# How do we know that the nucleus isn't a quark-gluon plasma?

The standard picture of the nucleus of atom is that is several distinct nucleons, which themselves are composed of quarks. However, it seems to me like a much simpler picture is that the nucleus is directly made out of quarks, without having nucleons as substructures. That is, that the nucleus is the ground state of a quark-gluon plasma. I can't find any evidence that this is false. For instance, if the distances between the nucleons was significantly larger than the size of the nucleons, there would be a difference in size between hydrogen and other atoms which can't be explained by this new framework, but according to wikipedia the diameter of all of the nuclei is the same order of magnitude. What is the evidence that large nuclei have nucleons as substructures?

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Because the interaction energies inside the nucleus are very low, and when we perform experiments on nucleons at those energies they behave primarily as discrete particles.

For a particular instance, take quasi-elastic nucleon ejection reactions like $A(e,e'p)$ (that is an electron scattering off a nucleus and neatly knocking out one proton without otherwise exciting or shattering the remnant). The figure of merit for such reactions is $Q^2 = -q \cdot q$, and in the range from about $1$--$8\text{+ GeV}^2$ (the upper limit is not yet experimentally known) the cross-section for this (per target proton) is a constant times the cross-section for the free reaction $p(e,e'p)$. The constant is called the "nuclear transparency" and expresses the probability that the scattered proton re-interacts before leaving the nucleus.

See this figure from my dissertation work

The nuclei (shown by different marker shapes and colors) are deuterium, carbon, iron and gold, and the different marker fill-states and sizes represent three experiments. Error bars are shown for all data and represent statistics plus point-to-point systematics (but not not systematics that would shift all the data for a single nucleus). The solid lines are a modified Glauber calculation.

A big part of what they do at Jefferson laboratory is to search for the change between nucleon--meson degrees of freedom (as reasonably well described by quantum hadrondynamics) and quark--gluon degrees of freedom (as described by quantum chromodynamics); but even the on-set of QCD dominated behavior does not correspond to quark--gluon plasma which occurs at much higher energies.

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This looks interesting. What do you mean by figure of merit? Since it has units of energy, I'm guessing you mean the energies in which this reaction can occur. –  Itai Bar-Natan Aug 16 '11 at 12:19
Figure of merit simply means the important number to use for comparing things. In this case $Q^2$ is a measure of how "hard" the reaction is. Particle physicists typically use a system of units where $c = \hbar = 1\text{ dimensionless}$, so everything ends up having units of energy-to-some-power. The $q$'s mentioned above are the four-vector difference of the initial and final electron momentum $q = k - k'$. To put it in terms of the Mandelstam variables $Q^2 = -t$. –  dmckee Aug 16 '11 at 15:58

What is the evidence that large nuclei have nucleons as substructures?

The periodic table of elements? This shows an organized internal substructure into nucleons, i.e. triplets of quarks in SU(2) representations:

The atomic masses in the table are within a percent multiples of the nucleon mass (the binding energy takes up the slack) . A quark gluon plasma would not show this approximate quantization in multiples of triplets.

A quark gluon plasma would not be constrained this way.

There are experiments looking for the signatures of a quark gluon plasma. Here is a review on such signatures.

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Scattering experiments are what tell us about substructure in atomic and nuclear physics. The higher the energy of the probe (usually a charged particle), the finer the resolution and thus the more substructure you can see. In the case of nuclei this process revealed the nucleons as substructure. In the case of the nucleons themselves, this revealed the existence of 3 'partons' and a background 'sea'. We now know these partons as quarks and gluons but whatever you call them, we saw them first as point like features in the distributions we pulled from early scattering experiments.

Experimental evidence for substructure usually comes from scattering.

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In the same way that we know that water vapour is composed of tiny (liquid) water droplets. There is an associated phase potential expressed as surface tensions that determine the boundary between different states of matter condensation. There is no further distinction above this.

If any, you can understand individual nucleons as an adiabatic approximation valid when the interaction energies and times are below the scales where asymptotic freedom dominates over confinement (which is the landmark that defines a true quark-gluon plasma). In other words, low energy reactions will have dominant nuclear reactions that mainly produce stable subproducts because they have time to thermalize before leaving the nucleus. But those most stable subproducts are themselves the nucleons (protons, neutrons, and aggregations of those, i.e:alpha). In that sense, we can tell that "there are nucleons" but only because they are particularly stable forms that will be produced in most but the most energetic reactions where such adiabatic approximation would be no longer valid

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