Molière theory of multiple Coulomb scattering with ionization and the transport mechanism of the multiple scattering process.

The Molière theory of multiple Coulomb scattering is improved to take account of ionization loss by applying a differential formulation of the theory. Distributions for the deflection angle theta over, as well as for any linear combination between theta over and the lateral displacement r over, under the ionization process are derived by a series expansion with the same universal functions f(n)(theta) of Molière, except that the values for both the expansion parameter B and the scale angle thetaM are corrected from those under the fixed-energy process. We find that Goudsmit-Saunderson angular distribution with ionization is also expressed by the same characteristic parameters B and thetaM derived above by the Molière theory. The transport mechanism of Molière process of multiple Coulomb scattering and the stochastic property of Molière series expansion are also investigated and discussed.