The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Atom in a resonant elliptically polarized field: the exact stationary solution

“…(23) In order to write an explicit and invariant form of we introduce the L-fold tensor product of the vector e23'24 . (24) which are proportional to the spherical harmonics of a complex direction nLM(e) (see in appendix (A)).…”

“…This work is partially supported by RFBR (grants # 01-02-17036 and 01-02-17744) and by grant For arbitrary complex vector a = a' + ia" a spherical harmonic of the rank L can be defined in terms of the tensor constructions (24): …”

Steady-state multipole moments of atoms in a resonant field with elliptical polarization

“…For the two other classes, J → J with J a half-integer and J → J + 1, where CPT is absent, the non-trivial solutions of equations (12) are realized. These solutions can be written as…”

“…of the same rank K has been developed by Manakov et al [11,12]. The use of this technique allows us to present the results of multipole moment calculations in their most compact form for the lower ranks.…”

Multi-particle photoionization by a single photon

“…where and n are unit vectors directed along the major axis of the polarization ellipse and the photon beam, respectively (for details see, e.g., equation ( 6) of [24]). We note that information on the imaginary parts of the parameters c 4-6 cannot be extracted from experiments with linearly polarized photons because in this case e = e * = (which implies ξ = 0, l = 1) and equation (63) will contain only terms with Re c 4-6 .…”