The proton-hydrogen-atom collision is described in terms of an impact parameter perturbed-stationary-states treatment. Spurious long-range couplings are avoided and Galilean invariance is enforced by the inclusion of momentum translation factors which are determined variationally by using an Euler-Lagrange formalism. The correct physical behaviour is obtained in both the separated-atoms and united-atoms limit. The effective electronic translational kinetic energy, averaged over all internuclear separations is shown to have less influence on the phase of the close-capture probability than has hitherto been thought the case. The locations of all seven turning points in the curve of capture probability against energy, for a scattering angle of 3 degrees, are in excellent agreement with experiment and compare more than favourably with previous extremely elaborate calculations. The adiabatic representation is thus shown to be remarkably adaptable even at energies as high as 25 keV.