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The '''rms charge radius''' is a measure of the size of an [[atomic nucleus]], particularly of a [[proton]] or a [[deuteron]]. It can be measured by the scattering of [[electron]]s by the nucleus and also inferred from the effects of finite nuclear size on electron energy levals as measured in [[Atomic spectrum|atomic spectra]].

==Definition==
The problem of defining a radius for the atomic nucleus is similar to the problem of [[atomic radius]], in that neither atoms nor their nuclei have definite boundaries. However, the nucleus can be modelled as a sphere of positive charge for the interpretation of electron scattering experiments: because there is no definite boundary to the nucleus, the electrons "see" a range of cross-sections, for which a mean can be taken. The qualification of "rms" (for "root mean square") arises because it is the nuclear cross-section, proportional to the square of the radius, which is important for electron scattering.

==History==
{{main|Geiger–Marsden experiment}}
The first estimate of a nuclear charge radius was made by [[Hans Geiger]] and [[Ernest Marsden]]  in 1909,<ref>{{citation | last1 = Geiger | first1 = H. | authorlink1 = Hans Geiger | last2 = Marsden | first2 = E. | authorlink2 = Ernest Marsden | title = On a Diffuse Reflection of the α-Particles | journal = Proc. Roy. Soc., Ser. A | year = 1909 | volume = 82 | pages = 495–500 | doi=10.1098/rspa.1909.0054 }}.</ref>  under the direction of [[Ernest Rutherford]] at the Physical Laboratories of the [[University of Manchester]], UK. The famous experiment involved the scattering of [[α-particle]]s by [[gold]] foil, with some of the particles being scattered through angles of more than 90°, that is coming back to the same side of the foil as the α-source. Rutherford was able to put an upper limit on the radius of the gold nucleus of 34&nbsp;femtometres.<ref>{{citation | last = Rutherford | first = E. | authorlink = Ernest Rutherford | title = The Scattering of α and β Particles by Matter and the Structure of the Atom | journal = Phil. Mag., Ser. 6 | year = 1911 | volume = 21 | pages = 669–88 | doi=10.1080/14786440508637080 }}.</ref>

==Modern measurements==
Modern direct measurements are based on the scattering of [[electron]]s by nuclei. There is most interest in knowing the charge radii of [[proton]]s and [[deuteron]]s, as these can be compared with the spectrum of atomic [[hydrogen]]/[[deuterium]]: the finite size of the nucleus causes a shift in the electronic energy levels which shows up as a change in the frequency of the spectral lines.<ref name="CODATA98">{{CODATA1998}}.</ref> Since 2002, the proton and deuteron charge radii have been independently refined parameters in the [[CODATA]] set of recommended values for physical constants, that is both scattering data and spectroscopic data are used to determine the recommended values.<ref name="CODATA02">{{CODATA2002}}.</ref>

==References==
{{reflist}}

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