The Pseudo-Atom : A Soluble Many Body Problem

Moshińsky, M.; Novaro, O.; Calles, A.

doi:10.1051/jphyscol:1970422

Cited by 11 publications

(10 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The agreement with our exact results puts the adiabatic-SCE and the adiabatic-ZPE approximations on firmer ground and gives confidence in employing the formalism of strictly correlated electrons in the adiabatic approximation for calculating response properties of strongly correlated systems. To illustrate some properties of the response function in the large interaction limit for an inhomogeneous system, let us analyze a model system of two harmonically confined electrons in three dimensions with a harmonic repulsion [59]. The Hamiltonian of the system is given bŷ…”

Section: Discussionmentioning

confidence: 99%

Time-dependent density-functional theory for strongly interacting electrons

et al. 2017

View full text Add to dashboard Cite

We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density response function, is studied in the limit of large repulsive interactions between the electrons and we give analytical results for these quantities as an asymptotic expansion in powers of the square root of the interaction strength. We find that in the strong interaction limit the three leading terms in the expansion of the kernel act instantaneously while memory terms only appear in the next orders. We further derive an alternative expansion for the kernel in the strong interaction limit on the basis of the theory developed previously [Phys. Chem. Chem. Phys. 18, 21092 (2016)] using the formalism of strictly correlated electrons in the adiabatic approximation. We find that the first two leading terms in this series, corresponding to the strictly correlated limit and its zero-point vibration correction, coincide with the two leading terms of the exact expansion. We finally analyze the spatial nonlocality of these terms and show when the adiabatic approximation breaks down. The ability to reproduce the exact kernel in the strong interaction limit indicates that the adiabatic strictly correlated electron formalism is useful for studying the density response and excitation properties of other systems with strong electronic interactions.

show abstract

Section: Discussionmentioning

confidence: 99%

Time-dependent density-functional theory for strongly interacting electrons

et al. 2017

View full text Add to dashboard Cite

show abstract

“…state energy at β 0 is equal to the energy of the first-excited state at β 1 ,is equal to the energy of 2th-excited state at β 2 etc, is equal to the energy of nth excited state at β n . 3 For the Coulomb the second-type representation is nothing but the well-known Sturm representation. 4 It belongs to the case VIII in the classification [5].…”

mentioning

confidence: 99%

“…In[3] so called pseudo atoms were introduced : quantum system made from atomic ones in which all Coulomb interactions are replaced by oscillator ones, attractive or repulsive as the case may be. The system described by (1) can be treated as modified twoelectron pseudo atom: where Coulomb attractive interactions are replaced by oscillator ones, while Coulomb repulsion remains unchanged or modified by the linear interaction.2 Precisely speaking, this means that for the parameters β 0 , β 1 , .…”

mentioning

confidence: 99%

Two electrons in an external oscillator potential: The hidden algebraic structure

Turbiner

1994

Phys. Rev. A

View full text Add to dashboard Cite

It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden sl 2 -algebraic structure being one of recently-discovered quasi-exactly-solvable problems. The origin of existing exact solutions to this problem, recently discovered by several authors, is explained. A degeneracy of energies in electron-electron and electron-positron correlation problems is found. It manifests the first appearence of hidden sl 2 -algebraic structure in atomic physics. PASC: 03.65.Fd and 03.65.Ge † On leave of absence from the

show abstract

“…A third example is the so-called pseudoatom model by Moshinsky and co-workers [14]. In this model both the electron-nucleus and electron-electron interactions are replaced by harmonic oscillator interactions (attractive in the first case and repulsive in the second).…”

Section: Discussionmentioning

confidence: 99%

Correlation energies of light atoms related to pairing between antiparallel spin electrons

Alonso

March

Cordero

et al. 2003

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

View full text Add to dashboard Cite

Early theoretical work emphasized the gross trend of the total correlation energy of neutral atoms with atomic number Z . This was later improved quantitatively, by focusing on the number of pairings between antiparallel-spin electrons in the same main shell (i.e., K, L, M . . . shells). Here, this viewpoint is pressed, and correlation energies associated with s-s, s-p and p-p pairings are extracted. The s-s energy turns out to be rather insensitive to a change from K to L shells, but a small increase is found to occur in the M shell. Also, the s-p and p-p pairing energies show a small increase from the L to the M shells. The s-s and s-p energies are ≈1 eV, the s-s contribution being the larger. The p-p energy is ≈1/3 eV. The effect of removing or adding one electron to the neutral atom has also been analysed. Wavefunction overlap and wavefunction localization appear to control the values of the pairing energies.

show abstract

The Pseudo-Atom : A Soluble Many Body Problem

Cited by 11 publications

References 2 publications

Time-dependent density-functional theory for strongly interacting electrons

Time-dependent density-functional theory for strongly interacting electrons

Two electrons in an external oscillator potential: The hidden algebraic structure

Correlation energies of light atoms related to pairing between antiparallel spin electrons

Contact Info

Product

Resources

About