Techniques for heavy-ion coupled-channels calculations. I. Long-range Coulomb coupling

Journal Article · Sun Jun 01 04:00:00 EDT 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.21.2417· OSTI ID:5315898

Rhoades-Brown, M; Macfarlane, M H; Pieper, S C

Direct-reaction calculations for heavy ions require special computational techniques that take advantage of the physical peculiarities of heavy-ion systems. This paper is the first of a series on quantum-mechanical coupled-channels calculations for heavy ions. It deals with the problems posed by the long range of the Coulomb coupling interaction. Our approach is to use the Alder-Pauli factorization whereby the channel wave functions are expressed as products of Coulomb functions and modulating amplitudes. The equations for the modulating amplitudes are used to integrate inwards from infinity to a nuclear matching radius ( approx. = 20 fm). To adequate accuracy, the equations for the amplitudes can be reduced to first order and solved in first Born approximation. The use of the Born approximation leads to rapid recursion relations for the solutions of the Alder-Pauli equations and hence to a great reduction in computational labor. The resulting coupled-channels Coulomb functions can then be matched in the usual way to solutions of the coupled radial equations in the interior region of r space. Numerical studies demonstrate the reliability of the various techniques introduced.

• Research Organization: Argonne National Laboratory, Argonne, Illinois 60439
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 5315898
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 21:6; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BORN APPROXIMATION
CHARGED-PARTICLE REACTIONS
COULOMB FIELD
COUPLED CHANNEL THEORY
ELECTRIC FIELDS
FUNCTIONS
HEAVY ION REACTIONS
INELASTIC SCATTERING
MATHEMATICS
MATRICES
MATRIX ELEMENTS
MECHANICS
NUCLEAR REACTIONS
NUMERICAL ANALYSIS
QUANTUM MECHANICS
S MATRIX
SCATTERING
WAVE FUNCTIONS