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Main Authors: Atoui, M., Hoballah, M., Lassaut, M., Van de Wiele, J.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.13340
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author Atoui, M.
Hoballah, M.
Lassaut, M.
Van de Wiele, J.
author_facet Atoui, M.
Hoballah, M.
Lassaut, M.
Van de Wiele, J.
contents The present paper proposes a robust evaluation of any radial density at small distances using negative-order radial moments evaluated in momentum space. This evaluation provides a valuable insight into the behavior of a given radial density in the vicinity of $r=0$, and puts strong emphasis on the importance of measuring form factors at large squared four-momentum transfer, a domain essential for the determination of negative order moments. A specific attention is paid to the regularization scheme directly affecting the numerical determination of the radial density's parametrization. The proposed method is applied to non-relativistic study cases of the nucleon electric ($G_{En}, G_{Ep}$), and proton magnetic $G_{Mp}$ form factors. The validation is performed through comparison of the results of the approach to the analytically determined Maclaurin expansion - in the vicinity of $r=0$ - of the radial density function. The method is also applied to the relativistic Dirac form factor $F_1$ of the proton. In such a non-trivial case, the Maclaurin development might not exist for the radial density, rendering the determination from the proposed method extremely important.
format Preprint
id arxiv_https___arxiv_org_abs_2410_13340
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Negative moments as the signature of the radial density at small distances
Atoui, M.
Hoballah, M.
Lassaut, M.
Van de Wiele, J.
Nuclear Theory
Nuclear Experiment
The present paper proposes a robust evaluation of any radial density at small distances using negative-order radial moments evaluated in momentum space. This evaluation provides a valuable insight into the behavior of a given radial density in the vicinity of $r=0$, and puts strong emphasis on the importance of measuring form factors at large squared four-momentum transfer, a domain essential for the determination of negative order moments. A specific attention is paid to the regularization scheme directly affecting the numerical determination of the radial density's parametrization. The proposed method is applied to non-relativistic study cases of the nucleon electric ($G_{En}, G_{Ep}$), and proton magnetic $G_{Mp}$ form factors. The validation is performed through comparison of the results of the approach to the analytically determined Maclaurin expansion - in the vicinity of $r=0$ - of the radial density function. The method is also applied to the relativistic Dirac form factor $F_1$ of the proton. In such a non-trivial case, the Maclaurin development might not exist for the radial density, rendering the determination from the proposed method extremely important.
title Negative moments as the signature of the radial density at small distances
topic Nuclear Theory
Nuclear Experiment
url https://arxiv.org/abs/2410.13340