Advertisement

Extension of the Faddeev equation to Nuclei

  • M. Fabre de la Ripelle
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 10)

Abstract

The Faddeev equation was derived for slving the three body problem. The wave function Ψ is written as the sum of three amplitudes. Each one \({\psi_{ij}}({r_{ij}},{r_k};\alpha )\) is described in one of the three available Jacobi coordinate systems: \({r_{ij}}={x_i}-{x_j},{r_k}= sqrt3({x_k}-X),X=\frac{1}{3}({x_1}+{x_2}+{x_3})\) in terms of the coordinates \({x_i},(i=1,2,3),\) of equal mass particles. The other degrees of freedom a can be spin, isospin etc… Each amplitude is the solution of one Faddeev equation
$$(T - E)\psi ij = - V({r_{ij}})\Psi $$
(1)
for pairwise potentials \(V({r_{ij}})\). Then each equation is projected on bipolar harmonics generating coupled two variables integrodifferential equations in coordinate space.

Keywords

Potential Harmonic Faddeev Equation Harmonic Polynomial Residual Interaction Pairwise Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Fabre de la Ripelle: C.R. Acad. Sc. Paris. 299 Serie II, 839 (1984)MathSciNetGoogle Scholar
  2. 2.
    M. Fabre de la Ripelle: In : Model and Methods in Few-Body Physics (Lecture Notes in Physics, vol. 283), p. 273. Berlin: Springer 1987Google Scholar
  3. 3.
    M. Fabre de la Ripelle, H. Fiedeldey, S. Sofianos: Phys. Rev. C38, 449 (1988)ADSGoogle Scholar
  4. 4.
    R. Brizzi, M. Fabre de la Ripelle, M. Lassaut: Nucl. Phys. A596, 199 (1996)ADSGoogle Scholar
  5. 5.
    R. Guardiola et al.: Nucí. Phys. A371, 79 (1981)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • M. Fabre de la Ripelle
    • 1
  1. 1.Institut de Physique NucléaireOrsay CedexFrance

Personalised recommendations