On the inversion of atomic scattering data: A new algorithm based on functional sensitivity analysis

Journal Article · Fri Dec 15 04:00:00 EST 1989 · Journal of Chemical Physics; (USA)

DOI:https://doi.org/10.1063/1.457281· OSTI ID:5019687

Ho, T; Rabitz, H ^[1]

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1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (US)

A new iterative inversion scheme of atomic scattering data within the framework of functional sensitivity analysis is presented. The inversion scheme is based on the first order Fredholm integral equation {delta}{sigma}({theta})={integral}{sup {infinity}}{sub 0}{ital K}({theta},{ital R}){delta}{ital V}({ital R}){ital R}{sup 2} {ital dR}, {ital K}({theta},{ital R}){equivalent to}{delta}{sigma}({theta})/{delta}{ital V}({ital R}), or symbolically, {delta}{sigma}={ital K}{delta}{ital V}, which relates infinitesimal functional changes in the elastic differential cross section {delta}{sigma}({theta}) and in the underlying interatomic potential {delta}{ital V}({ital R}). This equation can be written equivalently, via integration by parts, as {delta}{sigma}({theta})={integral}{sup {infinity}}{sub 0}{ital K}{sup ({ital n})}({theta},{ital R}) {l brace}{ital R}{sup {ital n}}{times}{delta}{ital V}{sup ({ital n})}({ital R}){r brace}{ital R}{sup 2} {ital dR}, or {delta}{sigma}={ital K}{sup ({ital n})}{l brace}{ital R}{sup {ital n}}{times}{delta}{ital V}{sup ({ital n})}{r brace}, under the {ital a} {ital priori} assumption that {l brace}{ital R}{sup (2+{ital n})}{times}{ital K}{sup ({ital n})}({theta},{ital R}){times}{delta}{ital V}{sup ({ital n}{minus}1)} ({ital R}){r brace}{vert bar}{sup {infinity}}{sub {ital R}=0}=0. Here {ital K}{sup ({ital n})}({theta},{ital R}){equivalent to}{minus}{ital R}{sup {minus}(2+{ital n})} {times}{integral}{sup {ital R}}{sub 0}{ital K}{sup ({ital n}{minus}1)}({theta},{ital R}{prime}) {ital R}{sup {prime}(1+{ital n})}{ital dR}{prime}, {delta}{ital V}{sup ({ital n})}({ital R}) {equivalent to}({ital d}{sup {ital n}}/{ital dR}{sup {ital n}}){delta}{ital V}({ital R}), with {ital n}=0,1,2,..., and {ital K}{sup (0)}({theta},{ital R}){equivalent to}{ital K}({theta},{ital R}).

• OSTI ID: 5019687
• Journal Information: Journal of Chemical Physics; (USA), Journal Name: Journal of Chemical Physics; (USA) Vol. 91:12; ISSN JCPSA; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
ATOM-ATOM COLLISIONS
COLLISIONS
CROSS SECTIONS
DIFFERENTIAL CROSS SECTIONS
ELASTIC SCATTERING
FUNCTIONALS
FUNCTIONS
INTERATOMIC FORCES
INVERSE SCATTERING PROBLEM
ITERATIVE METHODS
SCATTERING
SENSITIVITY ANALYSIS