1. Feb 6, 2008

### mist

how can you explain atomic nuclei. liquid, charged, solid what? and there are some words about nuclear radius rn, rp and rc. what is the meaning of these words. all these data are experimental results or calculated. one is "atomic data and nuclear data tables, vol 71, no. 1, 1999, G.A. Salazar, S.Raman, and P. Ring"

I believe all these data are theoretical not experimental results. is there any newest paper about nuclear radius. what is the meaning of "charged radius"

thanks

mist

2. Feb 7, 2008

### malawi_glenn

In realliy, the nucleus is a diffuse quantum obejct, just as the atom itself. So the concept of "nuclear radius" is as diffuse concept as atomic radius. Neither the nucleus nor the atom are solid object, so we cant measure its size, as we could to with a tennis ball or macroscopic liquid drop.

What differs from the nucleus and the atom is that the nucleus consists of two kinds of particles: Electric Neutral Neutons and Electrical charged Protons. So what we can have is both the "radius" of the nuclear matter (particles that feels the strong force, i.e Neutrons and protons), we can have the "charged" radius, i.e the "radius" of the charge distribution (the protons..).

So why do we keep talking about radius when in reality the nucleus is a diffuse quantum obeject with a probablity distribuion for the nucleons? And what do we mean by radius anyway? And how can we measure it?

First of all, we can measure the nuclear matter distribution as a function of radial distance (R) from center, and call 0.9R the radius. Where 0.9 means that at this distance, 90% of the nuclear matter is inside the distrubuion function. The distribution function used is often the "Fermi - function". $$p(r) = p_0 \dfrac{1}{1+\exp (r-R)/a}$$ Where R is the radius where p(R) = ½P_0, and a is the diffusness-contant, how sharp the "edge" is. (play with this forumula if you want for different R and a).

Second, we can use a distribution function and take the mean r - value of that, see my post #4 in this thread here: https://www.physicsforums.com/showthread.php?t=212195

Or take the square root of the r^2 (also see post above).

How do we measure all this? ans: We do scattering, with electrons, alpha and pions. We probe the nuclues with these particles and we get a diffraction pattern. Then we use model, as the Fermi function for example, and put that into the scattering forumula and play with parameters etc. And depending on what probe you use, you get different patterns, and that means that distribution of protons and neutrons may differ etc.

All this is usally covered in introductory Nulcear Physics textbooks, I hope my answer at least helped you something :) It is not so technical as it sounds, very basic quantum mechanics I would say. So the concept of radius is both experimental and theoretical I would say. It is not really the radius, but it is often the sqrt of <^2> that is tabelled.

3. Feb 23, 2008

### mist

can you give me the most recent study about nuclear radius. I am not working at any university. some papers dont give radius if A<10, I need from proton to all.

4. Feb 23, 2008

### malawi_glenn

"all" ? there are a lot of istopes between H and A=10 ;)

I have myself big problems to find a good source with Nuclear R.M.S radii for very many isotopes :(