  Superconductivity in the recently proposed ground-state structures of atomic
metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa.
Near molecular dissociation, the electron--phonon coupling $\lambda$ and
renormalized Coulomb repulsion are similar to the molecular phase. A continuous
increase in the critical temperature $T_c$ with pressure is therefore expected,
to $\jmmapprox 356$K near 500 GPa. As the atomic phase stabilizes with
increasing pressure, $\lambda$ increases, causing $T_c$ to approach $\jmmapprox
481$K near 700 GPa. At the first atomic--atomic structural phase transformation
($\jmmapprox 1$ -- 1.5 TPa), a discontinuous jump in $\lambda$ occurs, causing
a significant increase in $T_c$ of up to 764K.
