Abstract
In this paper using the approximate Rozental solution for the Thomas-Fermi function for free neutral atoms we derive a formula for the phase shifts for the Thomas-Fermi potential, which does not include the electrostatic self-interaction of the electron. The derivation of this formula for the considered phase shift is similar to the Born method, and the difference consists only in the fact that instead of Bessel functions we take hydrogenic functions.
Резюме
В настоящей работе с помощью приближенного решения Розенталя функции Томаса —ферми для нейтрального атома выводим такую формулу для сдвигов фаз потенциала Томаса—Ферми, которая не содержит электростатического собственного взаимодействия электрона. Вывод формулы аналогичен методу Борна, с той разницей, что мы пользуемся водородными функциями вместо Бесселевых функций.
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References
P. Gombás, Die statistische Theorie des Atoms, Springer Verlag, Wien, 1949.
N. F. Mott andH. S. W. Massey, The Theory of Atomic Collisions, p. 53, Oxford, Clarendon Press, 1949.
S. Rozental, Z. f. Physik,98, 742, 1936.
The integral equation (10) was discussed in detail in “The problem of vacuum polarisation in the proton-proton scattering problem” byL. Durand, Phys. Rev.,108, 1597, 1957.
The phase shifts of Thomas-Fermi and Hartree fields will be discussed in a forthcoming paper of the author, which will appear in Ann. d. Physik.
W. Henneberg, Z. f. Physik.,83, 555, 1933.
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Tietz, T. The phase shifts for the Thomas-Fermi potential corrected for the self-interaction of the electron. Acta Physica 10, 169–172 (1959). https://doi.org/10.1007/BF03156665
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DOI: https://doi.org/10.1007/BF03156665