TY - JOUR

T1 - Some exact results in the Hartree-Fock theory of a many-fermion system at high densities

AU - Lieb, E. H.

AU - De Llano, M.

N1 - 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.

PY - 1971/11/1

Y1 - 1971/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49649150699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49649150699&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(71)90566-1

DO - 10.1016/0370-2693(71)90566-1

M3 - Article

AN - SCOPUS:49649150699

VL - 37

SP - 47

EP - 49

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1

ER -