We consider scattering of x rays by H atoms in the presence of both a linea
rly polarized laser field and a static electric field. Results for the diff
erential cross section as a function of the number of photons n exchanged w
ith the laser field are presented. For x-ray-atom scattering in the presenc
e of a 10(14) W/cm(2) laser field the differential cross section has a plat
eau only for emitted photons (n < 0). Adding a static electric field gives
rise to an extended plateau for absorbed photons (n > 0), indicating a subs
tantial increase of the scattered x-ray energies. We present a quasiclassic
al explanation of these results. [S0031-9007(98)07847-8].