Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

SECOND-ORDER RAYLEIGH–SCHRÖDINGER PERTURBATION THEORY FOR THE GRASP2018 PACKAGE: THREE-PARTICLE FEYNMAN DIAGRAM CONTRIBUTION TO CORE–VALENCE CORRELATIONS
Gediminas Gaigalas, Pavel Rynkun, and Laima Kitovienė
Institute of Theoretical Physics and Astronomy, Faculty of Physics, Vilnius University, Saulėtekio 3, 10257 Vilnius, Lithuania
Email: gediminas.gaigalas@tfai.vu.lt; pavel.rynkun@tfai.vu.lt; laima.radziute@tfai.vu.lt

Received 3 February 2026; accepted 14 May 2026

In order to ascertain the precise atomic characteristics, it is important to incorporate a wide range of electron correlations in the computational analysis. However, it is important to note that undertaking such studies will result in substantial increases of the configuration state function expansions. The present publication, as well as the series of articles that have been published by G. Gaigalas, P. Rynkun, and L. Kitovienė, are dedicated to the analysis and resolution of the problem in question. In this series, a method was developed based on second-order perturbation theory to identify the most important core–valence, core, core–core, and valence–valence correlations. The method under discussion is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form. In this study, the method is further expanded to encompass additional core–valence electron correlations of the third and fourth types. Conversely, the correlations that are not encompassed by perturbation theory are addressed in a conventional manner. This method can be used to calculate the properties of an atom or ion with any number of valence and core electrons. As an example of its application, the atomic calculations of the energy structure and lifetime for Ne II are presented.
Keywords: configuration interaction, spin-angular integration, perturbation theory, tensorial algebra, valence–valence correlations, core–valence correlations, core correlations, core–core correlations

ANTROSIOS EILĖS RELĖJAUS IR ŠRĖDINGERIO TRIKDYMŲ TEORIJA GRASP2018 PROGRAMINIAM PAKETUI: TRIJŲ DALELIŲ FEINMANO DIAGRAMOS ĮTAKA KAMIENO–VALENTINĖMS KORELIACIJOMS
Gediminas Gaigalas, Pavel Rynkun, Laima Kitovienė

Vilniaus universiteto Fizikos fakulteto Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva

Išplėtotas antrosios eilės trikdymų teorija paremtas metodas, skirtas įvairių koreliacijų vertei nustatyti, įtraukiant kamieno–valentines koreliacijas, kurios aprašomos trijų dalelių Feinmano diagrama. Darbe pateiktas išplėtimas papildo kamieno–valentines, kamieno, kamieno–kamieno ir valentines–valentines koreliacijas, kurios buvo išplėtotos ankstesniuose G. Gaigalo, P. Rynkun ir L. Kitovienės darbuose, trečio ir ketvirto tipo kamieno–valentinėmis koreliacijomis. Kadangi šios koreliacijos aprašomos trijų dalelių Feinmano diagrama, papildomai buvo atlikti pakeitimai ir išplėtimai GRASP programos bibliotekoje „librang“, siekiant apskaičiuoti šios diagramos sukinines-kampines dalis. Remiantis pateiktuoju išplėtimu, buvo atrinktos svarbiausios konfigūracinių būsenų funkcijos reliatyvistiniui konfigūracijų superpozicijos metodui. Darbe, kaip metodo taikymo pavyzdys, taip pat pateikiami Ne II energijos struktūros, šuolių parametrų ir gyvavimo trukmės skaičiavimai.

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