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- W2024410166 abstract "It is demonstrated that a good share of the error Shakeshaft attributes to the failure to account for ionization in customary impact-parameter calculations for proton-hydrogen-atom scattering amplitudes really results from the inadequacy of the traveling hydrogenic basis set to account for the dynamic polarization of the hydrogen atom by the moving proton. The lower limit for the first-order bound can be reduced by using hydrogenlike basis functions that allow for this polarization. Bounds on the cross sections obtained by using the bound ${ensuremath{Delta}}_{1}$ need not be infinite. The inclusion of time-dependent adjustable parameters in the basis functions provides a method for modifying the projection of the deviation vector or error term in the Schrodinger equation in the continuum. The exploratory work of Storm and Rapp appears to offer hope that reasonably accurate bounds on at least the $1s$ charge exchange amplitudes and cross sections can be obtained by employing only square-integrable basis functions that contain time-dependent variable parameters. However, if it is necessary to account for the flux in the ionization channels, it is shown that an account could be made without the bound becoming infinite." @default.
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- W2024410166 date "1975-11-01" @default.
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- W2024410166 title "Reply to Limitation on numerical bounds on transition probabilities" @default.
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- W2024410166 doi "https://doi.org/10.1103/physreva.12.2234" @default.
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