An information theoretic synthesis and analysis of Compton profiles

Sears, Stephen B. ; Gadre, Shridhar R. (1981) An information theoretic synthesis and analysis of Compton profiles The Journal of Chemical Physics, 75 (9). pp. 4626-4635. ISSN 0021-9606

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The information theoretic technique of entropy maximization is applied to Compton profile (CP) data, employing single and double distribution moments <pn≳ as constraints. Emphasis is placed on the first and second (n = 1,2) moments— the average momentum and energy, respectively. Studies are made both on semi-infinite and finite ranges of the variable q in the Compton profile J(q). The quality of resulting maximum entropy profiles is judged by how well they predict familiar CP quantities— moments, the profiles' magnitude at the origin J(0), and the width at half-maximum q0.5. Information theoretic quantities— Shannon entropies, information contents, and surprisals— are also presented. Based upon the "sum" constraint <q+q2≳ , a relation is derived which approximately predicts J(0) given q0.5 (or vice versa) for a large class of molecular systems, i.e., J(0) = (2/N)exp[-K/4][K]1/2[(π 1/2/2)@(K1/2/2)]@qL -1, where K = ln 2/(q20.5+q0.5). The assimilation of more and more constraints (information) results in generally improved Compton profiles. The average momentum constraint contains the most information of all moment expectation values, as judged by its predictive capacity and by the information theory measures.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Compton Effect; Expectation Value; Information Theory; Atoms; Molecules
ID Code:86906
Deposited On:14 Mar 2012 07:48
Last Modified:14 Mar 2012 07:48

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