# Do Protons and Neutrons Move around in the Nucleus?

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1. Jun 28, 2015

### Ryan Reed

Protons and Neutrons vibrate in place, but do they change positions within the nucleus? Let's say that there's a helium atom which has two protons and two neutrons. If the particles were set up on the corners of a square for easy representation with a neutron on the top left and top right, and a proton on the bottom left and bottom right, could a proton move from bottom left to top left?

2. Jun 28, 2015

### andresB

Setting them up in the corners of a square is impossible by principle, things at that scale just don't work that way, any classical model like that just fail.

3. Jun 28, 2015

### Orodruin

Staff Emeritus
The classical picture you seem to have of a nucleus does not work. Also, the protons are exactly the same so there is no way of telling wether they have changed places or not.

4. Jun 29, 2015

### Ryan Reed

I did not believe the nucleus works like that, I used it for easy representation.

5. Jun 29, 2015

### Orodruin

Staff Emeritus
You misunderstand me. The notion of the particles "moving" and the thought that they are actually separable entities is what does not make sense on a quantum level.

6. Jul 1, 2015

### fermi

I think you got two good replies, but I have one more point to add to completely kill the classical view of two protons and and two neutrons vibrating in some fashion inside the nucleus. Had that been even approximately true, the Helium-4 nucleus will exhibit an electric dipole moment, which should be measurable. In fact there is none as far as we know, which says that the average charge distribution inside the He-4 nucleus should be spherically symmetric. As soon as you classically separate the two protons, you are going to get an electric dipole moment, no matter where you place them, and no matter how you arrange them to vibrate. The nucleus is not a classical world.

7. Jul 3, 2015

### ChrisVer

I guess that's a misconception caused by (for example) the liquid drop-model?

8. Jul 4, 2015

### Staff: Mentor

Hmm, I'd always thought that the protons and neutrons existed in energy levels like electrons do when they are in atomic/molecular orbitals.

9. Jul 4, 2015

Staff Emeritus
They do.

This thread has been troubled from the beginning because the title and the initial post ask different questions. One cannot paint a big red X on one proton and see if at a later time the X is in some other position. Even in principle. However one can ask about the expectation value of velocity (well, velocity squared) and that can be non-zero.

10. Jul 4, 2015

### Staff: Mentor

Okay. Well, I know about how electrons are arranged in atomic orbitals. Are nucleons arranged in anything similar? By 'arranged' I just mean that the orbitals have specific shapes, not that the electrons are rigidly set into specific orbitals.

11. Jul 4, 2015

### Staff: Mentor

A set of two classical charged spheres next to each other does not have a dipole moment. It has a quadrupole moment and higher moments.

Yes, but the orbitals look more complicated as the potential is not a simple 1/r potential.

12. Jul 4, 2015

### anorlunda

In an earlier thread Are subatomic particles spherical, I learned that we must treat a nucleus as a quantum particle. It has a quantum state, but the identity of its constituents are lost. Scattering experiments can attempt to probe the shape and other properties, but they can't expose the identity of individual nucleons.

You can see some liquid drop videos of nucleus shape changes, but the thread says that such simulations are not supported by QM calculations.

My knees shake to question a staff mentor, but I believe that the internal arrangement of a nucleus can not be defined in the same sense that you can't determine the spin of an electron in a singlet pair.

13. Jul 4, 2015

Staff Emeritus
Similar, but even electron orbitals don't have those pretty shapes. Those are for hydrogenic atoms. In many-electron atoms, each electron feels the fields from the others, and you have a much, much more complicated system, and the wavefunctions change shapes to accommodate this in a less-than-simple way.

Nuclear shapes are very complicated - and the last time I said something was very complicated, the level of discussion immediately ratcheted up about twelve notches, leaving the OP behind in the dust. To give a well-known example, U-238 is a 0+ nucleus, so it appears spherical to all measurements: there is no direction for an asymmetry to point. Np-239 is essentially a single proton orbiting a U-238 core. One can use this proton to "map out" the U-238 core, and when you do, you discover it's cigar-shaped.

14. Jul 4, 2015

### Staff: Mentor

Hmmm, I guess we didn't cover that in my Chemistry 151 class.

Smoke if you got 'em?

15. Jul 4, 2015

### e.bar.goum

You can of course do QM calculations that show non-spherical nuclei. In fact, the very thread you just linked to has an example from me -- I linked to a Time Dependent Hartree Fock calculation of 40Ca + 238U! You can clearly see the deformed nature (cigar shaped, as V50 points out) of 238U and the spherical structure of 40Ca.

And yes, nuclei have a shell structure, but it's rather complicated, as you don't have a nice 1/r potential. The shell structure is very important though - just like the noble gasses in chemistry, you have equivalently well bound nuclei - "doubly magic nuclei" - like 48Ca and 208Pb - where both the neutrons and protons are in closed shells. In fact, it's only near these closed shells that you're guaranteed to get spherical nuclei! In fact, if you didn't have the shell model, we'd have no explanation why the superheavy isotopes can exist at all - it's the shell structure that gives you enough stability.

Now, on the other end of the scale, we can talk about clustering in very light nuclei. Rather than talking about shells, you can talk about, say, 7Li as if it were a somewhat loosely bound $\alpha$ and $t$ pair. (That is, a large part of the ground-state wavefunction has an $\alpha$ and $t$ structure). 9Be is thought of as $\alpha + \alpha + n$. And so on - this is where halo nuclei can appear. For instance, 11Li can be thought of as a 9Li core + 2n halo. It has a cross section comparable to 208Pb! Tl;dr - nuclei are complicated, but interesting.

But of course, in all this, you can't "tag" individual protons and neutrons inside the nucleus, you're always talking about wavefunctions.

16. Jul 5, 2015

### anorlunda

I apologize e.bar.goum. I wrote what I did thinking that I was quoting you. But a recheck of the earlier thread:

shows that I quoted and misquoted you at the same time.

17. Jul 5, 2015

### e.bar.goum

No worries! I clicked the link wondering who on earth would say such a thing, and for a moment, I was afraid it was me!

18. Jul 5, 2015

Staff Emeritus
At the risk of complicating things, the idea that there is some sort of energetics - and thus motion - going on is strongly suggested by one very simple observation: there are 170 long-lived even-even nuclei. There are 110 even-odd nuclei. There are 9 odd-odd nuclei: deuterium, Li-6, B-10, N-14, and
K-40, V-50 (yay!), La-138, Lu-176, and Ta-180. If there were not some dynamics going on, this is very improbable.

19. Jul 5, 2015

### Ryan Reed

I've been trying to follow along so far and if I've understood this correctly, this thread has blown my mind. I always pictured nuclei as "static" objects, a bunch of spheres vibrating in place. Now my question is are the positive magnetic fields static or dynamic? If they are dynamic and change "shape", does the shape of the field determine where the electron orbitals are?

20. Jul 5, 2015