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)


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
$$(T - E)\psi ij = - V({r_{ij}})\Psi $$
for pairwise potentials \(V({r_{ij}})\). Then each equation is projected on bipolar harmonics generating coupled two variables integrodifferential equations in coordinate space.


Potential Harmonic Faddeev Equation Harmonic Polynomial Residual Interaction Pairwise Potential 
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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

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

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