@article{2e24d5b17ab546de9726a96b632dbde3,

title = "Some exact results in the Hartree-Fock theory of a many-fermion system at high densities",

abstract = "For high particle densities we show sufficient conditions on the two-particle interaction such that the Hartree-Fock homogeneous-density (plane-waves) ground state energy is exact and that lower-energy, granular-density solutions may exist when the above conditions are violated.",

author = "Lieb, {E. H.} and {De Llano}, M.",

note = "Funding Information: The perturbation theory \[1\]o f the ground state of a quantum liquid of fermions (e.g., nuclear matter or liquid 3He) has heretofore been analyzed in terms of plane-waves, single-particle solutions of the Hartree-Fock equations, under the implicit assumption \[2\]t hat they are the lowest-energy solutions at liquid densities. Although these solutions may be adequate for the weakly-interacting, low-density imperfect gas, it is far from obvious that they will be the lowest- energy solutions for the liquid, particularly since they become unstable \[3\]c onsiderably below the liquid equilibrium density for sufficently strong attractive interaction. The high-density limit on the other hand is relatively easier to analyze and may prove useful for an eventual understanding of intermediate densities. 1. Homogeneous HF solulions. If the two-body interaction v(r ir j) is translation-invariant (but not necessarily rotation-invariant), then it follows directly that the HF equations for spinless and chargeless particles are indeed satisfied by the set of plane-waves, normalized in a volume fL Since the HF ground state is (bo = (N'. )-1/2de t \[~ -1/2 exp (ik. r)lk </e F, with k F the Fermi momentum, the HF energy per particle (which by the variational principle is an upper bound to the exact energy per particle) * Work supported by U.S. National Science Foundation Grant GP26526. ** Work supported in part by Comisi6n Nacional de Energfa Nuclear, M~xico. Support from AFOSR Contract # 44620-71-C-0013 is also gratefully ack-nowledged.",

year = "1971",

month = nov,

day = "1",

doi = "https://doi.org/10.1016/0370-2693(71)90566-1",

language = "American English",

volume = "37",

pages = "47--49",

journal = "Physics Letters B",

issn = "0370-2693",

publisher = "Elsevier",

number = "1",

}