Spectra of confined two-electron atoms

Bielińska-Wąż, Dorota; Karwowski, Jacek; Diercksen, Geerd H. F.

doi:10.1088/0953-4075/34/10/312

Cited by 65 publications

(49 citation statements)

References 36 publications

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“…The results presented in table 12 and in figures 3 and 4 show that the initial exponents for s-, p-and d-type basis functions depend linearly on !. This rationalizes the linear selection rules of creating initial exponents used in the previous work [8,21,39,56]. The polarizabilities of the harmonic oscillator quantum dot calculated with the energy optimized initial exponents and with unoptimized initial exponents selected by the rules for calculations of spectral properties of quantum dots [8] are presented in table 13.…”

Section: The Polarizability Of the Quantum Dotsupporting

confidence: 72%

“…There is much less experience with the performance of basis sets in calculations of polarizabilities and other properties of quantum dots and/or confined atoms. To construct such basis sets one can take into account the asymptotic behaviour of the one-electron wavefunction describing an electron confined in a harmonic oscillator potential [39]. From a practical point of view it would be most comfortable to use standard basis sets, at least for the calculation of properties of atoms and molecules trapped in an external confinement.…”

Section: Optimization Of Basis Setsmentioning

confidence: 99%

“…First, there are specific basis sets in which the initial exponents are related to the strength of the confining potential !, see e.g. [39]. Such basis sets will be denoted as 'dynamic basis sets'.…”

Section: Optimization Of Basis Setsmentioning

confidence: 99%

“…The rules [39] by which the initial smallest and largest exponents ( 0 and m l , respectively) are related to the size of the confining potential are summarized in table 1. The fact that the size of the confining potential !…”

Section: Dynamic Basis Setsmentioning

confidence: 99%

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Polarizabilities of confined two-electron systems: the 2-electron quantum dot, the hydrogen anion, the helium atom and the lithium cation

et al. 2005

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The static dipole polarizabilities of two-electron systems confined by a spherical harmonic-oscillator potential ! have been calculated by the coupled-cluster CCSD method. The combined effect of the confining potential ! and the central electrostatic field on the polarizabilities of the quantum dot, and the confined systems, H À , He and Li þ , respectively, have been investigated. The polarizabilities of the quantum dot can be calculated analytically. The polarizability of the 2-electron quantum dot for ! ¼ 0.01 is calculated to be 19 996 au, in perfect agreement with the exact value, 20 000 au. Already medium confinement, ! ¼ 1.0, reduces to 2.00 au. The decrease of the polarizability is smaller for H À ( ¼ 216:1 au for ! ¼ 0.0 and 0.985 au for ! ¼ 1.0), and much smaller for He and Li þ (1.3819 and 0.3813 au for He for ! ¼ 0.0 and ! ¼ 1.0, respectively, and 0.1921 and 0.128 au for Li þ ). The theoretical polarizabilities for unconfined (! ¼ 0.0) H À , He and the Li þ cation are in very good agreement with the best published theoretical and/or experimental data. Our final polarizability for H À , 216:0 AE 0:5 au, appears to be one of the most accurate values published so far. The optimization procedures of basis sets applicable to calculations of polarizabilities of systems confined by a spherical harmonic-oscillator potential are presented.

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Section: The Polarizability Of the Quantum Dotsupporting

confidence: 72%

Section: Optimization Of Basis Setsmentioning

confidence: 99%

Section: Optimization Of Basis Setsmentioning

confidence: 99%

Section: Dynamic Basis Setsmentioning

confidence: 99%

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Polarizabilities of confined two-electron systems: the 2-electron quantum dot, the hydrogen anion, the helium atom and the lithium cation

et al. 2005

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“…Utilizando coordenadas elípticas confocais (4.10), podemos reescrever a função de onda molecular (4.18) da seguinte forma: 19) onde…”

Section: Movimento Eletrônicounclassified

Estudo de sistema molecular confinado

Silva¹

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AgradecimentosTenho inúmeras pessoas a agradecer por este trabalho. Entretanto, especialmente, gostaria de agradecer a algumas pessoas que tiveram participação direta.A Deus, que me proporciona o sopro de vida a cada dia.A minha mãe Versilei. Sempre me incentivou, apoiou e me deu todo o auxílio financeiro que necessitava.A Michele, minha esposa e grande incentivadora.Ao meu tio Lafaiete. Que muitas vezes foi muito mais que um tio e se transformou no "pai" que eu não tive.Ao pastor e irmão Rodrigo Barbom, pela revisão e correção do "abstract".

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Harmonium

Karwowski¹,

Cyrnek²

2004

Annalen der Physik

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The eigenvalue problem of a Hamiltonian describing two interacting particles confined by an external harmonic‐oscillator potential is analyzed. If the particles are identical, the system is referred to as harmonium. Harmonium belongs to very few non‐trivial two‐particle systems for which the Schrödinger equation is not only separable but also, for several interaction potentials and for a set of the coupling constants, quasi‐exactly solvable. In particular, the complete spectrum of harmonium has been obtained and analyzed. Also some aspects or relativistic generalizations of the model are briefly discussed.

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Spectra of confined two-electron atoms

Cited by 65 publications

References 36 publications

Polarizabilities of confined two-electron systems: the 2-electron quantum dot, the hydrogen anion, the helium atom and the lithium cation

Polarizabilities of confined two-electron systems: the 2-electron quantum dot, the hydrogen anion, the helium atom and the lithium cation

Estudo de sistema molecular confinado

Harmonium

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