The SNF and whether particles touch

[olioli86]

The SNF and whether particles "touch"

Hi there guys.

I'm intrigued when reading about the Strong Nuclear Force and how it becomes repulsive at 0.5fm as to whether protons and neutrons "touch" each other. As far as I am aware the diameter of a proton is approximately 1fm.
I am unsure whether to treat the force as acting from the whole proton or its centre. If I choose it to act from the centre then this would imply that the two nucleons are strongly attracted when touching each other, since the centres would need to be 1fm apart; or does it act from the centre of just one so that the other proton is considered as being 0.5fm away and just touching is equilibrium.
If I treat the force as acting from the whole proton this implies that the protons are constantly separated by 0.5fm.

So do the nucleons touch and if they do are they in equilibrium or constantly being pulled towards each other? (All this possibly making the mistake of considering them as billiard ball type things of course).

Thanks!

 

[bcrowell]

You need to interpret all these statements in terms of center-to-center distance, exactly as in Newtonian gravity. The force is attractive at a center-to-center distance of 1 fm. At a center-to-center distance of 0.5 fm, the two nucleons are actually overlapping a lot.

Don't attach too much absolute significance to statements about the properties of the strong force, e.g., that it has a repulsive core. All people actually do is make up force models with various adjustable parameters, and then try to fit the parameters to data. At energies where the repulsive core has big effects, you're probably talking about relativistic heavy ion physics, where it's probably more appropriate to describe everything as quarks and gluons rather than nucleons. At low energies, you can make models that don't have a hard core in them, and they may do just find at fitting the data. I suspect that the hard core is actually a way of mocking up the effect of the exclusion principle on the quarks.

 

[Vanadium 50]

The repulsive core is in addition to Pauli blocking. And you do see the repulsive core at low energies - that's what makes nuclei the size they are.

 

[bcrowell]

And you do see the repulsive core at low energies - that's what makes nuclei the size they are.

No, that's incorrect. The reason nuclei have the sizes they do is simply a particle in a box argument. If you make them smaller, you increase their kinetic energy for particle-in-a-box reasons. If you make them bigger, you increase their potential energy. They minimize their energy with the sizes they have. (Of course when you make a model of a nuclear interaction, it typically has 10 or 20 parameters, and they're all interrelated. If you turn a repulsive core on or off, it will have an effect on the size of nuclei, and you will have to adjust other parameters to compensate. But you can certainly get a physically reasonable self-consistent model that predicts the right sizes for nuclei, without having any repulsive core.)

The repulsive core is in addition to Pauli blocking.

This also seems wrong to me, although I won't swear to it. In interactions that include a repulsive core, that feature applies to all nucleons regardless of their spin and isospin, so, e.g., a neutron and a proton will experience the repulsive core, even though the exclusion principle doesn't apply (within this model, where the fundamental fermions are nucleons). So you don't get any Pauli blocking between a neutron and a proton (or between two neutrons with opposite spins, etc.) automatically in the model, and the only way to get such an effect is to mock it up using a repulsive core in the potential.

 

[Vanadium 50]

I am away from my copy of Krane, but Frauenfelder and Henley say this on p. 341: "We have already discussed the [nucleon-nucleon] potentials produced by scalar and pseudoscalar mesons. The potential produced by vector mesons can be obtained similarly. For example, the exchange of an omega meson gives rise to a repulsive core as indicated schematically in Fig. 12.15" (emphasis mine)

 

[bcrowell]

I am away from my copy of Krane, but Frauenfelder and Henley say this on p. 341: "We have already discussed the [nucleon-nucleon] potentials produced by scalar and pseudoscalar mesons. The potential produced by vector mesons can be obtained similarly. For example, the exchange of an omega meson gives rise to a repulsive core as indicated schematically in Fig. 12.15" (emphasis mine)

I'm perfectly willing to believe that. So that would say that if you try to build a model with a nucleon-nucleon potential parametrized in a certain way, and you want to match that up with a model involving certain types of meson exchange, then there is a contribution to one feature of one model (a hard repulsive core) from one feature of another model (exchange of omega mesons), and that the repulsive core in model #1 is not entirely due to mocking up of the exclusion principle. Of course this is all just a statement about a relationship between two models.

The fact that they're invoking the exchange of a relatively high-mass meson tends to reinforce my impression that the necessity for a hard core is more of an issue at high energies. My field is low-energy nuclear structure, and from my experience you basically don't ever need to talk about a repulsive core to explain anything of any interest in low-energy nuclear physics. That's not to say that a hard core doesn't exist. But I think the thing to keep in mind is that nucleon-nucleon potentials themselves don't really exist. To the extent that they have any absolute, model-independent physical meaning, it would only be in the limit of low energies. The general features of low-energy nuclear structure are actually amazingly insensitive to the details of the nuclear interactions. E.g., clusters of sodium atoms have the same first few magic numbers as the magic numbers in nuclear physics, because those magic numbers are determined solely by the short-range nature of the interaction.

 

[olioli86]

Thank you guys, went a bit beyond me towards the end but I'm gaining an understanding of this more now. Just to clarify a point...
If I'm treating the nucleons as points so as you said, when 0.5fm apart they would indeed overlap by quite a lot! So in a nucleus are all the nucleons touching each other experiencing a force towards each other then and if so is the force insufficient to do anymore than just hold everything in place?

 

[bcrowell]

So in a nucleus are all the nucleons touching each other experiencing a force towards each other then and if so is the force insufficient to do anymore than just hold everything in place?

The neutrons and protons are all physically passing through the same space all the time. Each neutron or proton's wavefunction basically covers the whole nucleus, so they're all overlapping. They're essentially not localized or held in place at all, except in the sense that they can't escape the nucleus as a whole. They're not packed together like oranges at the supermarket.

 

[Raghnar]

you basically don't ever need to talk about a repulsive core to explain anything of any interest in low-energy nuclear physics.

Totally Agree.
And from that the renormalization of realistic NN interaction (like Argonne, Paris...etc..) in effective interaction like v_low-k.

If you see the nucleus from a low-energy physics viewpoint (nuclear structure, <100 MeV nuclear reactions, to give an order) and so see the nucleons as elementary particles you don't really need an hard core interaction: a mean field approach treating fermions gives you a fair description of the nucleus without needing an hard core description.

Usually the thing is avoiding the hard core or it will needed to consider very high momenta (Fourier Space) that will slow you down (like the painful using of Argonne interaction) and introduce effects from physics that you don't want consider.

Only if you go to higher energies you can see an actual penetration and the repulsive core, at the ground state the nucleons weavefunctions spread all over the nuclear volume following the states imposed by the pauli blocking and overlapping with others without being forcefully repulsed, pretty like electrons in atoms.