Association of resonance states with the incomplete spectrum of finite complex-scaled Hamiltonian matrices

Journal Article · Fri Aug 01 04:00:00 EDT 1980 · Phys. Rev., A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.22.618· OSTI ID:5173950

Moiseyev, N; Friedland, S

The incomplete spectrum of finite complex-scaled Hamiltonian matrices H/sub eta/ is studied. It is pointed out that the occurrence of an incomplete spectrum of complex-scaled Hamiltonians in the finite-element approximation is neither accidental nor rare, and the existence of a defective eigenvector (orthogonal to itself) of H/sub eta/ can be associated with a complex-stationary point which represents the resonance state. A physical interpretation of the incomplete spectrum (the eigenvalues of a defective Hamiltonian matrix) is given, supported by numerical results for e/sup -/-He/sup +/ scattering worked out as an example. The numerical procedure suggested here for the purpose of identifying the resonance state with the eigenvalue associated with the defective eigenvector of H/sub eta/, may prove to be not very practical. This is so as long as only relatively small basis sets are used. However, in the finite-element approximation, this procedure does yield a better understanding of the behavior of the resonance solution.

• Research Organization: Department of Chemistry, Technion-Israel Institute of Technology, Haifa, Israel
• OSTI ID: 5173950
• Journal Information: Phys. Rev., A; (United States), Journal Name: Phys. Rev., A; (United States) Vol. 22:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOMIC MODELS
COLLISIONS
DIFFERENTIAL EQUATIONS
ELECTRON COLLISIONS
ELECTRON-ION COLLISIONS
ENERGY LEVELS
EQUATIONS
FUNCTIONS
HAMILTONIAN FUNCTION
HELIUM IONS
ION COLLISIONS
IONIZATION
MATHEMATICAL MODELS
SCHROEDINGER EQUATION
WAVE EQUATIONS