Theory and computation of electromagnetic transition matrix elements in the continuous spectrum of atoms

The present study examines the mathematical properties of the free-free ( f-f) matrix elements of the full electric field operator, of the multipolar Hamiltonian. Special methods are developed and applied for their computation, for the general case where the scattering wavefunctions are calculated numerically in the potential of the term-dependent (N-1) electron core, and are energy-normalized. It is found that, on the energy axis, the f-f matrix elements of the full operator have singularities of first order in the case of equal photoelectron energies. The numerical applications are for f-f transitions in Hydrogen and Neon, obeying electric dipole and quadrupole selection rules. In the limit of zero photon wave-number, the full operator reduces to the length form of the electric dipole approximation (EDA). It is found that the results for the EDA agree with those of the full operator, with the exception of a photon wave-number region about the singularity.Comment: 39 pages, 11 figure

THEORETICAL ASPECTS OF AUGER TRANSITIONS INVOLVING VALENCE ELECTRONS IN MOLECULES AND SOLIDS

THE OBJECT OF THIS THESIS IS THE EXAMINATION OF THEORETICAL ASPECTS OF AUGER TRANSITIONS INVOLVING A PAIR OF VALENCE ELECTRONS IN MOLECULES AND METALS. SUCH TRANSITIONS GIVE RISE TO SPECTRA OF MUCH GREATER COMPLEXITY THAN THOSE ARISING FROM PHOTOELECTRONS OR SOFT X-RAYS. THIS COMPLEXITY IS CONSEQUENTLY REFLECTED INTHE MATHEMATICAL TOOLS NECESSARY TO COPE WITH THE SITUATION. FOR BOTH, MOLECULAR AND SOLID STATE SPECTRA, THE NOTION OF THE SPECTRAL DENSITY FUNCTION OF A FERMION PAIR IS INTRODUCED BY ANALOGY TO THE SIMPLE SPECTRAL DENSITY FUNCTION THAT APPEARS IN THE LITERATURE. THROUGH THAT FUNDAMENTAL IDEA, THE AUGER SPECTRA ARE GIVEN AN ELEGANT FORMULATION. FOR MOLECULES, TREATED WITHIN THE LCAO APPROXIMATION, THIS FORMALISM MAKES APPARENT THE SIMILARITY WITH THE ATOMIC AUGER SPECTRA. FURTHERMORE, A WELL JUSTIFIED APPROXIMATION OF NEGLECT OF INTERATOMIC AUGER TRANSITION MATRIX ELEMENTS, ALLOWS