Theory of x-ray absorption by laser-dressed atoms

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser ($800\mathrm{nm}$, ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$). 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.

Figure 1

(Color online) X-ray photoabsorption cross section of the krypton atom near the $K$ edge with laser dressing ${\sigma }_{1s}({\omega }_X,{\vartheta }_{LX})$ and without it ${\sigma }_{1s,\mathrm{n}.\mathrm{l}.}\left({\omega }_X\right)$. The angle ${\vartheta }_{LX}$ is formed between the polarization vectors of the laser and the x rays. The laser operates at a wavelength of $800\mathrm{nm}$ with an intensity of ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$.

Figure 2

(Color online) Difference between x-ray photoabsorption cross sections of the krypton atom near the $K$ edge. Symbols as in Fig. 1.

Figure 3

(Color online) Behavior of the photoabsorption cross section without laser ${\sigma }_{1s,\mathrm{n}.\mathrm{l}.}\left({\omega }_X\right)$ of the krypton atom above the $K$ edge. The data are fitted to the ansatz in Eq. (56), which gives ${\sigma }_{1s,\mathrm{a}.\mathrm{e}.}=18623.8\mathrm{kb}{\mathrm{eV}}^n$ and $n=2.63$.