Complex‐coordinate studies of helium autoionizing resonances

Abstract

Several aspects of the numerical application of the complex-coordinate method for calculating helium autoionizing resonances are discussed. A direct-search algorithm is used to locate resonance eigensolutions that satisfy the virial theorem, and the influence of the basis set o n the accuracy of the calculated positions and widths is investigated. The complex-coordinate method is related to the stabilization method <of Holplien and Midtdal.

Complex-scaled multireference configuration-interaction method to study Be and Be-like cations' (B, C, N, O, Mg) Auger resonances1s2s22p1Zhang1, Yeager2 2012Phys. Rev. A211110View full textAdd to dashboardCite

“…[8,9,14]. The complex variational principle [17][18][19] ensures that the search for the stationary point may be performed in the same way as MCSCF by setting the first derivative of Q(X)with respect to the step-length vector to zero, which leads to the multidimensional Newton-Raphson equation [8][9][10]14]:…”

Obtaining positions and widths of scattering resonances from a complex multiconfigurational self‐consistent field state using the M1 method

“…It has been shown 2–4, 7, 35 that the eigenvalues of the dilated Hamiltonian corresponding to the resonances ( E ) are invariant to changes in η for θ greater than some system‐specific critical value (θ c ): and the corresponding eigenfunctions in this region are square‐integrable, which paves the way for the employment of bound state electronic structure methods to study resonances. The complex analogue of the variational principle 7, 35, 36 ensures that one can search for a stationary point in the complex energy hypersurface using such a method.…”

“…(1) holds true if an infinite basis set is used, but in an actual calculation only a finite basis set can be used. The use of a finite basis set makes the resonance energy, E (θ > θ c ), depend on η; and only a quasi‐stability in a very narrow neighborhood of some η = η o = α o exp ( i θ o ), described by indicates the appearance of the resonance 7. E (η o ) is taken as the best estimate for the resonance energy in a practical calculation.…”

“…For the past few decades, the challenge of theoretically investigating the resonances that occur in the electron‐atom and the electron‐molecule scattering experiments using low‐energy electron beam has attracted attention 1–16. Although the resonances lie in the continuum part of the Hamiltonian buried under the nonresonant scattering states, their quasi‐bound nature appealed to many theoreticians to apply bound state methods to study them.…”

Fast convergent approach for computing atomic resonances

“…In the 1970s Moiseyev, Certain, and Weinhold 27 investigated the usefulness of explicitly correlated functions for CCR computations of autoionizing resonances. Since then, many such computations have been performed: Ho 2 and Bhatia and Ho 10 used the Hylleraas‐type 2, 10 expansion for two‐electron systems.…”