The Coulomb Gas at low temperature and low density

We study the quantum Coulomb Gas of N particles with Hamiltonian H at low temperature and negative values of the chemical potential μ. If μ is sufficiently negative the Coulomb gas is approximately a perfect rare gas of charged particles, as expected. The interesting fact is that for higher (but still negative) values of μ the gas changes to a rare gas of some atom or molecule (which is most likely neutral). The type of molecule is determined by the ground state of the Hamiltonian H -μN with center of mass motion removed.