# Thread: How charge is distributed in nucleon, nucleus? Can proton share its charge with neutron?

1. Why neutron requires charge to become stable?
Why against Coulomb attraction, nucleus require charge?
How this charge is distributed inside nucleon (quarks)? Nucleus?
Large nuclei are believed to behave like a liquid – are nucleons freely swimming there, or maybe they are somehow clustered, like in neutron-proton(-neutron) parts?

I’m thinking of a topological soliton model of particles (concrete field structures for particles, with quantum numbers as topological charges), which doesn’t only restrict to mesons and baryons like the Skyrme model, but is an attempt to a more complete theory: which family of topological soltions would correspond to our whole particle menagerie. Extremely simple model seems to qualitatively fulfill these requirements: just real symmetric tensor field (like stress-energy tensor), but with Higgs-like potential: preferring some set of eigenvalues (different) – it can be imagined as ellipsoid field: eigenvectors are axes, eigenvalues are radii. Now e.g. simplest charges are hedgehog configurations of one of three axes and topology says there is some additional spin-like singularity required (hairy ball theorem) – we get three families of leptons etc.

This is all of nothing approach: a single discrepancy and it goes to trash. Instead it seems to bring succeeding simple answers, like for above questions:

Basic structures there are vacuum analogues of Abrikosov vortex: curve-like structure around which (“quantum phase”) two axes makes e.g. pi rotation for ½ spin. The axis along the curve can be chosen in three ways – call them electron, muon or taon spin curve correspondingly.
Now baryons would be the simplest knotted structures – like in the figure, two spin curves need to be of different type. The loop around enforces some rotation of the main axis of the internal curve – if it would be 180degrees, this axis would create hedgehog-like configuration, what corresponds to +1 charge. Locally however, such fractional rotation/charge may appear, but finally the sum has to be integer.
This picture explains why charge is required for baryon stability, that for this purpose proton can share its charge with neutron. Lengthening the charge requires energy, what makes two nucleons attracting in deuteron - by this strong short-ranged force.

To summarize, this simple model suggests that:
- neutron has quadrupole moment (!),
- nucleons cluster into “-n-p-“ or “-n-p-n-“ parts sharing charge,
- pairs of such clusters can couple, especially of the same type (stability of even-even nuclei),
- these clusters are parallel to the spin axis of nucleus(?).

How would you answer to above questions?
Do these suggestions sound reasonably?
Can neutron have quadrupole moment? (Shouldn’t it have dipole or quadrupole moment in quark model?)

Update: while it is obvious that proton should be lighter than neutron from the picture above, it seems far nontrivial using QCD: I've just found 4 year old news about calculating nucleon mass on Blue Gene using lattice QCD: 936MeV for both +-22 or 25MeV: http://physicsworld.com/cws/article/...rst-principles

2.

3. I don't quite understand what it is that you want from this forum? Professional takes on your theories?
Well, from my professional point of view, I don't understand what it is that you are doing. I see a lot of words that are named rapidly after another but not actually constitute to any relevant physics. Why do you refer to the Higgs mechanism? Why do you refer to the Energy-stress Tensor. As if you are really going to use topological theories in quantum field theory, you are going to be needing a lot of much higher order tensors to do that properly.
Second your pictures make no sense. You use Quark charges as interchangable entities between neutrons?!? That is not who quantum field theory works. Hell that isn't how quantum mechanics works. Were are your colours of gluons? Where are your Feynmann diagrams? Or, just the raw mathematics? And what is on the axis of your coloured pictures? What are they even about?

Also, you simple model suggests the same things that have been suggested decades ago. And some things have also been verified scientifically.
My professional view as a Theoretical Physicist, is that you have no idea what you are doing.

4. This thread was to discuss the basics of nuclear physics. I got some suggestions and wanted to confront them, but didn't want to focus only on this aproach.
Ok, I try to explain some basics of soliton approach ... everything is described in papers I've linked.

