Hyperspherical adiabatic approach for the helium atom

Masili, Mauro; Hornos, José Eduardo Martinho; Groote, J. J. De

doi:10.1103/physreva.52.3362

Cited by 16 publications

(20 citation statements)

References 16 publications

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“…͑12͔͒ acts as a compensation correction in the anticrossing region, resulting in a smooth Rϫ␣ wave function surface. 17 The system bound energies are defined by the lowest potential curve. For energies higher than the first ionization threshold, the channel of the first curve is open, meaning that states on the upper curves are autoionizing.…”

Section: Resultsmentioning

confidence: 99%

Bound states of the barium atom by the hyperspherical approach

Cebim

Groote²

2004

The Journal of Chemical Physics

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We present a nonadiabatic hyperspherical calculation of the highly excited and low lying doubly excited states of the barium atom using effective potentials for the two optically active electrons' interactions. Within the hyperspherical adiabatic approach the investigation of the spectra is performed with potential curves and nonadiabatic couplings of a unique radial variable, which allows clear identification of the states. The convergence of energy is obtained within well established bound limits, and the precision is comparable to accurate configuration interaction calculations. A very good agreement with experimental results is obtained with only few nonadiabatic couplings.

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Section: Resultsmentioning

confidence: 99%

Bound states of the barium atom by the hyperspherical approach

Cebim

Groote²

2004

The Journal of Chemical Physics

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“…A direct numerical solution of the radial equations is characterized by the existence of logarithmic singularities at Rϭ0. 71,72 A power series expansion in R and ln R is used to describe these singularities, 31,33,71,72 i.e., the radial functions are expanded as…”

Section: A Angular and Radial Solutionsmentioning

confidence: 99%

“…The hyperspherical method has been used in many fields of physics and chemistry, and an extensive application in atomic and molecular physics has been made. [27][28][29][30][31][32][33][34][35][36][37][38][39] The hyperspherical coordinates can also be found in nuclear physics [40][41][42][43][44][45] as well as in solid-state physics. 46 -51 The hyperspherical adiabatic representation of the wave function is well known to furnish a very good description of the correlation effects for twoelectron systems; its use has many motivations, such as universality, which permits its application to any few-body problem in an intuitive and elegant way with a description of physical states in terms of potential curves and their couplings, which are independent of the energy, similarly to the Born-Oppenheimer method.…”

Section: Introductionmentioning

confidence: 99%

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Electron affinity of the sodium atom within the coupled-channel hyperspherical approach

Groote¹,

Masili

2004

The Journal of Chemical Physics

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We present a nonadiabatic calculation, within the hyperspherical adiabatic approach, for the ground state energy of the alkali-metal negative ions. An application to the sodium negative ion (Na-) is considered. This system is treated as a two-electron problem in which a model potential is used for the interaction between the Na+ core and the valence electrons. Potential curves and nonadiabatic couplings are obtained by a direct numerical calculation, as well as the channel functions. An analysis of convergence is made and comparisons of the electron affinity with results of prior work of other authors are given.

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“…14 -19 The HS adiabatic approach was introduced in atomic calculations by Macek 20 in the late 1960s for the qualitative study of resonant states of the helium atom. Since then it has evolved to become a very precise method, 21-25,16 -18 allowing the calculation of energies of the ground state up to highly excited states 16,17 of atomic systems, as well as of general three-body problems. 24 -27 The method has also been applied to four-body systems.…”

Section: Introductionmentioning

confidence: 99%

Binding energies of excitons trapped by ionized donors in semiconductors

Santos

Masili²,

Groote

2001

Phys. Rev. B

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Using the hyperspherical adiabatic approach in a coupled-channel calculation, we present precise binding energies of excitons trapped by impurity donors in semiconductors within the effective-mass approximation. Energies for such three-body systems are presented as a function of the relative electron-hole mass in the range 1р1/р6, where the Born-Oppenheimer approach is not efficiently applicable. The hyperspherical approach leads to precise energies using the intuitive picture of potential curves and nonadiabatic couplings in an ab initio procedure. We also present an estimation for a critical value of ( crit ) for which no bound state can be found. Comparisons are given with results of prior work by other authors.

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Hyperspherical adiabatic approach for the helium atom

Cited by 16 publications

References 16 publications

Bound states of the barium atom by the hyperspherical approach

Bound states of the barium atom by the hyperspherical approach

Electron affinity of the sodium atom within the coupled-channel hyperspherical approach

Binding energies of excitons trapped by ionized donors in semiconductors

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