In-medium $T$ matrix for nuclear matter with three-body forces: Binding energy and single-particle properties

We present spectral calculations of nuclear matter properties including three-body forces. Within the in-medium $T$-matrix approach, implemented with the CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we compute the energy per particle in symmetric and neutron matter. The three-body forces are included via an effective density dependent two-body force in the in-medium $T$-matrix equations. After fine tuning the parameters of the three-body force to reproduce the phenomenological saturation point in symmetric nuclear matter, we calculate the incompressibility and the energy per particle in neutron matter. We find a soft equation of state in symmetric nuclear matter but a relatively large value of the symmetry energy. We study the the influence of the three-body forces on the single-particle properties. For symmetric matter the spectral function is broadened at all momenta and all densities, while an opposite effect is found for the case of neutrons only. Noticeable modification of the spectral functions are realized only for densities above the saturation density. The modifications of the self-energy and the effective mass are not very large and appear to be strongly suppressed above the Fermi momentum.

Figure 1

Energy per particle in symmetric nuclear matter as a function of density (in units of the nuclear saturation density ${\rho }_0=0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$). $T$-matrix calculations are compared to the variational [2] and BHF [9] approaches, both including TBF.

Figure 2

Spectral function at zero momentum for CD-Bonn interaction and symmetric nuclear matter, at ${\rho }_0,2{\rho }_0$, and $3{\rho }_0$.

Figure 3

Spectral function at $p=340$ MeV (left panel) and $p=510$ MeV (right panel) for CD-Bonn interaction in symmetric nuclear matter.

Figure 4

Nucleon self-energy for CD-Bonn interaction in symmetric nuclear matter at ${\rho }_0$ (left panel) and $3{\rho }_0$ (right panel).

Figure 5

Effective mass (in units of the nucleon mass $m=939$ MeV) for the CD-Bonn interaction and symmetric nuclear matter at ${\rho }_0$ (left panel) and $3{\rho }_0$ (right panel).

Figure 6

Energy per particle in neutron matter as a function of density (in units of the nuclear saturation density ${\rho }_0=0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$) for different potentials. The $T$-matrix calculations are compared to the variational [2], AFDMC [43], and BHF [9] approaches, all including TBF.

Figure 7

Symmetry energy as a function of the density. The $T$-matrix results are compared to the variational [2] and BHF [9] approaches.

Figure 8

Spectral function in neutron matter at zero momentum for the CD-Bonn interaction with and without TBF.

Figure 9

Nucleon spectral function in neutron matter at $3{\rho }_0$ for $p=280$ MeV (left panel) and $p=340$ MeV (right panel).

Figure 10

Different contributions to the self-energy $\mathrm{Re}\hspace{0.5em}\Sigma (\mathit{p},\omega )$ at ${\rho }_0$ and $3{\rho }_0$ in neutron matter (CD-Bonn interaction).

Figure 11

Effective mass in neutron matter (in units of the nucleon mass $m=939$ MeV) for the CD-Bonn interaction at ${\rho }_0$ (left panel) and $3{\rho }_0$ (right panel).