Trouble understanding definition of density of states

[cdot]

According to my thermo textbook the density of states should really be called the density of orbitals because "it refers to the solutions of a one particle problem and not to the states of the N particle system". This makes perfect sense to me but now I'm confused about references to the density of states of an electron gas. If we talk about the density of states of an electron gas is this the same thing as the density of orbitals for a single electron? How can that be?

 

[Khashishi]

In an electron gas, are there any nuclei? You only have orbitals if you have electrons bound to nuclei (or some other charged particle like a positron).
Your book is talking about very different things.