On the existence of solutions of the Brueckner equations for a many-fermion system

摘要: Abstract The Brueckner reaction matrix for a many-fermion system is frequently introduced as the formal “sum” of an infinite series which part complete many-body perturbation series. It shown that, when infinite, any “well-behaved” potential, there are always some unperturbed states diverges. Conditions existence solutions integral equations discussed and it that “Cooper-type” singularities arise potentials v(r) with not too strongly bound provided ∫0∞ sin2 kf rdr positive (ℏkF being Fermi momentum). Explicit calcutations show other types nuclear matter but liquid helium three. results provide potential foundation Belyaev's calculations spectra suggest should be no energy gap in spectrum