Three-electron systems with inner-shell vacancies

Abstract

A computational method is described for obtaining inner-shell-vacancy states of three-electron atoms which combines a block-diagonalization procedure with generalized Feshbach projection operators applicable to systems with three or more electrons. Typically, the accuracy is about 1.5 parts per thousand (6E/E=1. 5 X10 '). The strength of the method is that it provides many energy levels for each Rydberg series. A quantum-defect analysis is then applied that identifies the members of each series and yields reliable quantum defects and series limits. The method is particularly important in symmetries for which multiple Rydberg series exist. The present work reports on P' states of three-electron systems with 3 Z 10, which are compared with other calculations. The energies of S' states of C'+ are also presented as an example requiring both the multielectron Feshbach projection operators and the quantum-defect analysis developed here. Four distinct Rydberg series are found for this case and their series limits obtained.PACS number(s): 32.30. -r, 32.80.Dz, 31.50.+ w, 31.20.Tz

Hollow states of lithium

“…all the singly and doubly excited configurations are excluded. This latter restriction has been translated into projection-operator terminology [21] where the operators P, Q I , Q II project onto subspaces containing 0, 1, and 2 vacancies and where the eigenvalues of the operator Q II HQ II are the energy levels of the hollow atomic states with double-K-shell vacancies. This procedure yields different numbers of configurations depending on the particular L, S, π under consideration.…”

“…is the energy of a lowlying doubly-excited state (in this paper, both electrons are in the n i = 2 state) of the Li + ion. For full details, see [20] and [21]. The quantum defect (µ n ), defined as n − n * , is usually a slowly varying function of n when n is large, particularly in the case of a single isolated Rydberg series such as the (2p) 2 3 P e np 2 S o series converging on the doubly excited (2p) 2 3 P e state of the residual ion.…”

“…Theoretical calculations using the R-matrix approximation and the saddle-point technique have been used to identify these resonances. The truncated diagonalization method(TDM) has also been used to calculate the energies and wavefunctions of these triply excited states [20] and also of doubly excited states where there is just one vacancy in the K-shell [21]. One of the advantages of this method is that it yields complete Rydberg series converging on the doubly excited states of Li + all at once.…”

“…In Section 2 we give a brief outline of the TDM method [20,21]. In Section 3 we describe our calculations and present our results and comparison with others.…”

Continuous Monitoring of Electrical Activity of Pancreatic β-Cells Using Semiconductor-Based Biosensing Devices

“…They play an important role in various physical processes such as dielectronic recombination, photoabsorption, electron scattering, and multielectron phenomena in ionatom and atom-atom collisions (Conneely et al 1992). In these systems two or more electrons are excited to large distances from the residual ion, the dominant role of the nuclear Coulomb potential is reduced, and the correlation effects become important.…”