Electron scattering: nuclear radius to nucleon number relationship

[AlexCdeP]

Hi! I am extremely confused on what seems to be quite a simple question. The question contains a graph of root mean square radius <r^{2}> plotted against A^{1/3} where A is the nucleon number. In the lecture notes he specifies that <r^{2}> is not the same as R but does not really say specifically what the difference is. It is given that the gradient of the line in this graph is 0.96. I am meant to find the value of R_{0} in the relationship R=R_{0}A^{1/3} but I'm not certain how to find it because I don't know what the relationship between the rms r and R is.

Any help would be amazing.

I have worked through trying to use the charge radius but without success, he never mentioned the charge radius in the lecture so I'm not sure what to do. http://en.wikipedia.org/wiki/Charge_radius

 

[mfb]

If you have a uniform sphere of radius R, what is the (squared) rms radius <r²> of its volume? Hint: You'll need an integral (or a formula).

 

[AlexCdeP]

Thanks so much I think I'm on the right track now. So for a uniform sphere you use some spherical coordinate integrals to find that the rms radius is related to the radius by \frac{3}{5}R^{2}. Is this the correct formula to get?

Also am I right in saying that I am effectively finding the expectation value of r^{2}?

 

[AlexCdeP]

Finally got the answer! Thanks again man couldn't have done it without you!

 

[vela]

Thanks so much I think I'm on the right track now. So for a uniform sphere you use some spherical coordinate integrals to find that the rms radius is related to the radius by \frac{3}{5}R^{2}. Is this the correct formula to get?

Also am I right in saying that I am effectively finding the expectation value of r^{2}?

Yup.