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All of the ordinary hyperfine terms of the ${(p\ensuremath{\mu}p)}^{+}$, $L=1$, ortho, bound state, except for the muon-proton contact term, are evaluated to sufficient accuracy so that they would not mask a hyperfine discrepancy associated with proton structure effects. These and other pertinent contributions to the hyperfine structure are discussed in the light of recent interest in checking for a discrepancy in the hyperfine structure of a muon-proton system.

In obtaining the wave functions of three-body Coulomb systems in which two heavy equally charged, and one light oppositely charged, particles are involved, one can use a type of Born-Oppenheimer coupling scheme, to obtain nonadiabatic effects. In this paper we decompose the coupled differential equations of such a scheme in terms of the total orbital angular momentum and parity of the states, and reduce these equations to one-dimensional ones in a form suitable for calculation.