Coulomb excitation of nuclei
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1: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►Positive-energy functions correspond to processes such as Rutherford scattering and Coulomb excitation of nuclei (Alder et al. (1956)), and atomic photo-ionization and electron-ion collisions (Bethe and Salpeter (1977)).
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§33.22(i) Schrödinger Equation
… ►Attractive potentials: | , . |
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§33.22(iv) Klein–Gordon and Dirac Equations
…2: Bibliography B
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The attractive Coulomb potential polynomials.
Constr. Approx. 1 (2), pp. 103–119.
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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy.
Comput. Phys. Comm. 21 (3), pp. 297–314.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Quasinormal ringing of Kerr black holes: The excitation factors.
Phys. Rev. D 74 (104020), pp. 1–27.
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Coulomb functions for reactions of protons and alpha-particles with the lighter nuclei.
Rev. Modern Physics 23 (2), pp. 147–182.
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3: 33.17 Recurrence Relations and Derivatives
4: 33.15 Graphics
§33.15 Graphics
►§33.15(i) Line Graphs of the Coulomb Functions and
► … ►§33.15(ii) Surfaces of the Coulomb Functions , , , and
… ► …5: 33.2 Definitions and Basic Properties
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§33.2(i) Coulomb Wave Equation
… ►The functions are defined by … is the Coulomb phase shift. … ►§33.2(iv) Wronskians and Cross-Product
…6: 33.3 Graphics
§33.3 Graphics
►§33.3(i) Line Graphs of the Coulomb Radial Functions and
… ► … ►§33.3(ii) Surfaces of the Coulomb Radial Functions and
… ►7: 33.18 Limiting Forms for Large
8: 33.24 Tables
§33.24 Tables
►Abramowitz and Stegun (1964, Chapter 14) tabulates , , , and for and , 5S; for , 6S.
9: 18.39 Applications in the Physical Sciences
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The Quantum Coulomb Problem
… ►This is Coulomb’s Law. … ►c) Spherical Radial Coulomb Wave Functions
… ►The Relativistic Quantum Coulomb Problem
… ►The Coulomb–Pollaczek Polynomials
…10: 33.1 Special Notation
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►The main functions treated in this chapter are first the Coulomb radial functions , , (Sommerfeld (1928)), which are used in the case of repulsive Coulomb interactions, and secondly the functions , , , (Seaton (1982, 2002a)), which are used in the case of attractive Coulomb interactions.
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Curtis (1964a):
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Greene et al. (1979):
, .
, , .