Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

Ruiz, María Belén

doi:10.1007/s10910-008-9397-0

Cited by 27 publications

(36 citation statements)

References 53 publications

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“…Expressions for all these integrals are given in Refs. [13][14][15]. The calculation of the overlap between the wave functions of bound states requires only the usual two-and three-electron integrals.…”

Section: A Variational Wave Functionsmentioning

confidence: 99%

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Atomic excitations during the nuclearβ−decay in light atoms

Frolov

Ruiz

2010

Phys. Rev. A

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Probabilities of various final states are determined numerically for β − -decaying He, Li, and Be atoms. In our evaluations of the final-state probabilities we have used the highly accurate atomic wave functions constructed for each few-electron atom or ion. We also discuss an experimental possibility to observe negatively charged ions which form during the nuclear β + decays. Corrections on direct interaction between atomic electrons and fast β electrons or positrons are considered. It is shown that for our results obtained for β ± decays in few-electron atoms with the use of the sudden approximation such corrections are very small (≈α 4 ) and can be neglected.

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Section: A Variational Wave Functionsmentioning

confidence: 99%

“…Equation (12) is the closed expression for the differential cross section of electron-electron scattering which depends upon the parameter x, Eq. (13), and γ factor of the β − electron. As follows from Eq.…”

Section: Emission Of the Fast δ Electrons During The Nuclear β − Dmentioning

confidence: 99%

Atomic excitations during the nuclearβ−decay in light atoms

Frolov

Ruiz

2010

Phys. Rev. A

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“…For such wave functions, all integrals are limited to four-electron integrals. For nonrelativistic atomic systems, analytical integrations are thus possible [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

“…(2) some terms may have n K 1 = 0 and others may have ω ij,K 2 = 0. So, in actual calculations, we use not only the present formulations of the integrals, but also the existing ones [28][29][30][31][32][33]. Some time ago, we examined the optimized values of ω ij for the E-Hy-CI wave function of few-electron atoms [34].…”

Section: Introductionmentioning

confidence: 99%

Analytical evaluations of exponentially correlated unlinked one-center, three- and four-electron integrals

et al. 2012

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We discuss an extension of the Hylleraas configuration-interaction method by incorporation of an exponentially correlated term. The necessary unlinked one-center, three-and four-electron integrals are derived in a closed form. No three-or four-electron auxiliary integrals appear in the final expressions. The evaluation scheme is an extension of the recent development of Ruiz [J. Math. Chem. 46, 1322]. The prescription of combining diverged integrals to retrieve a finite value is avoided in the present approach.

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“…For the two-electron repulsion integrals over complex Slater orbitals, we have applied the formulas given in Ref. [13].…”

Section: Theorymentioning

confidence: 99%

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

Ruiz

Rojas

Chicón

et al. 2011

Int J of Quantum Chemistry

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Configuration Interaction (CI) calculations on the ground 2 P state of boron atom are presented using a wave function expansion constructed with L-S eigenfunction configurations of s-, p-, and d-Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy −24.63704575 a.u. Second, full-CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave −24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of −24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C + have been performed obtaining an energy of −37.41027598 a.u.

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Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

Cited by 27 publications

References 53 publications

Atomic excitations during the nuclearβ−decay in light atoms

Atomic excitations during the nuclearβ−decay in light atoms

Analytical evaluations of exponentially correlated unlinked one-center, three- and four-electron integrals

Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals

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Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

Cited by 27 publications

References 53 publications

Atomic excitations during the nuclearβ−decay in light atoms

Atomic excitations during the nuclearβ−decay in light atoms

Analytical evaluations of exponentially correlated unlinked one-center, three- and four-electron integrals

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

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Product

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Configuration interaction calculations on the ²P ground state of boron atom and C⁺ using Slater orbitals