# Are subatomic particles spherical?

1. Aug 1, 2014

### tonyxon22

We are very used to see diagrams of atoms as being composed by little spheres each one with their own characteristics, such as mass, electrical charge, etc.

I have also read and heard in many different scientific divulgation media about the scale of the nucleus’ dimension and the size of the electrons’ orbit. Some authors even compare the size of the nucleus in relation to the size of the atom with an scale analogy as comparing a tennis ball in the center of a football stadium, being the tennis ball the nucleus and the electrons then would move in an orbit at a distance equivalent to the outer walls of the stadium.

In other cases we hear about the weight a spoonful of a neutron star material will have on earth (being a “spoonful” a measurement of volume).

All this examples and many others give a little hint about we knowing, no just the size of atoms, but also the size neutrons, protons and electrons. Do we really know their size? Are we able to measure it? And if we do know their sizes, do we know their shape?

2. Aug 1, 2014

### e.bar.goum

This is all a bit "iffy", because naturally all of these are quantum mechanical objects.
So electrons are fundamental particles, so we treat them as "point like particles" - they have no dimension, and no shape.

Protons and neutrons are composite particles, and are therefore not point-like. For the proton, you can find the "charge radius", and the recommended NIST value is 0.8775 fm (rms). However, measuring this is a rather complex experiment (electron scattering off of protons, or measurements involving muonic hydrogen), it is my understanding that there is rather a large uncertainty on it. (It will certainly be on the order of 1 fm though). There is some evidence that protons aren't spherical: http://www.aps.org/units/dnp/research/proton.cfm

The same trick can't be played with a neutron, as it is uncharged. I don't know of any measurements of it relating to radius, but hopefully somebody else does.

So one thing in between atoms and nucleons are objects that have super interesting sizes and shapes - nuclei! As with protons, you can measure their charge radii, which gives you an idea of the size of the nucleus. But with other tricks, you can see where the neutrons are, and we find that some nuclei have extended neutron halos - these are called halo nuclei (unsurprisingly), and 11Li is about the same size as 208Pb, even though it's around 20 times lighter!

By examining the excited states of nuclei, you can find that nuclei (and different states of nuclei) have different shapes! (with some quantum superposition - you can have shape coexistence and such). Some protons are spherical, like 208Pb, but some are deformed prolately and some are oblate. Some are even triaxial. Super complex shapes!

3. Aug 1, 2014

### ShayanJ

Well, In fact its completely meaningless to talk about size of quantum particles.
In physics, defining a physical quantity means specifying a procedure for measuring it. The size of a particle can only be defined if you have a way for measuring it. But the point is, there isn't only one way of doing it. You can measure, kind of, size of particles by scattering experiments but that means measuring the particles cross sections for different interactions and they give different results. So you have "electromagnetic size" of protons, "strong size" of protons and "weak size" of protons I guess.Other notions of "size of quantum particles" are possible e.g. De-broglie wavelength and compton wavelength. And other notions are also possible, like classical electron radius which can be calculated for other particles too. So there is not even a unique definition of size of a quantum particle!
Also, for elementary particles like electrons, we only have upper limits for there sizes but I'm not sure what kind of a size they mean.
And about the shape, that's even more meaningless. For composite particles, the constituents can do different kinds of bizarre behaviours and also we have wave-particle duality and no shape is defined for composite particles. But for elementary particles, they are just considered to be points. A point, by definition, can have no shape.
Also, the wave behaviour of particles causes us to be unable to say that the particles are actually located somewhere but we only can say they're in a region of space and so its hard to think of a way of realizing a shape for them. Even if you had an electron in your hand, big enough to be seen and also if $\hbar$ weren't so small so quantum effects were observable in macroscopic world, you couldn't say how does the electron look like!!!

4. Aug 1, 2014

### e.bar.goum

Rather a lot of nuclear physicists disagree. In fact, rather a lot of people talk about the size and shape of nuclei.

(Each word a different abstract, fairly randomly picked from the top of a NASA ADS abstract search).

Just because an object is quantum-mechanical, doesn't mean you can't talk about "size" and "shape", you just have to be more precise in what you mean.

5. Aug 1, 2014

6. Aug 1, 2014

### e.bar.goum

There's a few wrong things in the above, but it's not science that is at fault, or Quantum Mechanics, which is of course the same thing. Possibly it is science reporting. Or the fact we're talking in English, not in mathematics, or formal physics terminology.

So what you need to know is that whenever anybody talks about the shape of something like an electron, they're referring to the electric dipole moment (EDM). The above work you linked to (nature paper here: http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html ) finds an upper limit for the dipole moment of de = (−2.4 ± 5.7stat ± 1.5syst) × 10−28e cm, which is consistent with zero. This is totally consistent with the standard model of particle physics (experiment is about 10 orders of magnitude too big here - the SM predicts it should be non-zero, but at most 10−38 e cm), and constrains where you can see BSM physics.

In addition, it is probably quite lazy to describe an electron as a point-like-particle ( I know I did it, sorry!). Due to the Heisenberg uncertainty principle, the electron will occupy a non-zero volume, determined by the energy. e.g. ~10-30 m3 for the electron in a hydrogen atom. However, obviously, electrons have no internal structure. But you cannot, of course, say that the electron has an intrinsic "size".

So in quantum mechanics, replace the word "point-like" with "fundamental particle", and you're all good!

It's sort of a matter of utility to describe fundamental particles as point-like, but the issue here is one of language, there's no conflict with quantum mechanics here.

Last edited by a moderator: May 6, 2017
7. Aug 1, 2014

### Malverin

OK. So we can measure the shape, location and size of electron's dipole moment, but the electron has no shape size and can be everywhere.
So electron and its dipole moment have not much in common
How we can even be sure we are measuring the electron's dipole moment?

