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The present study examines the mathematical properties of the free-free (f-f) matrix elements of the full electric field operator, of the multipolarHamiltonian. Special methods are developed and applied for their computation,for the general case where the scattering wavefunctions are calculatednumerically in the potential of the term-dependent (N-1) electron core, and areenergy-normalized. It is found that, on the energy axis, the f-f matrixelements of the full operator have singularities of first order in the case ofequal photoelectron energies. The numerical applications are for f-ftransitions in Hydrogen and Neon, obeying electric dipole and quadrupoleselection rules. In the limit of zero photon wave-number, the full operatorreduces to the length form of the electric dipole approximation (EDA). It isfound that the results for the EDA agree with those of the full operator, withthe exception of a photon wave-number region about the singularity.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Theory and computation of electromagnetic transition matrix elements in the continuous spectrum of atoms