On the Convergence of the Hylleraas Variational Method

Coolidge, Albert Sprague; James, Hubert M.

doi:10.1103/physrev.51.855

Cited by 73 publications

(38 citation statements)

References 3 publications

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“…The ansatz we chose was introduced by Coolidge and James [13,14] as part of a modification of the so-called Hylleraas method, and it uses the isoperimetrical coordinates: u = r 12 + r 23 − r 13 v = r 12 − r 23 + r 13 w = −r 12 + r 23 + r 13…”

Section: Coulomb Interactionmentioning

confidence: 99%

Testing confining potentials through meson/baryon hyperfine splittings

Keren-Zur

2008

Annals of Physics

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In this paper we discuss a quantity that can be derived from the hadronic spectrum -the ratio between the color hyperfine splitting of a K meson and that of a Σ baryon. It is shown that within the constituent quark model this ratio depends only on the ratio of contact probabilities in the hadrons. We compute this ratio assuming several phenomenological potential models, and show that the best agreement with data is obtained from the Cornell potential -Coulomb + linear. Thus the analysis of color hyperfine interactions corroborates the preference for the Cornell potential based on quarkonium spectra.

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Section: Coulomb Interactionmentioning

confidence: 99%

Testing confining potentials through meson/baryon hyperfine splittings

Keren-Zur

2008

Annals of Physics

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“…The problem is then recast in perimetric coordinates 26 defined as z i = r j + r k − r i ,w h e r ei, j, k denote cyclic permutation of 1, 2, and 3. Perimetric coordinates have the great advantage of being independent over their range from 0 to ∞ unlike the interparticle coordinates, which are connected by the triangular condition and thus have dependent domains.…”

Section: Methodsmentioning

confidence: 99%

The stability of S-states of unit-charge Coulomb three-body systems: From H− to H2+

King

Longford

Cox

2013

The Journal of Chemical Physics

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High accuracy non-relativistic quantum chemical calculations of the ground state energies and wavefunctions of symmetric three-particle Coulomb systems of the form {m ± 1 m ± 2 m ∓ 3 }, m 1 = m 2 , are calculated using an efficient and effective series solution method in a triple orthogonal Laguerre basis set. These energies are used to determine an accurate lower bound to the stability zone of unit-charge three-particle Coulomb systems using an expression for the width of the stability band in terms of g,t h ef r a c t i o n a la d d i t i o n a lb i n d i n gd u et oat h i r dp a r t i c l e .T h er e s u l t sa r ep r e s e n t e di nt h ef o r mo f areciprocalmassfractionternarydiagramandtheenergiesusedtoderi veaparameterisedfunction g(a 3 ), where a 3 = m 3 )isthereciprocalmassoftheuniquelychargedparticle. It is found that the function is not minimal at a 3 = 0whichcorrespondsto∞H − nor is it minimal at the positronium negative ion (Ps − )t h es y s t e mw i t ht h el e a s ta b s o l u t ee n e r g e t i cg a i nb ya s s o c iation with a third particle; the function g(a 3 )i sm i n i m a la tm 1 /m 3 = 0.49, and a possible physical interpretation in terms of the transition from atomic-like to molecular-like is provided. ©2013AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4834036]

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“…1(a), resulting in dependent integration domains. To overcome this difficulty, the problem is recast in perimetric coordinates [8]: linear combinations of r i which have the advantage of being independent over the range 0 → ∞ and take the form z i = r j + r k − r i . 3 , and (b) center-ofmass coordinates r 1 , r 2 ,a n ds i , i = 1o r2 ,w h e r ec is the center of mass.…”

Section: Methodsmentioning

confidence: 99%

Quantum effects of nuclear motion in three-particle diatomic ions

2016

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Article (Published Version) http://sro.sussex.ac.uk Baskerville, Adam L, King, Andrew W and Cox, Hazel (2016) Quantum effects of nuclear motion in three-particle diatomic ions. Physical Review A, 94. 042512. ISSN 1050-2947 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/65251/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.PHYSICAL REVIEW A 94, 042512 (2016) Quantum effects of nuclear motion in three-particle diatomic ions A high-accuracy, nonrelativistic wave function is used to study nuclear motion in the ground state of three-particle {a + 1 a + 2 a − 3 } electronic and muonic molecular systems without assuming the Born-Oppenheimer approximation. Intracule densities and center-of-mass particle densities show that as the mass ratio m a i /m a 3 , i = 1,2, becomes smaller, the localization of the like-charged particles (nuclei) a 1 and a 2 decreases. A coordinate system is presented to calculate center-of-mass particle densities for systems where a 1 = a 2 . It is shown that the nuclear motion is strongly correlated and depends on the relative masses of the nuclei a 1 and a 2 rather than just their absolute mass. The heavier particle is always more localized and the lighter the partner mass, the greater the localization. It is shown, for systems with m a 1

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On the Convergence of the Hylleraas Variational Method

Cited by 73 publications

References 3 publications

Testing confining potentials through meson/baryon hyperfine splittings

Testing confining potentials through meson/baryon hyperfine splittings

The stability of S-states of unit-charge Coulomb three-body systems: From H− to H2+

Quantum effects of nuclear motion in three-particle diatomic ions

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