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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.13340 |
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| _version_ | 1866916442765524992 |
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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 |