From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection

Abstract

The orthogonalizing pseudopotential (OPP) is the standard tool for suppressing Pauli-forbidden states in cluster models of light nuclei. Here it is shown to be the singular $\lambda \to \infty$ limit of a Feshbach--Schur projection. The auxiliary coupling $\lambda$ is eliminated in closed form: the result is a Schur-complement operator identity for a general multi-rank separable interaction, written in both momentum and configuration space. The projected equations contain no large parameter. The identity is verified in three-body Faddeev calculations of the ${}^6$He and ${}^6$Li ground states with separable two-body input. The binding energies at finite $\lambda$ follow the predicted $1/\lambda$ behavior over five orders of magnitude of $\lambda$ and converge to the result of the closed projected equations. The $\alpha N$ $D$-wave contribution, $7$~keV in ${}^6$He and $90$~keV in ${}^6$Li, does not depend on $\lambda$ and does not affect the projection.

Comments: 20 pages. v3: introduction and discussion shortened