Scattering of Mesons by Nuclear Particles

Cross sections for the scattering of mesons by nuclear particles are obtained quantum-mechanically on the basis of the Heitler-Peng version of the perturbation theory. The integral equation taking account of radiation damping in the quantum theory is solved in the classical approximation ($\hslash \to 0$). A comparison of these cross sections with those obtained classically reveals certain discrepancies. It is found that though the cross sections calculated classically and those calculated quantum-mechanically in the classical approximation ($\hslash \to 0$) broadly agree in most cases, usually one finds that some higher order terms which occur in the purely classical treatment are absent in the quantum-mechanical one. The discrepancy is further accentuated in the case of $g_2$-scattering where the differential cross sections have generally very different angular dependences and differ from each other in numerical coefficients also. These differences are, in general, such that they cannot be accounted for by postulating quantized orientations of the spin. The correspondence obtained between the classical methods and quantum mechanics by tending $\hslash$ to zero in the results obtained from the latter thus provides a test of the correctness of our theories, and, in the present case it suggests, assuming the classical theory as given by Dirac and Bhabha to be correct, the lines along which a new theory of radiation damping may be developed.