Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2603.03842

From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection

M. M. Nishonov
View original source ↗Read source document ↗Export metadata ↓

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 $λ\to \infty$ limit of a Feshbach--Schur projection. The auxiliary coupling $λ$ 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 $λ$ follow the predicted $1/λ$ behavior over five orders of magnitude of $λ$ and converge to the result of the closed projected equations. The $αN$ $D$-wave contribution, $7$~keV in $^6$He and $90$~keV in $^6$Li, does not depend on $λ$ and does not affect the projection.

Explore related subjects

nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. M. Nishonov. 2026-08-25. From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection. https://arxiv.org/abs/2603.03842

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Application of the Skyrme Hartree-Fock-Bogoliubov Theory to WIMP-Nucleus Interactions in 40Ar

WIMP scattering from 40Ar is investigated using a self-consistent Skyrme Hartree-Fock-Bogoliubov (HFB) approach. Nuclear form factors relevant to dark matter direct detection are calculated from the resulting one-body density matrix elements and compared with shell-model predictions. Good agreement is found for the spin-independent response, while significant differences are observed for the spin-orbit response due to variations in single-particle occupancies. The effects of particle-number projection are shown to be small for 40Ar. These results demonstrate the sensitivity of certain dark matter response channels to the underlying nuclear structure model and establish a framework for extending mean-field calculations to nuclei beyond the reach of large-scale shell-model studies.

nucl-th↗
arXiv2026

Breakdown of the Plane-Wave Trojan Horse Analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Fusion Reaction: Critical Role of Coulomb Distortions

Recently, a new Trojan Horse Method (THM) measurement of carbon-carbon fusion was reported by Li \textit{et al.} [Phys. Lett. B (2026) 140675]. The purpose of the present work is to demonstrate the breakdown of the plane-wave approximation used in the analysis of these data and the critical role of Coulomb distortions in the initial and final states. The reaction mechanism underlying the THM analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction using the $^{16}\mathrm{O}+{}^{12}\mathrm{C}\to α_s+α+{}^{20}\mathrm{Ne}$ reaction is investigated. Particular attention is paid to the spectator momentum distribution and to the dependence of the THM reaction amplitude on the relative carbon-carbon energy $E$. It is demonstrated that agreement with the measured spectator momentum distribution does not by itself validate the plane-wave approximation. Although the experimental momentum distribution can be reproduced, inclusion of Coulomb distortions in both the initial and final channels leads to an energy dependence of the THM amplitude that is completely different from the plane-wave result. Consequently, the energy dependence of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion cross section extracted from the THM data can be strongly distorted by the plane-wave treatment. It is concluded that the astrophysical factor extracted in the plane-wave analysis cannot be regarded as reliable and may lead to misleading conclusions concerning the low-energy $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction.

nucl-th↗