The scattering length for hydrogenic atoms with variable lepton mass, ranging from H to p mu, is calculated. The non-trivial sensitivity of the scattering length to non-adiabatic effects is investigated using the coupled-channel approach. The physical conditions for the Bose-Einstein condensation of exotic atoms are expressed in terms of this scattering length, which for the p mu atoms interacting via (3)Sigma(+)(u) potentials, is calculated to be 1.13 x 10(-2) au. The critical temperature for condensing the p mu atoms is estimated to be 0.5 K at a density of 2.2 x 10(20) cm(-3). Under these conditions the phonon velocity in the condensate is 2.2 m s(-1) and the coherence length is nearly 5 mu m.