Analytical Property of Scattering Matrix:Spectroscopy Phenomena and Sharp Overlapping Autoionization Resonances

Abstract

An extended atomic data base with sufficiently high precision is required in astrophysics studies and the energy researches. For example, there are “infinite” energy levels in discrete energy region as well as overlapping resonances in autoionization region. We show in this paper the merits of our relativistic eigenchannel R-matrix method R-R-Eigen based on the analytical continuation properties of scattering matrices for the calculations of the energy levels, overlapping resonances and the related transitions. Using Ne+ as an illustration example, the scattering matrices of Ne+ in both discrete and continuum energy regions are calculated by our R-R-Eigen method directly. Based on our proposed projected high dimensional quantum-defect graph (symmetrized), one can readily determine the accuracies of the calculated scattering matrices using the experimental energy levels in a systematical way. The calculated resonant photoionization cross sections in the autoionization region are in excellent agreement with the benchmark high resolution experiments. With the scattering matrices checked/calibrated against spectroscopy data in both discrete and continuum energy regions, the relevant dynamical processes should be calculated with adequate accuracies. It should then satisfy the needs of the astrophysical and energy researches.

Relativistic eigenchannelR-matrix studies of the strong intrashell electron correlations in highly chargedAr13+ions

“…The relativistic eigenchannel R-matrix method (R-R-eigen) [8][9][10][11][12][13][14] is applied in this study to stringently treat the complex atomic multielectron problem. Briefly, the coupling of Nelectron ion-core target states and an excited electron with the appropriate angular momentum forms channels for the N + 1-electron excited complex with a specific total angular momentum.…”

“…Our R-R-eigen method [8][9][10][11][12][13][14] differs from the traditional R-matrix method [22][23][24][25][26][27] mainly by definitions of physical channels, which includes not only opened channels (with positive orbital energies) but also several relevant closed channels (with negative orbital energies). Therefore, physical channels (the number of which is denoted as n p ) include all Rydbergtype bound electrons and their adjacent continua with orbital energy in the energy range of ε > −q 2 /l 2 (in Ry, where q is the charge of a long-range potential and l is the orbital angular momentum of the electron) owing to the mathematical properties of Coulomb wave functions [20].…”

“…Based on analytical continuation properties of scattering matrices, all discrete energy levels and autoionization resonances can be obtained without missing any one in the framework of the MQDT. On the other hand, one can readily check/calibrate the accuracy of scattering matrices using available spectroscopic data [9,13,14].…”

“…The eigenchannel wave functions J π α inside the reaction zone (r r 0 ) are calculated variationally [8][9][10][11][12][13][14]. Outside the reaction zone (r r 0 ), it can be expressed rigorously as…”

“…Based on analytical continuation properties of short-range scattering matrices, we have developed the relativistic eigenchannel R-matrix method (R-R-eigen code) [8][9][10][11][12][13][14], which has been successfully applied for many atomic processes, such as electron impact excitations [8,9], photoionizations [10,11,14], etc. In this method, we first calculate short-range scattering matrices, i.e., physical parameters associated with the multichannel quantum defect theory (MQDT) [15][16][17][18][19][20][21], and related wave functions for both discrete and continuous energy regions of interest.…”