  We consider the potential use of optical traps for precision measurements in
atomic hydrogen (H). Using an implicit summation method, we calculate the
atomic polarisability, the rates of elastic/inelastic scattering and the
ionisation rate in the wavelength range 395 to 1000 nm. We extend previous work
to predict three new magic wavelengths for the 1S--2S transition. At the magic
wavelengths, the 1S--2S transition is unavoidably and significantly broadened
due to trap-induced ionisation associated with the high intensity required to
trap the 1S state. However, we also find that this effect is partially
mitigated by the low mass of H, which increases the trap frequency, enabling
Lamb-Dicke confinement in shallow lattices. We find that a H optical lattice
clock, free from the motional systematics which dominate in beam experiments,
could operate with an intrinsic linewidth of O(1 kHz). Trap-induced losses are
shown not to limit measurements of other transitions.
