a- In the "jellium model" of a metal, the pressure P is given by P = -_ where E is the energy of the electron gas in uniform positive background. Express the pressure and the compressibility in terms of rs, using the Hatree-Fock approximation. b- A set of N fermions has a weak short-range two-body interaction V(r -r') ), and is confined to a box of volume 2. In the Hartree-Fock approximation, at T = 0, what is the value of the chemical potential / and what is the value of the density of states at the Fermi energy