Visualization of electron correlation in ground states of He and H−

Rehmus, Paul; Roothaan, C. C. J.; Berry, R. Stephen

doi:10.1016/0009-2614(78)85045-3

Cited by 40 publications

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“…In this paper, we study the second-order conditional electron density given [12][13][14][15][16] by c (2) N (r 1 |r 2 ) = D (2) N (r 1 , r 2 )/D N (r 2 ) (3) in the Hartree-Fock (HF) theory of N-electron atoms in their ground states. The conditional density c (2) N (r 1 |r 2 ) represents the probability density that when an electron is located at a specific radius r 2 , the other electron is found at r 1 , where we are focusing on any pair of electrons among all of the N electrons, as defined by equation (1).…”

Section: Introductionmentioning

confidence: 99%

Second-order Hartree–Fock conditional electron densities of atoms

Koga¹

2013

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

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The second-order conditional electron density c(2)N(r1|r2) associated with the electron-pair radial density D(2)N(r1, r2) is studied in the Hartree–Fock theory of atoms with N ( ⩾ 2) electrons. In particular, it is shown that when r2 → ∞, 2c(2)N(r1|r2) becomes DN − 1(r1) which is the single-electron radial density of the (N–1)-electron system arising from the removal of the outermost electron from the original system under the frozen orbital approximation. Namely, we can extract the electron density dh(r) of the outermost subshell h from the total electron-pair density D(2)N(r1, r2). Conditional expectations of multiplicative radial operators have the same properties as above. These results apply not only to the spherically averaged densities but also to the densities with angular variables though in some cases we have to specify angular values of the outgoing electron. A numerical illustration is given for the Kr atom.

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Section: Introductionmentioning

confidence: 99%

Second-order Hartree–Fock conditional electron densities of atoms

Koga¹

2013

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

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“…The spatial distribution of particles is also affected by the correlations. For manyelectron systems, the Coulomb repulsion between electrons yields the so called Coulomb hole, in which the distribution of the second electron is largely suppressed in the vicinity of the first electron [1,2]. In atomic nuclei, in contrast, an attractive nuclear force leads to the dineutron and diproton correlations, with which two nucleons are spatially localized in the surface region of nuclei [3,4].…”

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confidence: 99%

Correlated two-neutron emission in the decay of the unbound nucleus <span class="aps-inline-formula"><math><msup><mrow></mrow><mn>26</mn></msup><mi mathvariant="normal">O</mi></math></span>

Hagino

Sagawa

2014

Phys. Rev. C

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The particle unbound 26 O nucleus is located outside the neutron drip line, and spontaneously decays by emitting two neutrons with a relatively long life time due to the centrifugal barrier. We study the decay of this nucleus with a three-body model assuming an inert 24 O core and two valence neutrons. We first point out the importance of the neutron-neutron final state interaction in the observed decay energy spectrum. We also show that the energy and and angular distributions for the two emitted neutrons manifest a clear evidence for the strong neutron-neutron correlation in the three-body resonance state. In particular, we find an enhancement of two-neutron emission in back-to-back directions. This is interpreted as a consequence of dineutron correlation, with which the two neutrons are spatially localized before the emission.PACS numbers: 21.10. Tg,23.90.+w, Correlations among particles lead to a variety of rich phenomena in many-fermion systems, such as superconductivity and superfluidity. The spatial distribution of particles is also affected by the correlations. For manyelectron systems, the Coulomb repulsion between electrons yields the so called Coulomb hole, in which the distribution of the second electron is largely suppressed in the vicinity of the first electron [1,2]. In atomic nuclei, in contrast, an attractive nuclear force leads to the dineutron and diproton correlations, with which two nucleons are spatially localized in the surface region of nuclei [3,4]. These nuclear correlations have attracted lots of attention recently [5][6][7][8][9], in connection to physics of weakly bound nuclei.In order to probe the inter-particle correlation, it has been a standard way in atomic physics to measure a double ionization with strong laser fields [10][11][12][13]. It has been observed that the ionization rate is significantly enhanced due to the electronic correlation, and moreover, there is a strong momentum correlation between the two emitted electrons. The corresponding experiment in nuclear physics is the Coulomb breakup of the Borromean nuclei 11 Li and 6 He, in which those nuclei are broken up to the core nuclei, 9 Li and 4 He, and two neutrons in the Coulomb field of a target nucleus [14][15][16]. The observed breakup probabilities, especially those for the 11 Li nucleus, show a sharp peak in the low-energy region, which can be accounted for only by taking into account the neutron-neutron correlations. Furthermore, from the observed strength distribution, the opening angle between the valence neutrons in the ground state of the Borromean nuclei has been inferred employing the cluster sum rule [14,17,18]. For both 11 Li and 6 He, the extracted opening angles were significantly smaller than the value for the independent neutrons, that is, 90 degrees, and clearly indicate the existence of the dineutron correlation.A small drawback with the cluster sum rule approach is that it yields only an expectation value of the opening angle and a detailed angular distribution cannot be studied with this method. F...

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“…The rapid convergence of those wave functions is due both to the ease with which they can reproduce the Coulomb hole in the neighborhood of the cusp and to the fact that the Coulomb hole has a rather simple structure when viewed relative to one of the electrons, while it has a rather complex structure when viewed relative to a fixed set of axes [6]. Thus a description in terms of a superposition of configurations is both complicated and slowly convergent as has been graphically illustrated by Rehmus, Roothaan, and Berry [7].…”

Section: Introductionmentioning

confidence: 91%

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

Moskowitz

Kalos

1981

Int J of Quantum Chemistry

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We are engaged in research directed toward the development of compact and accurate correlation functions for many-electron systems. Our computational tool is the variational method in which the many-electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many-fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance r,, may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi "holes" are very easily obtained. Preliminary results are reported for He, H2, and Liz.

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Visualization of electron correlation in ground states of He and H−

Cited by 40 publications

References 9 publications

Second-order Hartree–Fock conditional electron densities of atoms

Second-order Hartree–Fock conditional electron densities of atoms

Correlated two-neutron emission in the decay of the unbound nucleus <span class="aps-inline-formula"><math><msup><mrow></mrow><mn>26</mn></msup><mi mathvariant="normal">O</mi></math></span>

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

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