Last edited by a moderator: May 6, 2017
8. Aug 1, 2014

### e.bar.goum

No. I'm sorry, I must not be communicating well, it's quite late here, but that's not at all what I said. Of course the electrons electric dipole moment has a lot in common with the electron. It is a fundamental property of the electron, like its charge. I don't think you can dispute that we know very well the charge of an electron.

The spatial extent of an electron is of course given by QM, so will depend on the situation, but like I said above, you can consider the extent of the wavepacket, FWHM and the like.

What else would you possibly be measuring? If you look at the paper, it is rather clear.

Look, electrons are easy. You can get a beam of electrons with a pointy bit of wire, another bit of wire about 20 cm away, a few thousand volts, and a half decent vacuum. Precision measurements are tricky, but it's hardly likely that experimentalists don't know what they are measuring.

9. Aug 1, 2014

### Malverin

That is what I am saying.
Both can not be truth - to know where is the electron (its dipole moment), to know the size of its dipole moment, and its shape and in the same time, not to know where the electron is.
Only one can be truth.
And I am asking which one? Because as you said, dipole moment is a fundamental property of the electron.

10. Aug 1, 2014

### e.bar.goum

I see no contradiction here. Fundamental particles have certain properties - charge, mass, dipole moment, spin, etc. etc. Fundamental particles are also quantum mechanical, and therefore are not localized in general.

I must emphasize that "to know where is the electron (its dipole moment)" is not correct. In the same way that charge does not imply location.

What's the problem?

11. Aug 1, 2014

### Malverin

12. Aug 1, 2014

### e.bar.goum

Like I said above (a few times). Dipole moment doesn't really imply classical shape. And any "size" you can give it is also a quantum mechanical analogy, such as FWHM of the |ψ(r)|^2 if it is localized at all, or in the case of electron orbitals, you use the uncertainty principle.

I also need to emphasize that "We don't know where it is" doesn't mean "it can literally be anywhere in space" in general. Wavepackets, for instance, can be quite spatially localized, but there is still some degree of uncertainty in the position.

To make a (slightly crude) classical analogy, you can throw a ball, but it still has properties of size, shape, colour etc. And you can also measure the colour of a moving ball if you need to, so why do you think you can't measure the dipole moment of a moving electron?

13. Aug 1, 2014

### Malverin

When you are measuring size of a moving object, even if you measure it very fast it will move in some direction and your accuracy will be low. To compensate that in final result you have to know exactly the speed and direction of movement of the object and how much and in what way it deforms while moving.

14. Aug 1, 2014

### e.bar.goum

But, like I've said a few times now, you're not measuring the size, you're measuring the electric dipole moment.

ETA: Here's a free version of the paper that measured the electron electric dipole moment, I suggest you read it. http://arxiv.org/pdf/1310.7534v2.pdf I'm going to bed, I hope reading the paper clears things up for you.

15. Aug 1, 2014

### Malverin

To determine a spherical shape you have to measure it. In meters, micrometers...
It looks like measuring a size(its diameter) to me.
Do you know some other way?

16. Aug 1, 2014

### e.bar.goum

I'm sorry, I don't know a clearer way to put this:

The electron electric dipole moment (EDM) is NOT found measuring the physical shape or size of the electron. The EDM does NOT exactly correspond to a classical shape. An EDM of zero is analogous to a spherical shape, but that does NOT imply an intrinsic size.

If you refer to the paper I have linked to several times now, the EDM is measured by a spin precession measurement. You take a beam of 232Th16O molecules, and pass them through a field in the z plane. A coherent superposition of two spin states, corresponding to spin aligned in the xy plane is produced with optical pumping. You then have parallel electric and magnetic fields which result in torque on the electric and magnetic dipole moments of the electrons, causing the spin vector to precess in the xy plane, the angle of which is measured with a laser and fluorescence detection. The degree to which this angle changes as the internal effective electric field is flipped is proportional to the EDM.

Thus, you find the EDM and thus all the articles in the news media describing the electron as "spherical".

It's all right there in the paper.

17. Aug 1, 2014

### anorlunda

To measure the size or shape of a particle, there must be an observable (in the QM sense). I don't think there is one for the size or shape of an electron or a nucleus; correct?

That quote makes it sound like a scattering cross section is size. I don't think q.bar.qoum meant that quite so literally.

A cross section is expressed in units of area but actually is a measure of probability, not size. Consider a neutron colliding with a nucleus. It can be absorbed, or scattered, or cause fission. Each type event has a different cross section, and they are all functions of the neutron energy, so they can not infer a size to the nucleus.

I have seen visualizations of a nucleus having a roiling shape with bulges that come and go. Sometimes a bulge can resemble a droplet breaking off from a drop as the nucleus emits an alpha particle. However, I don't believe that such visualizations are supported by QM. I think that the size and shape of a nucleus are not observables, directly or indirectly. Is that correct?

18. Aug 1, 2014

### e.bar.goum

I should have probably been more precise in my definition of charge radius. In electron scattering, IIRC, you take the mean of the electron scattering cross sections, for which there is a distribution. (Hence why it's called charge rms)

Are you thinking of simulations like these? http://inspirehep.net/record/1189218/files/dens.png

That's for a 40Ca + 238U collision at different orientations/angular momenta.

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.

ETA: The paper, if you're interested. http://arxiv.org/pdf/1210.1047.pdf

19. Aug 3, 2014

### Malverin

Yes you are right. They use precession to determine the dipole moment here.
I didn't understand how they are sure dipole moment is spherical (same value in all directions)?
They sense 2 states with the polarized rays - aligned and anti aligned.
So what spherical means here?

20. Aug 3, 2014