Complex coordinate calculations of resonances in N-electron atoms. [Wave function structure, position, width, variational methods]

Journal Article · Sun Oct 01 04:00:00 EDT 1978 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560140406· OSTI ID:6429799

Junker, B R

A discussion is presented of the functional dependences of the wave functions for bound, resonant, and scattering states on the radial coordinate rho and the rotation angle ..cap alpha.. in the complex coordinate method. It is concluded that for bound states and resonances, rho and ..cap alpha.. are constrained to appear in the wave functions only in the form rho exp (i..cap alpha..). On the other hand, this constraint is not obtained for the scattering states since the energy of the scattering states depends on ..cap alpha... In addition a partitioning of the resonant wave function into two parts--a boundlike or Q-space part and a scattering like or P-space part is suggested. With these concepts one can incorporate physical insight into the choice of configurations as one does in other methods and can apply the complex coordinate method to many electron systems with an expected rate of convergence similar to other techniques. Its advantages are that a single calculation yields the position and width of the resonance, only square integrable functions are used, only a solution of a straightforward eigenvalue problem is required unlike some methods, arbitrarily accurate target states are easily incorporated, and polarization terms can easily be explicitly included. Variational calculations for the position and width of the lowest /sup 2/S resonance in the negative helium ion are reported using trial wave functions containing 39, 43, 55, 24, and 32 P-space configurations, respectively. Values of 19.387 eV and 12.13 MeV are obtained for the position and width, respectively, for the resonance over a range in the rotation angle of almost two orders of magnitude. One also finds that inclusion of free-particle-like basis functions improves the representation of the scattering states. 21 references.

• Research Organization: Office of Naval Research, Arlington, VA
• OSTI ID: 6429799
• Journal Information: Int. J. Quant. Chem.; (United States), Journal Name: Int. J. Quant. Chem.; (United States) Vol. 14:4; ISSN IJQCB
• Country of Publication: United States
• Language: English

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Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
ANIONS
ATOMS
BOUND STATE
BOUNDARY CONDITIONS
CHARGED PARTICLES
CONFIGURATION
COORDINATES
EIGENVALUES
ENERGY LEVELS
EXCITED STATES
FUNCTIONALS
FUNCTIONS
HELIUM IONS
IONS
LEVEL WIDTHS
MATHEMATICAL SPACE
POLARIZATION
RESONANCE
ROTATIONAL STATES
SCATTERING
SPACE
VARIATIONAL METHODS
WAVE FUNCTIONS