Originally Posted by Kerling
Why do you refer to the Higgs mechanism?
Higgs potential, mexican hat, has minimum not in zero but in some asymmetric values on unitary circle - we have the same here and it also gives particles mass here. Dynamics inside this minimum are massless Goldstone bosons - corresponding to dynamics of electromagnetic field.
In Faber's electron, potential says that unit vector is energetically preferred.
The purpose of this reformulation of EM field is charge quantization: minimal nontrivial configuration of unit vector field is hedgehog - corresponding to elementary charge. Field curvature decreases from the center - defining electric field this way, Faber got standard EM interaction between such charges ( Particles as stable topological solitons - Abstract - Journal of Physics: Conference Series - IOPscience ).
Now what's happening in the center of such hedgehog? This unit vector field cannot be continuously glued there, so it has to get out of Higgs potential minimum e.g. to get zero vector in the center - giving some minimal rest energy to such topologically nontrivial situation: mass.
Like for ellipse field preferring some shape, it has to get out of the potential minimum in center of topological soliton:

Why do you refer to the Energy-stress Tensor.
Faber got only single family of leptons - this simple model has to be extended at least by a single degree of freedom what exactly I'm doing - of rotations around this unit vector. His unit vector field can be imagined as field of prolate ellipsoids, while I use field of tri-axial ellipsoids (three different radii). This additional dof of rotations corresponds to quantum phase (constantly rotate for wave nature of particles) and now hedgehog configuration can be made by one of 3 axes, getting 3 families of leptons ... and more properties as expected.
How to represent this ellipsoid field? By real-symmetric tensor field (like stress-energy tensor) - eigenvectors are axes, eigenvalues are radii and tensor Higgs potential prefers some set of eigenvalues.

You use Quark charges as interchangable entities between neutrons?!?
It is not what I assume like in quark model, but what comes out from this extremely simple ellipsoid field model - mechanism explaining the need for charge in neutron, nuclei, nucleon binding - the fundamental requirement I'm asking about...

ps. Another simple question: how short-range strong interaction explains Halo nuclei? Like Lithium 11 (8.75ms halftime!), which accordingly to CERN article ( http://cerncourier.com/cws/article/cern/29077 ) comparing to Pb208 should look like that:

Oh and another one: mass difference between tritium (3.0160492u) and helium 3 nucleus (3.0160293u) is only 18.6keV - how this decay can be beta decay if the difference between neutron and proton mass is 762+511keV?

5. Originally Posted by Jarek Duda
Higgs potential, mexican hat, has minimum not in zero but in some asymmetric values on unitary circle - we have the same here and it also gives particles mass here. Dynamics inside this minimum are massless Goldstone bosons - corresponding to dynamics of electromagnetic field.
In Faber's electron, potential says that unit vector is energetically preferred.
The purpose of this reformulation of EM field is charge quantization: minimal nontrivial configuration of unit vector field is hedgehog - corresponding to elementary charge. Field curvature decreases from the center - defining electric field this way, Faber got standard EM interaction between such charges
Again, you are just shooting terms here. Make complete well formulated sentences. There is no sense in juggling with terms when things conceirn High Energy particle physics. Also, if you want to use a Higgs potential, why, and where did you get it from. Do you just assume it? Or present it as a solution? That is a weird thing to do in Particle physics, where basically everything is derived from the basics of QFT.

Reformulation? As what, I've seen dozens of formulations of the EM field interactions. What is the one you propose?

A hedgehog is an animal, unless you explain what you mean with it. There is no use in discussing it. For all I know you mean the Ward-Takahashi identity which is the closest thing in physics I know of to come to a hedgehog.

Also, as a rule of algebra, the entire idea of a unity vector is that its size remains the same, even under coordinate transformation. And if you mean something else with your 'unit vector' explain what it means!

Also in general the idea of nontrivial things is that you elaborate on them for anyone to understand. If that wouldn't be necessary, you'd call it trivial. Or when it can be expected to be known in the field of publication.

Again your pictures don't actually state what they are. I could post a random graph here to elaborate this argument, but unless you elaborate on what they mean, there is no way for us to communicate.

