Comparative study of three-nucleon potentials in nuclear matter

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter (PNM) and symmetric nuclear matter (SNM) at zero temperature obtained using these models of three-nucleon forces. In particular, we have carried out both variational and auxiliary field diffusion Monte Carlo calculations of the equation of state of PNM, while in the case of SNM we have only the variational approach has been considered. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed.

Figure 1

TPE, OPE, and $\mathit{NNN}$ contact interactions of the chiral three-body force at NNLO.

Figure 2

Radial dependence of the function $Z_0\left(r\right)$, appearing in Eq. (27), plotted for different values of the cutoff $\Lambda$.

Figure 3

Cluster diagrams contributing to the expectation value of $V^{2\pi }$.

Figure 4

Same as in Fig. 3, but for $V^R$.

Figure 5

Equation of state of PNM obtained using the AFDMC (triangles) and FHNC/SOC (solid lines) approaches with the TM${}_1^{\prime }$ (a), TM${}_2^{\prime }$ (b), and TM${}_3^{\prime }$ (c) plus $v_8^{\prime }$ Hamiltonian.

Figure 6

Equation of state of SNM resulting from FHNC/SOC variational calculations with the TM${}^{\prime }$ plus $v_8^{\prime }$ Hamiltonian.

Figure 7

Same as Fig. 5, but for NNLOL${}_1$ (a), NNLOL${}_2$ (b), NNLOL${}_3$ (c), and NNLOL${}_4$ (d) plus $v_8^{\prime }$ Hamiltonian.

Figure 8

Same as Fig. 6, but for NNLOL plus $v_8^{\prime }$ Hamiltonian.