Projection-operator calculations for shape resonances: A new method based on the many-body optical-potential approach

Journal Article · Tue May 01 04:00:00 EDT 1984 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.29.2485· OSTI ID:6813911

Berman, M; Domcke, W

The projection-operator formalism of Feshbach defines a separation of the T matrix into a smooth background term and a resonant T matrix which may vary rapidly with energy. The resonance is characterized by an unperturbed energy epsilon/sub d/, a width function GAMMA(E), and a level-shift function ..delta..(E). Such a separation of the fixed-nuclei electron-molecule scattering T matrix is of considerable practical relevance for the treatment of nuclear dynamics in resonant electron-molecule scattering. We present an explicit realization of the projection-operator formalism for electron-molecule scattering within the framework of the many-body optical-potential approach. In contrast to the approach of Hazi (J. Phys. B 11, L259 (1978)) which is based on the use of Stieltjes moment techniques to compute GAMMA(E), we obtain explicitly the background T matrix as well as the information on the angular distribution of the resonant scattering. The performance of the method is illustrated for the well-known 2.3-eV shape resonance in electron scattering from the nitrogen molecule. The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) is adopted for the optical potential and the Schwinger variational principle is used to solve the background scattering problem. The resulting resonance parameters epsilon/sub d/, GAMMA(E), ..delta..(E), and the resonant eigenphase sum are in excellent agreement with results obtained previously by Hazi using different computational methods.

• Research Organization: Theoretische Chemie, Institut fuer Physikalische Chemie, im Neuenheimer Feld 253, Universitat Heidelberg, D-6900 Heidelberg, West Germany
• OSTI ID: 6813911
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 29:5; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR DISTRIBUTION
COLLISIONS
DISTRIBUTION
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ELEMENTS
INELASTIC SCATTERING
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATRICES
MOLECULE COLLISIONS
NITROGEN
NONMETALS
OPTICAL MODELS
PROJECTION OPERATORS
RESONANCE SCATTERING
S MATRIX
SCATTERING
SCHWINGER VARIATIONAL METHOD
TAMM-DANCOFF METHOD
VARIATIONAL METHODS