Wavelength dependence of high-harmonic yield in stretched molecules
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We derive the Scott correction to the atomic electron density in momentum space. The implied corrections to expectation values of powers of the momentum, as well as to the Compton profile, are then obtained.
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Thomas–Fermi model
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A series of increasingly accurate wavefunctions for H-, and He built from Gaussian geminals is presented. Such wavefunctions are found to be much more compact than configuration interaction wavefunctions of similar accuracy. Moreover, comparison with nearly exact values shows that they predict one- and two-electron moments in position space quite well but perform less satisfactorily with respect to point properties. The wavefunctions can be Fourier-Dirac transformed in closed form and are used to predict values of one- and two-electron momentum space properties including Compton profiles. Most of these momentum properties are expected to be of benchmark quality.
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Electronic correlation
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Helium atom
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Momentum space representations of helium P-state wavefunctions are derived, based on the Fourier transform of highly accurate coordinate space wavefunctions. Applications to the fine structure of helium, which can be used to determine the fine structure constant, are presented.
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Isotopes of helium
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We show how the momentum distribution of gaseous Bose-Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity was demonstrated in an earlier experiment [L. Deng et al., Phys. Rev. Lett. 83, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.
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ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTNumerical Methods for Finding Momentum Space DistributionsFrank Rioux View Author Information Department of Chemistry, Saint John''s University , Collegeville, MN 56321Cite this: J. Chem. Educ. 1997, 74, 5, 605Publication Date (Web):May 1, 1997Publication History Received3 August 2009Published online1 May 1997Published inissue 1 May 1997https://pubs.acs.org/doi/10.1021/ed074p605https://doi.org/10.1021/ed074p605research-articleACS PublicationsRequest reuse permissionsArticle Views242Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose SUBJECTS:Fourier transforms,Schrodinger equation Get e-Alerts
Momentum (technical analysis)
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Position (finance)
Electronic correlation
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Fourier integral techniques are used to generate non-diagonal first-order density matrices (1-matrices) from two-electron atomic wavefunctions containing exponential correlation terms. Although the techniques presented here can be applied to larger systems, the lengthy amounts of algebra limit their usefulness. The 1-matrices generated from two-electron correlated wavefunctions have been transformed to momentum space. The Compton profile obtained from a He wavefunction yielding over 99% of the correlation energy is presented.
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Electronic correlation
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Momentum (technical analysis)
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The authors report results on the wavefunction representation of doubly excited states of He and on their autoionisation probability amplitudes in momentum space. These are presented in terms of conditional probability density and differential transition amplitude plots. The correlated momentum wavefunctions are obtained by Fourier-transforming position wavefunctions computed by multiconfigurational Hartree-Fock and variational procedures. Special techniques are developed for the Fourier transform of the numerical Hartree-Fock scattering orbitals. The differential transition amplitude plots lead to the same conclusions regarding the mechanism of autoionisation as did the previous work in position space.
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Momentum (technical analysis)
Configuration space
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