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New Faddeev-type equations for the three-body problem

Bengt R. Karlsson, Enrique M. Zeiger

Open publisher page 41 citations

Abstract

We present new Faddeev-type equations for the three-body problem. Although obtained from the rigorous Faddeev theory, they only require two-body bound-state wave functions and half-off-shell transition amplitudes as input. In addition, their "effective potentials" are independent of the three-body energy, and can easily be made real after an angular momentum decomposition. The equations are formulated in terms of physical transition amplitudes for three-body processes, except that in the breakup case the partial-wave amplitudes differ from the corresponding full amplitudes by a Watson final-state interaction factor.

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What this paper is about

We present new Faddeev-type equations for the three-body problem. Although obtained from the rigorous Faddeev theory, they only require two-body bound-state wave functions and half-off-shell transition amplitudes as input. In addition, their "effective potentials" are independent of the three-body energy, and can easily be made real after an angular momentum decomposition. The equations are formulated in terms of physical transition amplitudes for three-body processes, except that in the breakup case the partial-wave amplitudes differ from the corresponding full amplitudes by a Watson final-state interaction factor.

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Available abstract

We present new Faddeev-type equations for the three-body problem. Although obtained from the rigorous Faddeev theory, they only require two-body bound-state wave functions and half-off-shell transition amplitudes as input. In addition, their "effective potentials" are independent of the three-body energy, and can easily be made real after an angular momentum decomposition. The equations are formulated in terms of physical transition amplitudes for three-body processes, except that in the breakup case the partial-wave amplitudes differ from the corresponding full amplitudes by a Watson final-state interaction factor.

Key concepts: Faddeev equations, Physics, Three-body problem, Breakup, Amplitude, Two-body problem, Angular momentum, Many-body problem

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