  An ab initio theory is devised for the x-ray photoabsorption cross section of
atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2).
The laser dresses the core-excited atomic states, which introduces a dependence
of the cross section on the angle between the polarization vectors of the two
linearly polarized radiation sources. We use the Hartree-Fock-Slater
approximation to describe the atomic many-particle problem in conjunction with
a nonrelativistic quantum-electrodynamic approach to treat the photon-electron
interaction. The continuum wave functions of ejected electrons are treated with
a complex absorbing potential that is derived from smooth exterior complex
scaling. The solution to the two-color (x-ray plus laser) problem is discussed
in terms of a direct diagonalization of the complex symmetric matrix
representation of the Hamiltonian. Alternative treatments with time-independent
and time-dependent non-Hermitian perturbation theories are presented that
exploit the weak interaction strength between x rays and atoms. We apply the
theory to study the photoabsorption cross section of krypton atoms near the K
edge. A pronounced modification of the cross section is found in the presence
of the optical laser.
