The mean-square charge radius of the neutron, $\langle{}\mathit r{}^{2}_{{{\mathit n}}}\rangle{}$, is related to the neutron-electron scattering length $\mathit b_{ {{\mathit n}} {{\mathit e}} }$ by $\langle{}\mathit r{}^{2}_{{{\mathit n}}}\rangle{}$ = 3(${\mathit m}_{{{\mathit e}}}\mathit a_{0}/{\mathit m}_{{{\mathit n}}})\mathit b_{ {{\mathit n}} {{\mathit e}} }$, where ${\mathit m}_{{{\mathit e}}}$ and ${\mathit m}_{{{\mathit n}}}$ are the masses of the electron and neutron, and $\mathit a_{0}$ is the Bohr radius. Numerically, $\langle{}\mathit r{}^{2}_{{{\mathit n}}}\rangle{}$ = $86.34~\mathit b_{ {{\mathit n}} {{\mathit e}} }$, if we use $\mathit a_{0}$ for a nucleus with infinite mass.

VALUE (fm${}^{2}$) DOCUMENT ID  COMMENT $\bf{ -0.1155 \pm0.0017}$ OUR AVERAGE $-0.115$ $\pm0.002$ $\pm0.003$ KOPECKY 1997 ${{\mathit n}}{{\mathit e}}$ scattering (Pb) $-0.124$ $\pm0.003$ $\pm0.005$ KOPECKY 1997 ${{\mathit n}}{{\mathit e}}$ scattering (Bi) $-0.114$ $\pm0.003$ KOESTER 1995 ${{\mathit n}}{{\mathit e}}$ scattering (Pb, Bi) $-0.115$ $\pm0.003$ 1 KROHN 1973 ${{\mathit n}}{{\mathit e}}$ scattering (Ne, Ar, Kr, Xe) • • We do not use the following data for averages, fits, limits, etc. • • $-0.1101$ $\pm0.0089$ 2 HEACOCK 2021 ${{\mathit n}}$ interferometry $-0.106$ ${}^{+0.007}_{-0.005}$ 3 FILIN 2020 chiral EFT analysis $-0.117$ ${}^{+0.007}_{-0.011}$ BELUSHKIN 2007 Dispersion analysis $-0.113$ $\pm0.003$ $\pm0.004$ KOPECKY 1995 ${{\mathit n}}{{\mathit e}}$ scattering (Pb) $-0.134$ $\pm0.009$ ALEKSANDROV 1986 ${{\mathit n}}{{\mathit e}}$ scattering (Bi) $-0.114$ $\pm0.003$ KOESTER 1986 ${{\mathit n}}{{\mathit e}}$ scattering (Pb, Bi) $-0.118$ $\pm0.002$ KOESTER 1976 ${{\mathit n}}{{\mathit e}}$ scattering (Pb) $-0.120$ $\pm0.002$ KOESTER 1976 ${{\mathit n}}{{\mathit e}}$ scattering (Bi) $-0.116$ $\pm0.003$ KROHN 1966 ${{\mathit n}}{{\mathit e}}$ scattering (Ne, Ar, Kr, Xe) 1  KROHN 1973 measured $-0.112$ $\pm0.003$ fm${}^{2}$. This value is as corrected by KOESTER 1976 . 2  HEACOCK 2021 extract the value from Pendelloesung interferometry to measure the neutron structure factors of silicon. This value is strongly anti-correlated with the mean-square thermal atomic displacement. 3  FILIN 2020 extract the value based on their chiral-EFT calculation of the deuteron structure radius and use as input the atomic data for the difference of the deuteron and proton charge radii.

References:

HEACOCK 2021 SCI 373 1239 FILIN 2020 PRL 124 082501 Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius BELUSHKIN 2007 PR C75 035202 Dispersion Analysis of the Nucleon Form Factors Including Meson Continua KOPECKY 1997 PR C56 2229 Neutron Charge Radius Determined from the Energy Dependence of the Neutron Transmission of Liquid ${}^{208}\mathrm {Pb}$ and ${}^{209}\mathrm {Bi}$ KOESTER 1995 PR C51 3363 Neutrino Electron Scattering Length and Electric Polarizability of the Neutron Derived from Cross Sections of Bismuth and of Lead and its Isotopes KOPECKY 1995 PRL 74 2427 New Measurement of the Charge Radius of the Neutron ALEKSANDROV 1986 SJNP 44 900 Neutron RMS Radius and Electric Polarizability from Data on the Interaction of Slow Neutrons with Bismuth KOESTER 1986 Physica B137 282 Neutron Scattering Lengths and Neutron-Electron Interaction KOESTER 1976 PRL 36 1021 Measurement of the Neutron-Electron Interaction by the Scattering of Neutrons by Lead and Bismuth KROHN 1973 PR D8 1305 Reconsiderations of the Electron-Neutron Scattering Length as Measured by the Scattering of Thermal Neutrons by Noble Gases KROHN 1966 PR 148 1303 Measurement of the Electron-Neutron Interaction by the Asymmetrical Scattering of Thermal Neutrons by Noble Gases