arXiv subjects

M. M. Nishonov

Publications and source records attributed to M. M. Nishonov.

5 recordsLinked to original sources

arXiv2026

The Fock representation of the Coulomb interaction. II. Three-body bound states

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 $^{3}$H--$^{3}$He 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 $^{6}$Li, $^{9}$Be and $^{12}$C and of the $^{9}$Be--$^{9}$B mirror pair are given. The eigenstate condition is tested in $^{9}$Be and $^{12}$C 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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arXiv2026

The Fock representation of the Coulomb interaction. I. Two-body problem

The unscreened Coulomb interaction is exactly separable in momentum space at negative energies, by the stereographic projection of Fock, with analytic form factors and strengths. It is derived here as an operator identity for the potential and added, without screening or fitting, as a block of separable terms to the separable nuclear input of a charged pair. The representation is compared with the screening--renormalization method and with Coulomb-distorted form factors on two-body benchmarks: the off-shell $t$~matrix, the Coulomb displacement of the $αp$ Pauli-forbidden state, and the Coulomb-modified phases of the $pp$, $αp$ and $αα$ pairs. The Feshbach--Schur projection of the Pauli-forbidden state is shown to require the Coulomb-dressed eigenstate, which the Fock block provides within the same separable problem. At positive energy a finite truncation is a screened Coulomb potential with an analytic, momentum-dependent radius.

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arXiv2026

Separable representations of two-body interactions for Faddeev calculations of light nuclei

Separable representations of the Ernst--Shakin--Thaler type are constructed for the charge-dependent Bonn (CD~Bonn) nucleon--nucleon potential ($j\le4$; $nn$, $np$, $pp$), for the Kanada--Kaneko--Nagata--Nomoto (KKNN) $αN$ interaction, and for the Buck--Friedrich--Wheatley (BFW) $αα$ interaction. They serve as input for momentum-space Faddeev calculations of $A=3$, $6$, $9$, and $12$ systems. The representations are tested against six acceptance criteria: off-shell accuracy at the pair energies sampled by the three-body kernel, phase shifts, effective-range parameters, bound and resonant states, and numerical stability.

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arXiv2026

From Orthogonalizing Pseudopotential to the Feshbach-Schur Projection

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.

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arXiv2001

Proton-Deuteron Elastic Scattering from 2.5 to 22.5 MeV

We present the results of a calculation of differential cross sections and polarization observables for proton-deuteron elastic scattering, for proton laboratory energies from 2.5 to 22.5 MeV. The Paris potential parametrisation of the nuclear force is used. As solution method for the charged-composite particle equations the 'screening and renormalisation approach' is adopted which allows to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl. Phys. A422, 81 (1984)].

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