Spin-orbit and tensor interactions in homogeneous matter of nucleons: accuracy of modern many-body theories

Abstract

We study the energy per particle of symmetric nuclear matter and pure neutron matter using realistic nucleon--nucleon potentials having non central tensor and spin--orbit components, up to three times the empirical nuclear matter saturation density, $ρ_0=0.16$ fm$^{-3}$. The calculations are carried out within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the methods. The two hole--line approximation, with the continuous choice for the single particle auxiliary potential, is adopted for the BBG approach, whereas the variational Fermi Hypernetted Chain/Single Operator Chain theory, corrected at the second order perturbative expansion level, is used in the CBF one. The energies are then compared with the available Quantum and Variational Monte Carlo results in neutron matter and with the BBG, up to the three hole--line diagrams. For neutron matter and potentials without spin--orbit components all methods, but perturbative CBF, are in reasonable agreement up to $ρ\sim$ 3 $ρ_0$. After the inclusion of the LS interactions, we still find agreement around $ρ_0$, whereas it is spoiled at larger densities. The spin--orbit potential lowers the energy of neutron matter at $ρ_0$ by $\sim$ 3--4 MeV per nucleon. In symmetric nuclear matter, the BBG and the variational results are in agreement up to $\sim$ 1.5 $ρ_0$. Beyond this density, and in contrast with neutron matter, we find good agreement only for the potential having spin--orbit components.