Line Shapes in a Magnetic Field: Trajectory Modifications II: Full Collision-Time Statistics

In a previous paper\cite{simplified}, a variation of the Collision-time Statistics method was applied to identify the relevant perturbers for line broadening under the action of a constant magnetic field. As discussed, that version was simplified and inadequate for low magnetic field and/or large perturber mass (ions). The purpose of the present work is to augment the previous work, so that such cases, corresponding to the Larmor radius exceeding the maximum impact parameter, can be handed efficiently. The results may also be used to construct analytic, i.e. impact/unified models under the usual assumptions in these models.