  We revisit the derivation of the covariant two-body scalar-fermion equation
with a Coulomb interaction, presented in a previous paper. We show that it can
be given the formal aspect of a Dirac equation, but for the fact that the
eigenvalue is also contained in one of the coefficients and thus it is not
linearly included. The discussion of the boundary value problem is therefore
different, although some properties of the Dirac equation can be recovered in
an approximation bringing back to the concept of reduced mass. We discuss a
mixed analytic-numerical method of solution which allows to obtain very
accurate results and we calculate the lowest levels, states and QED corrections
for pionic and kaonic atoms.
