Advantages of high-energy heavy-ion collisions over proton-proton collisions?

As a clarification the energy per nucleon is always lower: for example, currently in the LHC the proton top energy is 3.5 TeV. Now the Pb energy is 3.5 TeV times Z so the energy per nucleon is 3.5*Z/A and A is greater than Z for every nucleus (except the proton where it is equal to one).

But the goal of ion-ion collision is not to increase the total energy or the energy per nucleon: it is to obtain a different type of collision.

It should be noted than in a proton-proton collision, the energy involved in the real collision process is variable: each quark and gluon carry a fraction of the energy of the proton, and hard collision involve a collision between a quark/gluon of one proton against a quark/gluon of the other.

In the case of ion-ion collision you have the same process: the energy is shared by the protons/neutrons and they can have different energies.

The goal of such collision is also to obtain a volume (bigger than in a p-p collision) with a very high energy density. In such a volume, a "state of matter" called quark-gluon-plasma is believed to be possibly created. The study of this QGP is one of the main goal of the ALICE experiment at the LHC.

A few references:

• The ALICE experiment at CERN
• Live control screen of the LHC now running as a Pb-Pb collider at 574 TeV in the center of mass