Variational and parquet-diagram calculations for neutron matter. II. Twisted chain diagrams

Variational and parquet-diagram calculations for neutron matter: Structure and energetics

“…where we have omitted all spin (and possibly isospin) dependencies for ease of writing. The VI (r) is in our case the important contribution of "twisted-chain" diagrams [7].…”

“…The symmetrization is necessary because the operators Ôα (i, j) and Ôβ (i, k) do not necessarily commute. We have highlighted recently [7] (see also Ref. 36) the importance of a proper symmetrization in cases where the bare interaction is different in spin-singlet and spin-triplet channels.…”

“…71 and disregard this term. As already mentioned above, we can also safely disregard the "twisted-chain" corrections [7]. These corrections are important when the interactions in the spin-singlet and the spin-triplet case are very different as it is the case for both the Reid and the Argonne potentials.…”

“…The relevant approximations have been dubbed as FHNC//0 or parquet//0. More complicated exchange diagrams are also important and routinely kept [6,7] but we shall restrict ourselves for the purpose of discussions to the simplest case. A brief discussion of how we include exchange effects will be given in Sec.…”

“…We have in previous work [6,7] studied v 6 models of the nucleon-nucleon interaction, the next step in the treatment of successively more realistic nucleon-nucleon interactions is the inclusion of the spin-orbit interaction. Its operator structure has the form Ô7 (i, j; r ij , p ij ) = r ij × p ij • S , Ô8 (i, j; r ij , p ij ) = Ô7 (i, j; r ij , p ij )τ i • τ j , (1.3) with S ≡ 1 2 (σ i +σ j ) is the total spin, and p ij = 1 2 (p i −p j ) is the relative momentum operator of the pair of particles.…”