The Fock representation of the Coulomb interaction. II. Three-body bound states
Abstract
The Fock representation of the unscreened Coulomb interaction, a block of separable terms with analytic form factors and strengths, is included in the momentum-space Faddeev kernel of three-body bound states beside the separable nuclear terms. A bound-state kernel evaluates every pair interaction at negative pair energies, where the representation is exact and convergent, so the Coulomb force enters without a screening radius and without a limiting procedure. With this representation the 3H--3He splitting of the CD~Bonn potential is in very good agreement with the exact Faddeev result; in the S-wave model space the Coulomb-distorted form factors give about half the Fock value. The Feshbach--Schur projection of the Pauli-forbidden states acts on the forbidden eigenstates of the nuclear-plus-Coulomb pair Hamiltonian, the Coulomb-dressed states obtained inside the extended separable problem, as the eigenstate condition requires. The Coulomb displacements of the cluster-model states of 6Li, 9Be and 12C and of the 9Be--9B mirror pair are given. The eigenstate condition is tested in 9Be and 12C by replacing the Coulomb-dressed forbidden states with those of the Coulomb-subtracted interaction and with the oscillator functions of the orthogonality-condition model.
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BibTeX
@misc{nishonov2026fock,
title = {{The Fock representation of the Coulomb interaction. II. Three-body bound states}},
author = {M. M. Nishonov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08520},
eprint = {2610.08520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08520},
}
RIS
TY - UNPB
TI - The Fock representation of the Coulomb interaction. II. Three-body bound states
AU - M. M. Nishonov
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.08520
UR - https://arxiv.org/abs/2610.08520
AB - The Fock representation of the unscreened Coulomb interaction, a block of separable terms with analytic form factors and strengths, is included in the momentum-space Faddeev kernel of three-body bound states beside the separable nuclear terms. A bound-state kernel evaluates every pair interaction at negative pair energies, where the representation is exact and convergent, so the Coulomb force enters without a screening radius and without a limiting procedure. With this representation the ^3H--^3He splitting of the CD~Bonn potential is in very good agreement with the exact Faddeev result; in the S-wave model space the Coulomb-distorted form factors give about half the Fock value. The Feshbach--Schur projection of the Pauli-forbidden states acts on the forbidden eigenstates of the nuclear-plus-Coulomb pair Hamiltonian, the Coulomb-dressed states obtained inside the extended separable problem, as the eigenstate condition requires. The Coulomb displacements of the cluster-model states of ^6Li, ^9Be and ^12C and of the ^9Be--^9B mirror pair are given. The eigenstate condition is tested in ^9Be and ^12C by replacing the Coulomb-dressed forbidden states with those of the Coulomb-subtracted interaction and with the oscillator functions of the orthogonality-condition model.
ER -