Localized integral equation formulation of molecular scattering

Journal Article · Fri Jan 01 04:00:00 EST 1982 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.442739· OSTI ID:5970892

Saha, S; Rabitz, H

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.

• Research Organization: Chemistry Department, Princeton University, Princeton, New Jersey 08544
• OSTI ID: 5970892
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 76:1; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
COLLISIONS
EQUATIONS
INTEGRAL EQUATIONS
MECHANICS
MOLECULE COLLISIONS
QUANTUM MECHANICS
SCATTERING