Methods Involving Complex Coordinates Applied to Atoms

Polarizability and hyperpolarizability of Li+ calculated from the DC-Stark shift

“…The P space contains states that represent the multichannel continuous spectrum. These states are expanded in terms of L 2 functions, since a complex coordinate transformation makes them square integrable [7,12,13]. The Stark Hamiltonian matrix, which is derived from this choice of the basis functions is…”

“…The continuum wave functions are calculated by the wellknown complex-coordinate rotation method [12,13]. The open channel components of the resonant wave functions are represented as,…”

Resonance energies and autoionization widths of the , and doubly excited states of the helium isoelectronic sequence

“…For the calculations we suggest a partitioning of the resonant wave function into two parts: a bound-like or Q-space part and a scatteringlike or P-space part. With this partitioning one can incorporate physical insight into the choice of electron configurations and can apply the complex coordinate method to many electron systems with an expected rate of convergence faster than that expected by the conventional complex-coordinate rotation methods [4]. Following this approach, the resonance wave-function for each state is given by the form:…”

“…(ii) After construction and computation of the localized part of the total wave function, the spatially asymptotic part, Ψ (n) P , which includes all the information coming from the open channels and contributes to the decay of the state, was computed in terms of L 2 basis sets with complex coordinates for the outgoing electron [4,10]:…”

Fast convergent approach for computing atomic resonances

“…Various approaches using this technique and many of the results obtained by them are reviewed in Refs. 1–6. Particular methods belonging to this group differ in the way the complex coordinate rotation is applied 1, 3–6 and, therefore, in how the wavefunction is transformed under the complex rotation.…”