Corrections to the Glauber model for intermediate energy proton-alpha elastic scattering

Corrections to the Glauber model for intermediate energy proton-$\alpha$ elastic scattering have been calculated at the lab energies $K_L=0.58,1,\mathrm{and}2.1$ GeV using the multiple diffraction expansion formalism. In this expansion, the Glauber amplitude appears as a leading term in a perturbation series. Leading corrections due to (i) wave spreading (noneikonal), (ii) internal excitation (recoil), as well as (iii) zero-point motion (different Galilean frames) effects are obtained in a simple model. Their structures are analyzed and their energy dependences are examined. The wave-spreading and internal-excitation corrections agree with those obtained by Wallace. The use of Wallace's relativistic kinematics changes the differential cross section significantly. A new zero-point motion correction is found to be important. A simple dependence of the results on the sign of $\rho$ ($\equiv \frac{\mathrm{Re}f}{\mathrm{Im}f}$ of the $\mathrm{NN}$ scattering amplitude) is pointed out. The relative importance of these corrections decreases as energy increases, as expected. The significance of our results is briefly discussed.