Jellium is the name given to an homogeneous electron gas. The motion of the electrons in the gas is not only affected by the coulomb interaction between them. There is also a purely quantum mechanical process at work. The motion of the electrons is correlated by the Pauli Exclusion principle. The electrons with parallel spins, must maintain a certain separation. The anti-parallel spin electrons keep apart to lower their mutual coulomb repulsion. So we can gain energy in two ways. Moving parallel spin electron apart will lower the exchange energy, moving anti-parallel spins apart will lower the correlation energy.
For the case of a homogeneous electron gas we can work out the average exchange-correlation energy per electron. In fact, values for the exchange-correlation energy for any reasonable electron density can be taken from parameterisations of calculated data.
The mutual exclusion zone or exchange-correlation hole around an electron in jellium. The radius of the hole corresponds to the exclusion of a single electron thereby giving the hole a single positive charge. The overall charge of the quasiparticle (the electron and its exchange-correlation hole together) is zero. Of course in reality, there is no marked boundary for the exclusion zone as drawn, the boundary is diffuse.