Hi Based on what I know (it might be wrong) properties of nuclei are calculated based on the different (simplified) models of the p and n "particles" (shells, droplets etc). I have 2 questions: 1. To what extent can we assume that n and p are "elementary" particles bound by residual strong force versus true picture on 3*(n+p) valence quarks and pure QCD? If we could calculate using both models - quark and hardon, what would be the level of inaccuracy of the simplified hardon model? 2. I've also heard that the computational complexity in QCD increases exponentially with the number of particles (when matter is cold enough). How far are is the current computational power (I don't mean a single computer, but huge networks like SETI@home, or power of video cards wasted on "mining bitcoins"). So how far is that power from being useful to calculate nuclear properties using "pure" QCD? May be not Uranium, but lighter elements? Thank you
Calculating properties of nuclei from QCD is indeed very hard. I think the current state of the art is that we can approximately calculate the binding energies of helium-3 and helium-4 in an unphysical scenario where the up and down quarks are much heavier than they are in the real world. The cost of the simulation increases as the quark mass decreases, so it will take some effort to do even this simple nucleus at the lighter, physical values of the up and down quark masses. I don't know if it's at the right level, but you could take a look at this overview.
For (1) see ChrisVer. They are still struggling with some mesons (-> XYZ spectroscopy) or precise ab initio mass predictions for individual baryons. Without effective models in some way, it is hard to do anything.
OMG, just for few quarks... So it is THAT bad... Which means, that even we had TOE right now, we wouldn't be able to make any calculations->predictions, because near Planck energies we would have to take into account a cloud of all types of virtual particles, including quarks and gluons, all that QCD stuff.
At higher energies I think that it's possible to make QCD calculations, since the coupling constant gets smaller and so you can work with the 3 valance quarks (the sea quarks and gluons get to zero).
Yes and no. The sea quarks and gluons matter more and more at higher energies (see fig 16.4 in the PDG summary on structure functions http://pdg.lbl.gov/2011/reviews/rpp2011-rev-structure-functions.pdf). However, higher energies mean that the strong coupling constant is weaker, which means that you are further and further into the deep inelastic scattering (DIS) regime, where you can use perturbation theory to high accuracy - you just need to know the parton pdfs.
tzimie, regarding your first question: there is an experimental effect called the EMC effect where conventional nuclear physics (treating the nucleus as a bound system of protons and neutrons) is inadequate. If deep inelastic scattering (DIS)—and I recommend Orodruin's link on this—is performed on a nucleus, and on a deuteron, then the ratio of their cross sections, given as a function of Bjorken x, has a dip in the region 0.3<x<0.7 that cannot be explained simply by accounting for the motion or binding energy of nucleons. For this reason, everyone seems to believe that calculations should be done with quarks and gluons in order to explain the EMC effect, but no-one really agrees on how.