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arXiv · 2603.03842

From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection

M. M. Nishonov
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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.

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M. M. Nishonov. 2026-03-04. From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection. https://arxiv.org/abs/2603.03842

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