$0.5$ GeV/$c$, where final-state interactions, relativistic corrections, and nonnucleonic components may be important.