Having glanced over the article you posted, are you trying to discuss that using the knowledge from that, yet without sharing it? You should really elaborate on the things you say. I now know that your hedge-hog is just some isotropic vectorfield. But I wouldn't have known this from your description.
If you want to discuss you need to: 1 make an introduction, and introduce the things you want to discuss. 2 thoroughly describe the things you want to discuss, if you use articles refer to them preferably with in-article quotations like formula references in the case of the hedge-hog it would be formula (5). 3. formulate good questions that you want to discuss.
4. Use proper english sentences.

So to your question: "how [does] short-range strong [nuclear] interaction explain [s] Halo nuclei"
It doesn't of course. However remind yourself that gluons are spin 1 particles. there is no reason why they should be solely attractive. They can be repulsive aswell. And considering Gluons make up 70 percent of the mass. You could wonder how gluon fields come to be. And they therefore fit much better in an idea like the nuclear shell model. Explaining its relative succes.

I'd love to discuss more with you, but you have to make things more clear. It is very unclear what it is that you want to discuss, and that is a luxury you cannot afford when discussing hard science.

6. This thread was intended to be about nuclear physics - I obtained some suggestions and requirements (like quadrupole electric moment of neutron) and wanted to compare them to a general feelings and generally discuss about nuclear physics e.g. to discredit this approach.
And it is expansion by a single degree of freedom of the model of prof. Faber, he probably explains it better: Particles as stable topological solitons - Abstract - Journal of Physics: Conference Series - IOPscience , http://arxiv.org/PS_cache/hep-th/pdf/9910/9910221v4.pdf
To get some intuition about 2D topological solitons of unit vector field you can use: Wolfram Demonstrations Project - Separation of topological singularities

Having unit vector field - unit vector assigned to each point, hedgehog configuration is that all of them are directed outwards: v(x)=x/|x|.
The problem is gluing this field in zero in continuous way - the field cannot longer be unit vector field there. This vector field preferred to be unitary because of Higgs-like potential e.g. V(x)=(|x|-1)^2. So in the center it has to get out of the potential minimum to x=0, like for ellipse field picture above (the darker, the larger potential energy) - topological constrain has made that this construction has some minimal energy - rest mass.
Here you have nice animation of releasing this mass/energy while soliton-antisoliton annihilation, prisoned because of topologically nontrivial minimum of the potential: Topological defect - Wikipedia, the free encyclopedia

In mathematics, topological charge of unit vector field is e.g. called Conley index - you look at vectors from a sphere (2 or 3 dimensional in our case), getting a function from sphere to itself - the number of times it covers itself (homotopy type) is the integer topological charge. For example hedgehog has charge 1, constant function has charge 0, in complex plane normalized x^k function has index k (counting total charge there is taking contour integer of ln(f)'=f'/f).

Returning to electromagnetism, we know that charge is quantized - the reformulation is to make this fundamental property deeply written there - use topology to make electromagnetism impossible to create noninteger macroscopic charges.
It is done in Faber's approach - fundamental is unit vector field and looking at it around elementary charge: hedgehog configuration, he defines electric field - finally getting standard EM interaction between such charges. The fact that looking at a closed surface, the unit vector field has to enclose itself, means the charge just has to be quantized there.

Standard physics was built on introducing new interactions/fields every time something was wrong/missing. This process has accumulated into something extremely complex - topological soliton approach is about starting once again - this time trying to understand the structure of particles, searching for something simple, recreating the qualitative level - using great resemblance between topological solitons (like Abrikosov vortex) and particles - e.g. automatically getting spin/charge quantization on topological level. The perfect situation would be having a field which family of topological solitons corresponds to our whole particle menagerie - no more, no less. There is rather no place for adding some new fields as usual - topology agrees or it goes to trash ... and it turns out that extremely simple field (SO(3)) seems to perfectly agree - a coincidence?
And of course the next step is finding correspondence with the standard approach.

What else you don't understand?

So to your question: "how [does] short-range strong [nuclear] interaction explain [s] Halo nuclei"