Orthogonality nodes and the three-body bound state collapse.

Abstract

In this paper, the three-body bound state collapse (BSC) is investigated in connection with the short-range orthogonality node by making use of the unitary pole approximation of a deep local 2N potential model. A rank-1 effective $^{3}$${\mathit{S}}_{1}$ potential derived with respect to the excited bound state (the physical deuteron) supports two 3N bound states. The lower state shows a feature of the BSC when the node behavior is significant. When we impose a strict orthogonality condition with respect to the unphysical deep 2N state, such a collapsed state does not appear and we obtain only one 3N bound state. In the case where we do not impose the orthogonality condition, the collapsed state gets deeper as the mode behavior becomes more significant. When the node behavior is reduced, the BSC becomes less significant and disappears at a certain degree of node behavior, and the other bound state becomes the lowest state. The binding energy of this state is close to the binding energy of the 3N ground state obtained with the orthogonality condition, for both large and small degrees of node behavior.