Autoionizing states in beryllium-like atomic systems using explicitly correlated coordinates

Abstract

A theoretical approach to obtain accurate values for autoionizing states parameters in Be-like systems is presented. The method is based on the configuration-interaction expansion of the two-active (outer) electron wavefunction in terms of correlated coordinates containing r12 explicitly and by including a model potential to represent the effect of the 1s2 core. Within our approach, 1snl core states are removed from the basis of correlated configurations by using a Phillips–Kleinman projection operator, and resonance parameters (energies and widths) are determined through the stabilization method. Illustrative examples of our implementation are given for doubly-excited states of Be and Ne6+.

Information and entanglement measures applied to the analysis of complexity in doubly excited states of helium

“…Extensions of this work to alkaline-earth atoms is feasible [54], assuming they behave as systems with outer-shell two-active electrons with a core interaction. The role of a polarizable core is not only that of a simple screening, but it also has an effect on the different combinations that generate their particular DESB states.…”

“…(16) in power series of the density matrix and keeping only the leading terms (along with the property Tr[ρ] = 1) to give From the previous expressions for S L and S V N it might seem that the computation of these quantities require up to 12dimensional integrals, which have been previously calculated using Monte Carlo numerical integration methods [19,29] using explicitly correlated Kinoshita-type basis functions, although they can be performed analytically when using explicitly correlated Hylleraas basis sets, as shown in [33]. Indeed we have experience in using Hylleraas-type basis sets in CI methods [54] but we have chosen an uncorrelated CI method that incorporates antisymmetrized products of orthogonal orbitals, which makes not only the application of the Feshbach projection method and the subsequent analysis in terms of DESB much more simple, but also the calculation of S L and S V N entropies. Using the CI expansion of Eq.…”

“…Since they are immersed in the electronic continuum, a direct diagonalization of the Hamiltonian cannot uncover the energy location of these resonances. Different methods have been proposed to characterize these resonance states, such as the stabilization method [56], the complex coordinate scaling [57], the Feshbach method [58], or scattering methods [59], among others, previously used by us in other contexts [54,60,61]. The Feshbach method is a projection operator formalism which separates the total resonance wave function (eigenfunction of H) into two orthogonal half spaces: its bound-like part Q and its scattering-like part P , such that = Q + P .…”

Feshbach projection approach to study plasma effects on doubly excited autoionizing states in helium

“…an expression in whichr i = r i /r i is a unit vector and∇ Y i = r i ∇ Y i , where ∇ Y i corresponds to the angular part of the gradient operator. We have previously used a similar Hamiltonian in our Hylleraas configuration interaction (HyCI) approach to compute resonances in berylliumlike atoms [25], but where Coulomb interactions are now replaced with screened Yukawalike interactions. In that previous work [25] we built all ingredients necessary to uncover resonant states in isolated Be-like atoms by implementing the stabilization procedure.…”

“…We have previously used a similar Hamiltonian in our Hylleraas configuration interaction (HyCI) approach to compute resonances in berylliumlike atoms [25], but where Coulomb interactions are now replaced with screened Yukawalike interactions. In that previous work [25] we built all ingredients necessary to uncover resonant states in isolated Be-like atoms by implementing the stabilization procedure. For the reasons stated in the Introduction we now choose instead the Feshbach approach.…”