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Prog. Theor. Phys. Vol. 25 No. 3 (1961) pp. 467-474
Variational Calculation of the Scattering Lengths in Electron-Hydrogen Scattering
Yasuo Hara,
Takashi Ohmura* and
Takahiko Yamanouchi
Department of Physics, University of Tokyo, Tokyo
*Division of Pure Physics, National Research Council of Canada, Ottawa, Canada
and
Department of Physics, Washington University, St. Louis, Mo., U.S.A.
(Received November 25, 1960)
Abstract:
The non-relativistic Schrödinger equation of electron plus
hydrogen-atom system is solved by the Hulthén type variational
method at the limit of zero incident electron energy. 8 and 5
parameter trial functions are used for the singlet and triplet states
respectively, and the following upper bounds on the scattering length
a are obtained,
as ≦6.217a0 (singlet), at ≦2.272a0 (triplet).
Some discussions are given on the accuracy of the result. It is shown that the relation aOH > aSH > aK > a (true) holds for trial functions of the same form if a(true) is positive.
URL :
http://ptp.ipap.jp/link?PTP/25/467/
DOI : 10.1143/PTP.25.467
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