The general theory of the extended method of calulation of atomic structures

Abstract

AbstractsA general theory of the extended method of calculation of atomic structures having complex configurations is presented. It is based on the correspondence between the radial integrals of the ordinary method and the linear combinations of those of the extended method. The rules for going over from the ordinary method to the extended one are given.On prtsente une thtorie gtntrale de la mtthode du calcul tlargie des structures atomiq u a aux configurations complexes. Elle est baste sur la correspondance des inttgrales de la mtthode ordinaire aux combinaisons lintaires des inttgrales de la mtthode du calcul tlargie. Les rtgles de passage de la mtthode ordinaire du calcul A la mtthode tlargie sont donnCes.Es wird eine verallgemeinerte Theorie des erweiterten Rechnungsverfahrens fur atomare Komplexkonfigurationen beschrieben. Sie beruht auf der Entsprechung zwischen den Radialintegralen des gewohnlichen Rechnungsverfahrens und den Linearkombinationen der Radialintegrale des erweiterten Rechnungsverfahrens. Die Ubergangsregeln von dem gewohnlichen zu dem erweiterten Rechnungsverfahren werden gegeben.

Nonresonance Compton scattering of an X-ray photon by an atom with the core of the d symmetry

“…In this work, the radial relaxation effect is taken into account by the methods of the the ory of nonorthogonal orbitals [10,11]. Thus, for example, in the case of the scattering channel 3p → εd in (1), the transition probability amplitudes in expression (8) are modified as follows: (13) .…”

Self-consistent field method in various approximations: 'forgotten ideas'

“…The numerical calculations, carried out for the ground states of lithium-and beryllium-like atomic systems, illustrate the e ciency of the method. A general theory of the extended method of calculations of atomic structures for complex electronic con® gurations is described in [32]. Papers [24,31,32] are discussed also by Froese Fischer in her monograph [1].…”

Extended Hartree–Fock self‐consistent field with some results for berylliumlike atomic systems

“…While expressing the kinetic energy including the electrostatic interaction energy of the electrons with the nuclear charge according to the rules given in refs. [7 and 81 columns (or rows) of the permanent (l), one by one, must be substituted by integrals where (7) 2 indicating the nuclear charge (in atomic units).…”

“…However, ensuring this orthogonality is rather a difficult task in the case of complex configurations, and the calculations performed up until now using analytical radial orbitals (cf. [7]) show that in the extended method of calculation the orthogonality assumption must be withdrawn in order to obtain the correct radial correlation effect.…”