Exact solution of the Brueckner-Bethe-Goldstone equation with three-body forces in nuclear matter

An exact treatment of the operators $Q/e\left(\omega \right)$ and the total momentum is adopted to solve the nuclear matter Bruecker-Bethe-Goldstone equation with two- and three-body forces. The single-particle potential, equation of state, and nucleon effective mass are calculated from the exact $G$ matrix. The results are compared with those obtained under the angle-average approximation and the angle-average approximation with total momentum approximation. It is found that the angle-average procedure, whereas preventing huge calculations of coupled channels, nevertheless provides a fairly accurate approximation. On the contrary, the total momentum approximation turns out to be quite inaccurate compared to its exact counterpart.

Figure 1

Nuclear potential as calculated from the off-diagonal matrix elements of the $G$ matrix with the angular dependence of the propagator $Q/e\left(\omega \right)$. The upper (lower) panel corresponds to the neutron-proton (neutron-neutron) in the isospin singlet (triplet) state.

Figure 2

BHF optical potential and neutron effective-mass $m_n^{*}/m$ as a function of the momentum $k$ for symmetric nuclear matter at two densities with the exact calculation, the AA approximation, and the AA approximation with TMA, respectively.

Figure 3

Equation of state (EOS) of symmetric nuclear matter with the exact calculation, the AA approximation, and the AA approximation with TMA, respectively. The star marks the saturation point in the three calculations.

Figure 4

Nucleon effective mass as a function of the density $\rho$ and the isospin asymmetry $\beta$ within the exact calculation, the AA approximation, and the AA approximation with TMA, respectively.