FOR A COMPLETE ANALOGY TO BE DRAWN, THE COMPONENTS OF A MOLECULAR SPECTRUM BEING EXPRESSED IN TERMS OF THE COMPONENTS OF THE ATOMIC SPECTRUM OF THE ELEMENT DIRECTLY INVOLVED. COMPARISON IS MADE WITH AVAILABLE EXPERIMENTAL DATA ON FREE MOLECULE SPECTRA. FOR METALS, THE SPECTRAL DENSITY OF THE FERMION PAIR IS INTRODUCED WITHIN THE CONTEXT OF THE OCCUPATION NUNBER FORMALISM AND PROVIDES A NATURAL WAY TO EXAMINE THE EFFECT OF DYNAMICAL PAIR CORRELATIONS ON THE AUGER SPECTRUM.ΤΟ ΑΝΤΙΚΕΙΜΕΝΟ ΑΥΤΗΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΕΙΝΑΙ Η ΕΞΕΤΑΣΗ ΤΩΝ ΘΕΩΡΗΤΙΚΩΝ ΠΡΟΒΛΗΜΑΤΩΝ ΤΩΝ ΜΕΤΑΒΑΣΕΩΝ AUGER ΠΟΥ ΠΕΡΙΛΑΜΒΑΝΟΥΝ ΕΝΑ ΖΕΥΓΟΣ ΗΛΕΚΤΡΟΝΙΩΝ ΣΘΕΝΟΥΣ ΣΕ ΜΟΡΙΑ ΚΑΙ ΜΕΤΑΛΛΑ. ΜΕΤΑΒΑΣΕΙΣ ΑΥΤΟΥ ΤΟΥ ΕΙΔΟΥΣ ΔΙΝΟΥΝ ΦΑΣΜΑΤΑ ΜΕΓΑΛΥΤΕΡΗΣ ΠΟΛΥΠΛΟΚΟΤΗΤΑΣ ΑΠΟ ΑΥΤΑ ΠΟΥ ΠΡΟΕΡΧΟΝΤΑΙ ΑΠΟ ΦΩΤΟΗΛΕΚΤΡΟΝΙΑ 'Η ΜΑΛΑΚΕΣ ΑΚΤΙΝΕΣ-Χ. ΑΥΤΗ Η ΠΟΛΥΠΛΟΚΟΤΗΤΑ ΑΝΤΙΚΑΤΟΠΤΡΙΖΕΤΑΙ ΚΑΙ ΣΤΑ ΜΑΘΗΜΑΤΙΚΑ ΠΟΥ ΧΡΗΣΙΜΟΠΟΙΟΥΝΤΑΙ ΓΙΑ ΝΑ ΠΕΡΙΓΡΑΨΟΥΝ ΤΗΝ ΚΑΤΑΣΤΑΣΗ. ΓΙΑ ΤΑ ΜΟΡΙΑΚΑ ΦΑΣΜΑΤΑ, ΚΑΘΩΣ ΚΑΙ ΓΙ'ΑΥΤΑ ΠΟΥ ΠΡΟΕΡΧΟΝΤΑΙ ΑΠΟ ΣΤΕΡΕΑ, Η ΕΝΝΟΙΑ ΤΗΣ ΣΥΝΑΡΤΗΣΗΣ ΦΑΣΜΑΤΙΚΗΣ ΠΥΚΝΟΤΗΤΑΣ ΕΝΟΣ ΖΕΥΓΟΥΣ ΦΕΡΜΙΟΝΙΩΝ ΕΙΣΑΓΕΤΑΙ ΣΕ ΑΝΑΛΟΓΙΑ ΤΗΣ ΑΝΤΙΣΤΟΙΧΗΣ ΣΥΝΑΡΤΗΣΗΣ ΕΝΟΣ ΦΕΡΜΙΟΝΙΟΥ ΠΟΥ ΥΠΑΡΧΕΙ ΣΤΗΝ ΒΙΒΛΙΟΓΡΑΦΙΑ. ΜΕΣΑ ΑΠΟ ΑΥΤΗΝ ΤΗΝ ΘΕΜΕΛΙΩΔΗ ΕΝΝΟΙΑ, ΤΑ ΦΑΣΜΑΤΑ ΤΩΝ ΜΕΤΑΒΑΣΕΩΝ AUGER ΑΠΟΚΤΟΥΝ ΕΝΑ ΚΟΜΨΟ ΦΟΡΜΑΛΙΣΜΟ. ΓΙΑ ΤΑ ΜΟΡΙΑΚΑ ΦΑΣΜΑΤΑ ΤΩΝ ΜΕΤΑΒΑΣΕΩΝ AUGER, ΥΠΟΛΟΓΙΣΜΕΝΑ ΜΕ ΤΗΝ LCAO ΠΡΟΣΕΓΓΙΣΗ, ΑΥΤΟΣ Ο ΦΟΡΜΑΛΙΣΜΟΣ ΚΑΝΕΙ ΠΡΟΦΑΝΗ ΤΗΝ ΟΜΟΙΟΤΗΤΑ ΜΕ ΤΑ ΑΝΤΙΣΤΟΙΧΑ ΑΤΟΜΙΚΑ. ΕΠΙΠΛΕΟΝ ΜΙΑ ΕΥΛΟΓΗ ΠΡΟΣΕΓΓΙΣΗ ΟΠΟΥ ΠΑΡΑΛΕΙΠΟΝΤΑΙ ΤΑ ΔΙΑ-ΑΞΟΝΙΚΑ ΣΤΟΙΧΕΙΑ ΠΙΝΑΚΑ ΤΗΣ ΜΕΤΑΒΑΣΕΩΣ AUGER ΕΠΙΤΡΕΠΕΙ ΜΙΑ ΠΛΗΡΗ ΑΝΑΛΟΓΙΑ ΟΠΟΥ ΤΑ ΣΥΣΤΑΤΙΚΑ ΜΕΡΗ ΤΟΥ ΜΟΡΙΑΚΟΥ ΦΑΣΜΑΤΟΣ ΕΚΦΡΑΖΟΝΤΑΙ ΣΕ ΟΡΟΥΣ ΤΩΝ ΣΥΣΤΑΤΙΚΩΝ ΤΟΥ ΦΑΣΜΑΤΟΣ ΤΟΥ ΑΤΟΜΟΥ ΠΟΥ ΣΥΜΜΕΤΕΧΕΙ ΑΜΕΣΑ ΣΤΗΝ ΜΕΤΑΒΑΣΗ. ΣΥΓΚΡΙΣΗ ΓΙΝΕΤΑΙ ΜΕ ΠΕΙΡΑΜΑΤΙΚΑ ΔΕΔΟΜΕΝΑ ΠΟΥ ΠΡΟΕΡΧΟΝΤΑΙ ΑΠΟ ΦΑΣΜΑΤΑ ΕΛΕΥΘΕΡΩΝ ΜΟΡΙΩΝ. ΠΡΟΚΕΙΜΕΝΟΥ ΓΙΑ ΦΑΣΜΑΤΑ ΜΕΤΑΛΛΩΝ Η ΣΥΝΑΡΤΗΣΗ ΦΑΣΜΑΤΙΚΗΣ ΠΥΚΝΟΤΗΤΑΣ ΖΕΥΓΟΥΣ ΗΛΕΚΤΡΟΝΙΩΝ ΕΙΣΑΓΕΤΑΙ ΜΕΣΑ ΣΤΑ ΠΛΑΙΣΙΑ ΤΟΥ ΦΟΡΜΑΛΙΣΜΟΥ ΤΩΝ ΑΡΙΘΜΩΝ ΚΑΤΑΛΗΞΕΩΣΚΑΙ ΠΡΟΣΦΕΡΕΙ ΕΝΑ ΦΥΣΙΚΟ ΤΡΟΠΟ ΓΙΑ ΝΑ ΕΞΕΤΑΣΤΟΥΝ ΟΙ ΕΠΙΠΤΩΣΕΙΣ ΤΗΣ ΔΥΝΑΜΙΚΗΣ ΗΛΕΚΤΡΟΝΙΑΚΗΣ ΣΥΣΧΕΤΙΣΗΣ ΕΝΟΣ ΖΕΥΓΟΥΣ ΦΕΡΜΙΟΝΙΩΝ ΣΤΟ ΦΑΣΜΑ ΤΩΝ ΜΕΤΑΒΑΣΕΩΝ AUGER

