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This paper concludes the presentation of the non-relativistic effective fieldtheory formalism designed to calculate the radiative corrections that enhancethe pair-annihilation cross sections of slowly moving neutralinos and charginoswithin the general minimal supersymmetric standard model (MSSM). While papers Iand II focused on the computation of the tree-level annihilation rates thatfeed into the short-distance part, here we describe in detail the method toobtain the Sommerfeld factors that contain the enhanced long-distancecorrections. This includes the computation of the potential interactions in theMSSM, which are provided in compact analytic form, and a novel solution of themulti-state Schr\"odinger equation that is free from the numericalinstabilities generated by large mass splittings between the scattering states.Our results allow for a precise computation of the MSSM neutralino dark matterrelic abundance and pair-annihilation rates in the present Universe, whenSommerfeld enhancements are important.

Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos III. Computation of the Sommerfeld enhancements