This paper presents multi-path, two-photon excitation cross-section calculations for krypton, using first-order perturbation theory. For evaluation of the two-photon-transition matrix element, this paper formulates the two-photon cross-section calculation as a matrix mechanics problem. From a finite basis of states, consisting of 4, 5, 6, 7, 5, 6, 4, 5, and 6 orbitals, electric dipole matrix elements are constructed, and a Green's function is expressed as a truncated, spectral expansion of solutions, satisfying the Schrödinger equation.
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