A localized integral equation formulation of molecular scattering

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Abstract

A new integral equation formulation is presented for molecular scattering. This is obtained by exactly transforming the common close-coupling theory into an equivalent nonlocal integral equation form which is not a set of coupled discrete basis equations. The integral equation is formally localized by the introduction of a translation operator, thereby leading to a Hamiltonian (or portion of it) that is a Fourier transform of the original kernel. The theory makes no use of Green's functions and this overall approach has two attractive features. Firstly, an examination of the integral kernels allows the development of optimal quadrature schemes for each problem and, secondly, judicious approximations of the localized Hamiltonian operator lead to very attractive practical equations. As an illustration of the latter point, the method is applied to replace the differential internal Hamiltonian operator by an effective local function which can act to correct the usual sudden approximation without excess computational effort. Various asymptotic limits of the theory are also discussed.

Original languageEnglish (US)
Pages (from-to)417-428
Number of pages12
JournalThe Journal of Chemical Physics
Volume76
Issue number1
DOIs
StatePublished - Jan 1 1982

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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