Resonances and Pseudoresonances in the Kohn Variational Method and the Feshbach Method

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概要

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• An operator formalism of the general single-channel Kohn method is developed, and Schwartz's theory of singularities in the Kohn method is generalized; any approximation method described in the framework of the Kohn method is shown to have, in general, singularities, some of which may correspond to true (either closed-channel or shape) resonances. Caution is urged against simple interpretation of "resonance results" of close-coupling calculations and other expansion methods. The Feshbach 〓H〓 eigenvalues are shown to be approximations to the positions of the Kohn-method singularities. A correction to the Schwartz theory leads to the Harris method. Precisely at the characteristic Harris eigenvalues, the Hulthen condition <Ψ∣E-H∣Ψ>=0 cannot be satisfied in general, though, as was shown previously, a well-defined limiting value (which is equal to the Harris value, and has a first-order error contrary to a variational phase shift) of the Hulthen phase shift exists. An elaborate Kohn-method calculation of e+H elastic scattering produces the lowest singlet resonance position which gives the level shift of 1.0×10^<-5> Rydberg from the autoionizing-state energy calculated by Bhatia, Temkin, and Perkins.

• 社団法人日本物理学会の論文
• 1971-09-05

著者

• Shimamura Isao

  Department Of Applied Physics Faculty Of Engineering University Of Tokyo

関連論文

• A Harris-Method Calculation of Electron and Positron Scattering by Hydrogen Atoms
• Bounds on Weighted Mean Errors of Approximate Wave Functions. : I. Theory
• Harris-Method Calculations of Electron and Positron Scattering by Hydrogen-Like Ions
• Variational Upper and Lower Bounds on Phase Shifts
• Resonances and Pseudoresonances in the Kohn Variational Method and the Feshbach Method

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