The compressed helium atom variationally treated via a correlated Hylleraas wave function

Aquino, N.; Flores-Riveros, A.; Rivas-Silva, J.F.

doi:10.1016/s0375-9601(02)01767-x

Cited by 72 publications

(91 citation statements)

References 35 publications

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“…In the strong confinement regime (that is for small values of r c ) the maximum difference between our results and those of Ref. [18,19] is of the order of 0.006 a.u..…”

Section: A Ground Statecontrasting

confidence: 59%

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Calculation of ground- and excited-state energies of confined helium atom

2006

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“…In the strong confinement regime (that is for small values of r c ) the maximum difference between our results and those of Ref. [18,19] is of the order of 0.006 a.u..…”

Section: A Ground Statecontrasting

confidence: 59%

“…In Table I Hylleraas wave function variational calculation [19] and the most accurate QMC based method. In the strong confinement regime (that is for small values of r c ) the maximum difference between our results and those of Ref.…”

Section: A Ground Statementioning

confidence: 99%

Calculation of ground- and excited-state energies of confined helium atom

2006

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“…In particular, the research activity has expanded towards investigating properties of confined real two electron systems. The impact of confinement on the properties of helium atom and its iso-electronic ions was mainly addressed in literature in connection with impenetrable spherical walls [3][4][5][6][7][8][9][10]. Physical properties of such systems e.g.…”

Section: Introductionmentioning

confidence: 99%

Ground-State Entanglement Properties of Helium Atom in a Finite Spherical Cavity

Kościk

Saha

2015

Few-Body Syst

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“…Contrary to the free helium atom, the confined helium has not been described with a very high accuracy until recently, when we have developed a Lagrange-mesh method to study this system [1]. This method improves by several order of magnitudes the accuracy of previous approaches [2][3][4].The outlines of the model are the following. The assumed-infinite-mass nucleus is fixed and the electrons are characterized by coordinates r 1 and r 2 with respect to this nucleus.…”

mentioning

confidence: 99%

“…Ground-state energies and mean interparticle distances for several confinement radii R are given in table 1. The pressure acting on the confined helium atom is also given in calculated from the radius dependence of the energies E(R) by the formula [2][3][4],…”

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confidence: 99%

Helium atom under pressure

Dohet-Eraly

Baye

2016

EPJ Web of Conferences

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Abstract. Hard-sphere confinement is used to study helium atoms under pressure. The confined-helium Schrödinger equation is solved with a high accuracy by a Lagrangemesh method.The effects of high pressure on a helium gas can be estimated by studying the helium atom in a hard confinement, i.e. confined at the centre of an impenetrable spherical cavity, for different cavity radii. Contrary to the free helium atom, the confined helium has not been described with a very high accuracy until recently, when we have developed a Lagrange-mesh method to study this system [1]. This method improves by several order of magnitudes the accuracy of previous approaches [2][3][4].The outlines of the model are the following. The assumed-infinite-mass nucleus is fixed and the electrons are characterized by coordinates r 1 and r 2 with respect to this nucleus. In atomic units, the Hamiltonian of the helium atom readswhere r 12 = r 1 − r 2 and Δ 1 and Δ 2 are the Laplacians with respect to r 1 and r 2 . The confinement is introduced by forcing the wave function into some spherical cavity of radius R (r 1 , r 2 ≤ R). The wave function ψ(r 1 , r 2 , r 12 ) of an S state must thus verify the Schrödinger equationand vanishes at r 1 = R and r 2 = R. The coordinates (r 1 , r 2 , r 12 ) are advantageously replaced by the coordinates (u, v, w) defined over [0,1] byThe confinement implies that the wave function ψ(u, v, w) vanishes at u = 1, v = 1, and w = 1. The Schrödinger equation is solved by the Lagrange-mesh method [5][6][7], an approximate variational approach taking the form of a system of mesh equations by computing the Hamiltonian and overlap matrix elements with a Gauss quadrature. Using the coordinates (u, v, w) is essential for an easy treatment of the confinement and an high accuracy of the Gauss quadrature. The ground-state energy and wave function are obtained by diagonalizing a rather large (matrix dimension≈ 10 3 ∼ 2×10 4 ) but sparse matrix. Ground-state energies and mean interparticle distances for several confinement radii R are given in table 1. The pressure acting on the confined helium atom is also given in table 1. It is a

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The compressed helium atom variationally treated via a correlated Hylleraas wave function

Cited by 72 publications

References 35 publications

Calculation of ground- and excited-state energies of confined helium atom

Calculation of ground- and excited-state energies of confined helium atom

Ground-State Entanglement Properties of Helium Atom in a Finite Spherical Cavity

Helium atom under pressure

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