Treatment of the two-body Coulomb problem as a short-range potential

Journal Article · Tue Dec 15 04:00:00 EST 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.062717· OSTI ID:21352361

Gasaneo, G ^[1]; Ancarani, L U ^[2]

---

1. Departamento de Fisica, Universidad Nacional del Sur and Consejo Nacional de Investigaciones Cientificas y Tecnicas, 8000 Bahia Blanca, Buenos Aires (Argentina)
2. Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine-Metz, 57078 Metz (France)

The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.

• OSTI ID: 21352361
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
DISTORTED WAVE THEORY
ENERGY
FUNCTIONS
GREEN FUNCTION
HYPERGEOMETRIC FUNCTIONS
MANY-BODY PROBLEM
POTENTIAL ENERGY
POTENTIALS
POWER SERIES
SCATTERING
SERIES EXPANSION
THREE-BODY PROBLEM
TRANSITION AMPLITUDES
TWO-BODY PROBLEM
WAVE FUNCTIONS