Evaluation of some three-body variational integrals

Caro, J.

doi:10.1103/physreve.58.6781

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…The two-electron correlated integrals with Slater-type functions have been studied extensively in the literature and formulas are available for a number of cases [32][33][34][35][36].…”

Section: Special Casesmentioning

confidence: 99%

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On the evaluation of four-electron correlated integrals with a Slater basis: some simplifications and some closed form examples

King¹

2013

J. Phys. B: At. Mol. Opt. Phys.

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Four-electron correlated integrals with explicit rij dependence and derived from a Slater-type basis set are discussed. Attention is directed to the more complex cases where the powers on the rij factors are odd. Particular effort is focused on the case where there are five factors of rij raised to odd powers, a case that has considerable practical significance. Several integral cases involving three and four rij factors raised to odd powers are evaluated in closed form.

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“…The two-electron correlated integrals with Slater-type functions have been studied extensively in the literature and formulas are available for a number of cases [32][33][34][35][36].…”

Section: Special Casesmentioning

confidence: 99%

“…34> e −αr 1 −βr 2 −γ r 3 −δr 4 dr 1 dr 2 dr 3 dr 4 . (34) On writing r i r j r −1 i j> in the form r i r j r −1 i j> = r j H(r i − r j ) + r i H(r j − r i ), (35) where H(x) denotes a Heaviside step function, then equation ( 34) can be expressed as…”

Section: Special Casesmentioning

confidence: 99%

On the evaluation of four-electron correlated integrals with a Slater basis: some simplifications and some closed form examples

King¹

2013

J. Phys. B: At. Mol. Opt. Phys.

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“…Among these integrals, the exponentially correlated two-electron integrals (3) have been derived by Calais and Löwdin [28] for the regular case. The singular two-electron integrals were studied by Yan and Drake [38,39], Caro [40], Korobov [41], and Harris et al [42]. Three-electron integrals were evaluated analytically by Fromm and Hill [30].…”

Section: Integrals Appearing In the E-hy-ci Ansatzmentioning

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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“…To compute the matrix elements of the non-local part of the ΛΛ interaction, integrals of the type Γ l,m,−1 , with l, m = 0, 1, 2 • • • are also needed. These can be obtained from a recursion as well [66],…”

Section: Appendix Matrix Elements In the Var Schemementioning

confidence: 99%

Double-Λ hypernuclei and the nuclear medium effective ΛΛ interaction

1999

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We fit the 1 S 0 ΛΛ interaction in the nuclear medium to the masses of the experimentally known double−Λ hypernuclei: 6 ΛΛ He, 10 ΛΛ Be and 13 ΛΛ B. We derive this effective interaction from OBE Jülich ΛΛ-type potentials and using both HartreeFock and variational approaches. We find that the inclusion of ΛΛ correlations in the variational scheme leads to significant differences and a better understanding of the dynamical features of the system. We investigate the sensitivity of the binding energies and the mesonic decay widths of the above double−Λ hypernuclei to the ωΛΛ coupling and the form factor at the σΛΛ vertex. We also use this effective interaction to predict binding energies and pionic decay widths of heavier double−Λ hypernuclei, not discovered yet. Finally, we discard the existence of 1 S 0 ΛΛ bound states provided the ΛΛ − ΞN coupling can be neglected.

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Evaluation of some three-body variational integrals

Cited by 3 publications

References 14 publications

On the evaluation of four-electron correlated integrals with a Slater basis: some simplifications and some closed form examples

On the evaluation of four-electron correlated integrals with a Slater basis: some simplifications and some closed form examples

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

Double-Λ hypernuclei and the nuclear medium effective ΛΛ interaction

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