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, ${\rho }_0=0.16$ 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 $\rho \sim$ 3 ${\rho }_0$. After the inclusion of the LS interactions, we still find agreement around ${\rho }_0$, whereas it is spoiled at larger densities. The spin--orbit potential lowers the energy of neutron matter at ${\rho }_0$ 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 ${\rho }_0$. Beyond this density, and in contrast with neutron matter, we find good agreement only for the potential having spin--orbit components.

18 pages, 4 tables. Accepted in PLB

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• Construction of high-quality Nucleon-Nucleon potential models
• Quantum Monte Carlo calculations of nuclei with A \leq 7
• Quantum Monte Carlo Calculations of $A\le 6$ Nuclei
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• Probing the High Density Behaviour of Nuclear Symmetry Energy with High Energy Heavy-Ion Collisions
• Quantum Monte Carlo Calculations of Neutron Matter
• Spin susceptibility of neutron matter at zero temperature
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• Spin-orbit correlation energy in neutron matter

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• Quantum Monte Carlo calculations of symmetric nuclear matter
• Effects of $\varphi$-meson on properties of hyperon stars in density dependent relativistic mean field model
• Tensor force effects and high-momentum components in the nuclear symmetry energy
• Extended Skyrme pseudo-potential deduced from infinite matter properties
• Microscopic Study of ${}^1{S}_0$ Superfluidity in Dilute Neutron Matter
• The Auxiliary Field Diffusion Monte Carlo Method for Nuclear Physics and Nuclear Astrophysics
• Density-dependent nucleon-nucleon interaction from UIX three-nucleon force
• Variational and parquet-diagram calculations for neutron matter. IV. Spin-orbit interactions and linear response
• Variational and parquet-diagram calculations for neutron matter. II. Twisted Chain Diagrams
• Ab initio calculations on nuclear matter properties including the effects of three-nucleons interaction
• Saturation of nuclear matter in effective field theory
• Finite particle-number description of symmetric nuclear matter with spin excitations of high-momentum pairs induced by tensor force