Direct iteration-variation method for scattering problems

Journal Article · Thu May 01 04:00:00 EDT 1986 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.33.2970· OSTI ID:5960668

Schneider, B I; Collins, L A

We propose a direct iterative-variational scheme to solve the large sets of coupled integro-differential equations that arise in a variety of atomic and molecular scattering problems. The method, which is similar to direct configuration-interaction schemes of quantum chemistry, is applied within the linear algebraic (LA) prescription and involves the construction of an orthonormal basis from successive applications of the general LA matrix, labeled by channels and mesh points, to an initial guess for the solution vector. The solution vector is expanded in this basis, and the linear coefficients determined by a variational scheme. Since the basis is orthonormal, the procedure is guaranteed to converge within n iterations, where n is the order of the matrix. For all cases treated, the convergence is much more rapid. In addition, since a direct method is employed, only the potential, Green's function, and solution vector need be stored. This formulation drastically reduces the central storage requirements of the LA method as well as improves the solution times since the integrals involved can be constructed from recursion relations. We apply the method to elastic scattering of electrons by N/sub 2/ and LiH as well as inelastic collisions from H/sub 2/ /sup +/.

• Research Organization: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 5960668
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 33:5; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ALGEBRA
ALKALI METAL COMPOUNDS
CATIONS
CHARGED PARTICLES
COLLISIONS
ELASTIC SCATTERING
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ELEMENTS
HYDRIDES
HYDROGEN COMPOUNDS
HYDROGEN IONS
HYDROGEN IONS 2 PLUS
INELASTIC SCATTERING
IONS
ITERATIVE METHODS
LITHIUM COMPOUNDS
LITHIUM HYDRIDES
MATHEMATICS
MOLECULAR IONS
MOLECULE COLLISIONS
NITROGEN
NONMETALS
SCATTERING
VARIATIONAL METHODS