Do Protons and Neutrons Move around in the Nucleus?

[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?

 

[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.

 

[Orodruin]

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.

 

[Ryan Reed]

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

 

[Orodruin]

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.

 

[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.

 

[ChrisVer]

two protons and and two neutrons vibrating in some fashion inside the nucleus.

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

 

[Drakkith]

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

 

[Vanadium 50]

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

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.

 

[Drakkith]

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.

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.

 

[mfb]

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.

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.

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.

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

 

[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.

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.

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.

 

[Vanadium 50]

Are nucleons arranged in anything similar?

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.

 

[Drakkith]

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.

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

One can use this proton to "map out" the U-238 core, and when you do, you discover it's cigar-shaped.

Smoke if you got 'em?

 

[e.bar.goum]

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

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.

 

[anorlunda]

You can of course do QM calculations that show non-spherical nuclei.

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

The simulation I linked to is actually totally quantum mechanical - that's a Time Dependent Hartree Fock calculation. I believe what is plotted there is density isosurfaces(which is of course an observable).

You do occasionally see liquid drop model simulations that look an awful lot like that, and you're right, that's not quantum mechanical.

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

 

[e.bar.goum]

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.

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!

 

[Vanadium 50]

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.

 

[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?

 

[Vanadium 50]

Now my question is are the positive magnetic fields static or dynamic?

This is the first mention of magnetic fields in this thread. What are you talking about?

 

[Ryan Reed]

This is the first mention of magnetic fields in this thread. What are you talking about?

Not that It has been mentioned before, I'm saying that the conversation has brought this to mind.

 

[Vanadium 50]

Yes, but without giving us any context, it's a total non sequitur. "How about magnetic fields?" is like "How about them Red Sox?". You're going to have to link them up for us, because I sure can't figure out the connection.

 

[mfb]

The inner details of the nucleus are (nearly) irrelevant for the electron orbitals. The nucleus is simply too small. The innermost electrons of very heavy elements are an exception, and if you want to do spectroscopy at the 14th significant digit it is relevant for lighter nuclei as well, but usually the effects are completely negligible.

 

[Ryan Reed]

Yes, but without giving us any context, it's a total non sequitur. "How about magnetic fields?" is like "How about them Red Sox?". You're going to have to link them up for us, because I sure can't figure out the connection.

I have an idea of something and have set "goals". Having one of my "goals" answered above, I moved onto another goal which I believed could be quickly answered without starting a new thread.

 

[Vanadium 50]

Are you saying it's a different question entirely? Then you should start a new thread.

 

[Dale]

I agree. Please post the new question to a new thread. The connection to this thread is tenuous at best, as far as I can tell.

 

[stedwards]

You can of course do QM calculations that show non-spherical nuclei.

Very nice picture, and more. The dogleg shaped nuclei are a big surprise to me. Are these time independent?

 

[e.bar.goum]

Very nice picture, and more. The dogleg shaped nuclei are a big surprise to me. Are these time independent?

Ah, no, it's a Time Dependent Hartree Fock calculation of the 40Ca + 238U quasi-fission reaction, shown at two different angular momenta, what you're seeing is different time-steps. For the L=80 case, for instance, you see the 40Ca come in, the two nuclei form a neck between them, they rotate for about a 1/4 turn, then re-separate, with fairly similar masses to what they started with. The L =20 case is similar, except the sticking time is longer, and the mass-transfer is larger.

Usually, when you see these simulations they're done as a video. I don't have any to hand, but I will see if I can dig one up, they're really neat.

 

[e.bar.goum]

Ah, no, it's a Time Dependent Hartree Fock calculation of the 40Ca + 238U quasi-fission reaction, shown at two different angular momenta, what you're seeing is different time-steps. For the L=80 case, for instance, you see the 40Ca come in, the two nuclei form a neck between them, they rotate for about a 1/4 turn, then re-separate, with fairly similar masses to what they started with. The L =20 case is similar, except the sticking time is longer, and the mass-transfer is larger.

Usually, when you see these simulations they're done as a video. I don't have any to hand, but I will see if I can dig one up, they're really neat.

Success! Found some gif's in Wakhle et. al. PRL. 113 (2014). http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.182502
Bonus: It's also 40Ca + 238U. Each frame is 0.3 zs.
L=20

L=80

ETA: The L=20 case doesn't seem to auto-loop. Refresh the page if you can't see it move.

 

[stedwards]

Ah, no, it's a Time Dependent Hartree Fock calculation of the 40Ca + 238U quasi-fission reaction, shown at two different angular momenta, what you're seeing is different time-steps.

Of, course, how foolish of me.

Usually, when you see these simulations they're done as a video. I don't have any to hand, but I will see if I can dig one up, they're really neat.

That would be very nice to see.

I did a short search on images of "nuclear orbitals" and came up empty. Do you have anything like this? It would be fairly in line with the OPs initial question.