Abstract
We used the method of phase functions to solve the radial relativistic Dirac equation and nonrelativistic Schroedinger equation. With these solutions, we investigated the elastic scattering of slow electrons by a uranium atom, and obtained numerical values for the total cross section and elastic scattering phases. In order to check the correctness of the results found from the method of phase functions, in all cases we also solved the Dirac and Schroedinger equations by direct numerical integration. Several types of polarization and exchange potentials were used to simulate the scattering process. We conclude that the strong dependence of the cross section for elastic scattering of an electron by uranium on the shape of the effective potential of the latter at small kinetic energies (E k<5 eV) makes it impossible to predict the presence or absence of a Ramsauer effect reliably.
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References
L. P. Kudrin and A. A. Drozdov, Atomnaya Energiya 27, 39 (1969) [in Russian].
F. Calogero, Variable Phase Approach to Potential Scattering (Academic Press, New York, 1967; Russ transl. Mir, Moscow, 1972).
V. V. Babikov, The Method of Phase Functions in Quantum Mechanics (Nauka, Moscow, 1988).
P. Gombàs, Theorie und Lösungsmethoden des Mehrteilchenproblems der Wellenmekanik (Many-Body Problems in Wave Mechanics: Theory and Solution Methods) (Birkhauser, Basel, 1950; Russ transl. IL, Moscow, 1952).
D. R. Hartree, The Calculation of Atomic Structures (Wiley, New York, 1957; Russ. transl. IL, Moscow, 1960).
D. P. Grechukhin and A. V. Lomonosov, Preprint NAE 5789/12 (1994).
D. P. Grechukhin and A. V. Lomonosov, JETP Lett. 60, 779 (1994).
A. I. Akheizer and V. B. Berestetskii, Quantum Electrodynamics (Nauka, Moscow, 1969 [3rd edition]; Eng. transl. Wiley, New York, 1965).
Handbook of Special Functions, M. I. Abramowitz and I. A. Stegun eds. (Dover, New York, 1965; Nauka, Moscow, 1969).
J. C. Slater, The Self-Consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974; Mir, Moscow, 1978).
U. von Barth and L. Hedin, J. Phys. C 4, 2064 (1971).
J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
S. H. Volsko, L. Wijk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
J. K. O’Connel and N. F. Lane, Phys. Rev. A 27, 1893 (1983).
J. Hara, J. Phys. Soc. Jpn. 22, 710 (1967).
M. E. Riley and D. G. Truhler, J. Chem. Phys. 63, 2182 (1975).
G. A. Korn and T. M. Korn, Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1961; Nauka, Moscow, 1972).
D. P. Grechukhin and A. V. Lomonosov, Preprint NAE 5992/12 (1996).
H. P. Saha, Phys. Rev. A 43, 4712 (1991).
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Zh. Éksp. Teor. Fiz. 111, 1214–1228 (April 1997)
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Grechukhin, D.P., Lomonosov, A.V. Elastic scattering of low-energy electrons by a uranium atom: Reliability of theoretical predictions of based on a model description. J. Exp. Theor. Phys. 84, 669–677 (1997). https://doi.org/10.1134/1.558199
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DOI: https://doi.org/10.1134/1.558199