The root-mean-square (rms) charge radius has been measured for the ground states of many
nuclei. For a spherical charge density, \( \rho(\boldsymbol{r}) \), the mean-square radius is defined by
$$
\langle r^2\rangle = \frac{ \int d \boldsymbol{r} \rho(\boldsymbol{r}) r^2}{ \int d \boldsymbol{r} \rho(\boldsymbol{r})},
$$
and the rms radius is the square root of this quantity denoted by
$$
R =\sqrt{ \langle r^2\rangle}.
$$