On the Equivalence of the LS Triad and the Faddeev Equation : Nuclear Physics

概要

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It is pointed out that the generally accepted equivalence of the usual triad of homogeneous and inhomogeneous three-body Lippmann-Schwinger (LS) equations to the Faddeev equation is not immediately applicable, because the connectivity of the LS kernel is not well-defined due to the lack of a built-in algorithm to guarantee the connectivity. In contradistinction, the alternative expression proposed by Glockle a long time ago is seen to have no such defect. The recognition of the above simple fact has an important implication on the Moller operator approach of Sandhas. Although it leads to the usual LS triad, it cannot derive the alternative LS triad that is truely equivalent to the Faddeev equation. This fact reveals the necessity for the consideration of the compactness of integral kernels in addition to and independent of the Moller operator approach in general. In particular, contrary to the conjecture drawn naturally from the approach, the LS triad should not be degraded to a single three-body LS equation even when there are no rearrangement channels.
理論物理学刊行会の論文
1988-06-25