Email: gediminas.gaigalas@tfai.vu.lt; pavel.rynkun@tfai.vu.lt;
laima.radziute@tfai.vu.lt
GRASP package is
based on the relativistic configuration interaction in which
accurate calculations, accounting for valence,
valence–valence, core–valence, core and core–core electron
correlations, often rely on massive CSF expansions. This paper
presents a further development of the method based on the
second-order perturbation theory for finding the most
important CSFs that have the greatest influence on the
core–valence, core and core–core correlations. This method 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 [G. Gaigalas, P. Rynkun, and L.
Kitovienė, Second-order Rayleigh–Schrödinger perturbation
theory for the GRASP2018 package:
Core–valence correlations, Lith. J. Phys. 64(1), 20–39
(2024), https://doi.org/10.3952/physics.2024.64.1.3, and G.
Gaigalas, P. Rynkun, and L. Kitovienė, Second-order
Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core correlations, Lith.
J. Phys. 64(2), 73–81 (2024),
https://doi.org/10.3952/physics.2024.64.2.1]. In this
extension, the perturbation theory takes into account electron
core–valence, core and core–core correlations, where an atom
or ion has any number of valence electrons, for calculation of
energy spectra and other properties. Meanwhile, the rest of
the correlations are taken into account in a traditional way.
This allows a significant reduction of the space of the
configuration state function for complex atoms and ions. We
also demonstrate how this method works for calculations of the
energy structure and E1 transition properties of Fe XV ion.
Keywords: configuration interaction, spin-angular
integration, perturbation theory, tensorial algebra, core–core
correlations, core–valence correlations, core correlations
* Dedicated to the memory of professor Adolfas
Jucys (1904–1974), pioneer of contemporary theoretical
physics in Lithuania, initiator of the ‘Lithuanian Physics
Collection’, on the occasion of his birth and death
anniversaries.
Vilniaus universiteto
Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva
GRASP programinis
paketas grindžiamas reliatyvistinės superpozicijos metodu,
kuriuo tikslūs skaičiavimai atliekami, kai į juos įtraukiamos
valentinės–valentinės, kamieno–valentinės, kamieno ir
kamieno–kamieno elektronų koreliacijos per konfigūracinių
būsenų funkcijas (KBF). Tai veda prie didelės KBF erdvės,
todėl pagal šį metodą sunkiau atlikti pačius skaičiavimus.
Darbe pristatomas tolesnis antrosios eilės trikdymų teorija
grįsto metodo (G. Gaigalas, P. Rynkun, L. Kitovienė,
Second-order Rayleigh–Schrödinger perturbation theory for the
GRASP2018 package: Core–valence
correlations, Lith. J. Phys. 64(1), 20–39 (2024),
https://doi.org/10.3952/physics.2024.64.1.3) ir (G. Gaigalas,
P. Rynkun, L. Kitovienė, Second-order Rayleigh–Schrödinger
perturbation theory for the GRASP2018
package: Core correlations, Lith. J. Phys. 64(2),
73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1),
skirto svarbiausioms KBF, turinčioms didžiausią įtaką
kamieno–valentinėms, kamieno ir kamieno–kamieno koreliacijoms,
surasti, tobulinimas. Šis metodas paremtas reliatyvistinės
superpozicijos ir stacionariosios antrosios eilės Relėjaus ir
Šrėdingerio daugelio kūnų trikdymų teorijos neredukuotinėje
tensorinėje formoje metodų deriniu.
Darbe pateiktame trikdymų teorijos išplėtime atsižvelgiama į
elektronų kamieno–valentines, kamieno ir kamieno–kamieno
koreliacijas, kai atomas ar jonas turi bet kokį valentinių
elektronų skaičių. O į kitas koreliacijas jame atsižvelgiama
tradiciniu būdu. Tai leidžia gerokai sumažinti KBF erdvę
skaičiuojant sudėtingų atomų ir jonų įvairias
charakteristikas. Taip pat darbe pateikiamas pavyzdys,
parodantis, kaip šiuo metodu atlikti Fe XV jono energijos
spektro struktūros ir E1 šuolių charakteristikų skaičiavimus.
* Skiriama šiuolaikinės teorinės fizikos
Lietuvoje pradininko, „Lietuvos fizikos rinkinio“
iniciatoriaus akad. Adolfo Jucio (1904–1974) gimimo ir
mirties sukaktims paminėti.
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