Coulomb Wave Functions in the Transition Region

Milton Abramowitz; H. A. Antosiewicz

doi:10.1103/PhysRev.96.75

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Coulomb Wave Functions in the Transition Region

Milton Abramowitz

H. A. Antosiewicz

Computation Laboratory, National Bureau of Standards, Washington, D. C.

Mathematics Department, The American University, Washington, D. C.

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Phys. Rev. 96, 75 – Published 1 October, 1954

DOI: https://doi.org/10.1103/PhysRev.96.75

Abstract

Expansions, involving the Airy integrals, of the functions $F_{L} (η, ρ)$ , $G_{L} (η, ρ)$ are obtained from a study of the Coulomb wave equation. These expansions are convergent in the region $| ρ - ρ_{1} | < ρ_{1}$ , where $ρ_{1} = η + {[η^{2} + L (L + 1)]}^{\frac{1}{2}} .$

References (5)

Tables of Coulomb Wave Functions, National Bureau of Standards, Applied Mathematics Series 17 (U. S. Government Printing Office, Washington, D. C., 1952), Vol. 1
Bloch, Hull, Broyles, Bouricius, Freeman, and Breit, Phys. Rev. 80, 553 (1950) T. D. Newton, Atomic Energy of Canada, Limited. Unclassified Report, CRT-526 (unpublished)
T. D. NewtonThe Airy Integral (British Association for the Advancement of Science, Cambridge, 1946)
[M. Abramowitz and P. Rabinowitz, Phys. Rev. 96, 77 (1954)]
H. A. Antosiewicz and M. Abramowitz, "A Representation for Solutions of Analytic Systems of Linear Differential Equations," J. Wash. Acad. Sci. (to be published)

[c1] Tables of Coulomb Wave Functions, National Bureau of Standards, Applied Mathematics Series 17 (U. S. Government Printing Office, Washington, D. C., 1952), Vol. 1

[c2] Bloch, Hull, Broyles, Bouricius, Freeman, and Breit, Phys. Rev. 80, 553 (1950) T. D. Newton, Atomic Energy of Canada, Limited. Unclassified Report, CRT-526 (unpublished)

[c3] T. D. NewtonThe Airy Integral (British Association for the Advancement of Science, Cambridge, 1946)

[c4] [M. Abramowitz and P. Rabinowitz, Phys. Rev. 96, 77 (1954)]

[c5] H. A. Antosiewicz and M. Abramowitz, "A Representation for Solutions of Analytic Systems of Linear Differential Equations," J. Wash. Acad. Sci. (to be published)

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Coulomb Wave Functions in the Transition Region

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References (5)

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