Why is it said that density of nucleons in a nucleus is constant? Question:Why is it said that density of nucleons in a nucleus is constant?
I am studying an introductory course in nuclear and subnuclear physics. Based on the context in which it is cited (I cannot cite the notes because they are private notes) I do not understand if it is a theoretical assumption or hypothesis derived from an experiment.
I searched in literature, 
especially on the book Krane-Introuctory Nuclear Physics but my doubt has not been clarified.
 A: Robert Hofstadter received a Nobel Prize for his research regarding The electron-scattering  method  and  its  application to the structure of nuclei and nucleons 
Hofstadter fired high energy electrons at the nuclei of atoms and from the resulting scattering and diffraction effects he was able to map out the charge density within a nucleus and hence show that the charge density was approximately constant within a nucleus and he also was able to estimate the radii of nuclei.  
What he found was that the radius of a nucleus $R$ is related to the mass number of the nucleus $A$ as follows $R = R_0 A^{\frac 13}$ where $R_0$ was a constant approximately equal to $1.2 \,\rm fm$ which is good evidence for nucleii being of the same constant density.  
$R_0$ is not actually constant but and varies a little by about $0.2 \,\rm fm$ depending on the nucleus being considered.    
The relationship $R = R_0 A^{\frac 13}$ can be thought of as coming from the idea that a nucleon has a fixed volume $V$ and there are $A$ nucleons in a nucleus.  
So the volume of a nucleus is related to $VA$ which means that a linear dimension (the radius) of a nucleus is related to $(VA)^{\frac 13} \propto A^{\frac 13}$ if $V$ is constant.  
Since Hofstadter's paper was published in 1957 much more research has been done on the structure of the nucleus and of the constituent particles.
A: High-energy electron scattering gives a very direct measure of the density of the protons, and the density is found to be fairly constant.
Another example of the type of evidence that supports this is that measurements of the Coulomb barrier for nuclear fusion are consistent with a nuclear radius that varies as $A^{1/3}$, which is what is expected if the density is constant.
