Comparative study of three-nucleon force models in nuclear matter

We calculate the energy per particle of symmetric nuclear matter and pure neutron matter using the microscopic many-body Brueckner-Hartree-Fock (BHF) approach and employing the Argonne V18 (AV18) nucleon-nucleon (NN) potential supplemented with two different three-nucleon force models recently constructed to reproduce the binding energy of ${}^3\mathrm{H},{}^3\mathrm{He}$, and ${}^4\mathrm{He}$ nuclei as well as the neutron-deuteron doublet scattering length. We find that none of these new three-nucleon force models is able to reproduce simultaneously the empirical saturation point of symmetric nuclear matter and the properties of three- and four-nucleon systems.

Figure 1

Diagrams representing the contribution of terms $a$ [diagram (a)], $b,d$ [diagram (b)], $D$ [diagram (c)], and $E$ [diagram (d)] to the generic three-nucleon force $W(1,2,3)$ of Eq. (2).

Figure 2

Coordinates of a three-particle system.

Figure 3

Energy per particle $E/A$ of symmetric nuclear matter as a function of the nucleonic number density $\rho$ for the three parametrizations of the ${\mathrm{TM}}^{\prime }$ model [panel (a)] and the four parametrizations of the N2LOL one [panel (b)] considered in the present work. The green double-dash-dotted line, in both panels, represents the energy per particle with no three-body force contribution and using the AV18 NN potential. The empirical saturation point of nuclear matter ${\rho }_0=0.16\pm 0.01{\mathrm{fm}}^{-3},{E/A|}_{{\rho }_0}=-16.0\pm 1.0\mathrm{MeV}$ is denoted by the green box in both panels.

Figure 4

Energy per particle $E/A$ of pure neutron matter as a function of the nucleonic number density $\rho$ for the three parametrizations of the ${\mathrm{TM}}^{\prime }$ model [panel (a)] and the four parametrizations of the N2LOL one [panel (b)] considered in the present work. The green double-dash-dotted line, in both panels, represents the energy per particle with no three-body force contribution and using the AV18 NN potential.

Figure 5

Symmetry energy as a function of the nucleonic number density $\rho$ for the three parametrizations of the ${\mathrm{TM}}^{\prime }$ model [panel (a)] and the four parametrizations of the N2LOL one [panel (b)] considered in the present work. The green double-dash-dotted line, in both panels, represents the symmetry energy with no three-body force contribution and using the AV18 NN potential.