The Wannier 2-Electron Ionization Ladder in Many-Electron Systems - the He P-1(0) Doubly Excited-States

Journal URL: http://www.iop.org/EJ/journal/0953-407

Multichannel Reaction Matrix-Theory and Configuration-Interaction in the Discrete and in the Continuous-Spectrum - Inclusion of Closed Channels and Derivation of Quantum Defect Theory

Journal URL: http://www.springerlink.com/content/100381

Theory and computation of the profile of the free-free transition probability between autoionizing (resonant) states

Journal URL: http://www.iop.org/EJ/journal/0953-407

Electronic-Structure and the Mechanism of Autoionization for Doubly Excited-States

Journal URL: http://www.springerlink.com/content/100381

Attosecond dynamics of electron correlation in doubly excited atomic states

Journal URL: http://www.iop.org/EJ/journal/0953-407

Bound states and decay mechanisms of He-

Detailed electron-correlation calculations which include the mixing of closed channel with open channels, suggest that He- has only two bound states: The 1s2s2p Po4 and the 2p3So4. The 1s2p2P4 and P2 states are above the He 1s2p Po3 threshold and therefore qualify only as core-excited shape resonances. This conclusion contradicts certain previous theoretical and experimental findings which implied the existence of bound He- P4 and P2 states. Both Po4 and So4 autoionize to the adjacent continuum via spin-dependent forces-a well-known decay mechanism. However, there are two more decay mechanisms: nonrelativistic (for So4) and relativistic (for Po4) radiative autoionization (RA). The probability for RA of the So4 state in the Hartree-Fock approximation is computed to be 1.14×1010 sec-1 © 1981 The American Physical Society