Ritz variational method for the high‐lying nonautoionizing doubly excited ^1,3F^e states of two‐electron atoms

Abstract

Energy eigenvalues of nonautoionizing doubly excited 1,3Fe states originating from 2pnf ( n=4−20) configuration of two‐electron atoms Z=3−18 have been calculated by expanding the basis set in explicitly correlated Hylleraas coordinates under the framework of Ritz variational method. A detailed discussion on the evaluation of correlated basis integrals is given. The energy eigenvalues of a number of these doubly excited states are being reported for the first time especially for the high lying states. The effective quantum numbers ( n∗) for the states mentioned above have been calculated by using the theory of quantum defect.

Electronic structure calculations of compressed Li atom using composite technique under Ritz variational framework

“…By suitably tuning the geometrical ratio γ c , we can control the radial space in a flexible manner. Such type of basis set has successfully been used in structure calculations for both free and plasma embedded two‐electron atoms [46–58]. The linear variational parameters, that is, C i 's (Equation ) along with the energy eigenvalues of the core electrons E c are obtained by solving the generalized eigenvalue equation where is the Hamiltonian matrix, is the overlap matrix and is the column matrix consisting of linear variational parameters.…”

Extensive investigations for metastable‐bound and resonance 3Fe states of He atom

“…The three coordinates of two‐electron atom are the sides of the triangle ( r 1 , r 2 , r 12 ) formed by the two electrons and the nucleus of two‐electron atom where the rotation of the triangle in space can be defined by three Eulerian angles ( θ , ϕ , ψ ). Following the work of Bhatia and Temkin, we can write the wave function of 1, 3 F e state of a two‐electron atom as, where are the real angular momentum Wigner functions . are the eigenfunctions of the two‐electronic angular momentum operator , that is, (in a.u.…”

“…In the beginning of this century, Tanner et al published a review article on the studies of two‐electron atoms. Investigations on two‐electron atoms are of immense interest in recent years due to the nonseparability of the dynamical equation of motion . It provides a fundamental testing ground for various quantum chemical approximation methods for example, Feshbach projection operator formalism, close‐coupling approximation method, multiconfigurational Hatree‐Fock method, hyperspherical close‐coupling method based on numerical basis set, complex‐coordinate‐rotation (CCR) method with a finite numerical basis set built on the solutions of discretized one particle Hamiltonian, CCR method with minor operational modifications, stabilization method, and so forth.…”

“…There exists numerous investigations in the literature related to structural and spectral features of DESs of two‐electron atoms up to D state, among which few references are given . In contrast, the same studies for F e states are rather scanty . The estimations of the energy eigenvalues of metastable bound 1, 3 F e states of the He atom were done by a group of theoreticians by using different quantum chemical approximation methods.…”

“…We have adopted stabilization method with “soft wall” strategy for the calculation of resonance parameters of resonance 3 F e states above He + (2 p ) threshold. The wavefunction used by Dutta et al is being modified in the present work by introducing dd configuration. Explicitly correlated multiexponent Hylleraas type basis set is being used in the present communication.…”