Asymptotic form of the charge-exchange cross section in three-body rearrangement collisions

Details Asymptotic form of the charge-exchange cross section in three-body rearrangement collisions Asymptotic form of the charge-exchange cross section in three-body rearrangement collisions

Sep 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrva..12..911o&link_type=abstract

Physical Review A - General Physics, 3rd Series, vol. 12, Sept. 1975, p. 911-926.

Physics

General Physics

27

Born Approximation, Charge Exchange, Electron Capture, Particle Collisions, Scattering Cross Sections, Angular Momentum, Asymptotic Methods, Atomic Collisions, Electron States, Ground State, Hydrogen Atoms, Scaling Laws, Wave Functions

Scientific paper

A three-body general-type rearrangement collision is considered in which the initial and final bound states are described by hydrogen-like wave functions. It is shown that the charge-exchange amplitude in the first Born approximation can be expanded at all incident energies in terms of the inverse powers of the principal quantum number (n). By expanding the exchange amplitude in this way, it is demonstrated conclusively that the cross section for capture into the s, p, and d states as well as for the sum over all the angular-momentum states is proportional to 1/n-cubed plus terms proportional to higher inverse odd powers of n. It is found that the low-lying levels cannot be scaled to the 1/n-cubed law irrespective of the value of the incident energy except in the case of capture into the s states in accordance with the Oppenheimer-Brinkman-Kramers approximation. Zeros and minima in the differential cross sections are given in the limit of high principal quantum number for electron capture by protons from atomic hydrogen and for positronium formation by proton-atomic hydrogen collisions.

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