The remarkable results of Everhart et al. in observing resonant charge exchange in wide angle (small impact parameter) ion-atom collisions, are discussed in terms of the well-known impact parameter method. It is shown that previous theories based on adiabatic potential curves are inconsistent with the results of He+-He experiments. However, experimental results are correctly predicted from a Heisenberg representation consisting of the basis set of single configuration wave functions built up from molecular orbitals (independent-particle model). This set includes virtual (autoionized) states. In this representation, the collision can be assumed to be adiabatic except for very short or very long collision times. The case of double charge exchange is treated, and it is shown that a three-state approximation is required. The presence of phase shifts in empirical equations is a result of the breakdown of interference at zero-collision time. Damping is discussed. The results include the work of previous authors and are general enough to include new cases. In particular, charge exchange in He++-He, Li+-Li, and Li++-Li collisions is discussed and predictions of experimental results are made.