Effect of three-body forces on response functions in infinite neutron matter

We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the noncentral part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.

Figure 1

(a) central Landau parameters $F_{\ell }$ and $G_{\ell }$ associated with the chiral nuclear force at the cutoff scale $\Lambda =450$ MeV as a function of the density of the system. (b) Same as panel (a) but for the noncentral Landau parameters ${\tilde{H}}_{\ell },{\tilde{K}}_{\ell }$, and ${\tilde{L}}_{\ell }$. Black circles, red squares, and blue diamonds correspond to multipoles $\ell =0,1,2$, respectively. Dashed lines and open symbols refer to results obtained when only two-body interactions are included, while solid lines and symbols refer to the full two- and three-body interactions. See text for details.

Figure 2

Static susceptibility from the chiral nuclear potential for $\Lambda =450$ MeV as a function of density. In the left panel the complete interaction is considered, while in the right panel the contributions arising from 3NF has been removed. In the $S=0$ channel, the ratio of the interacting and noninteracting static susceptibilities is multiplied by $\frac{1}{4}$ in the right panel.

Figure 3

Nuclear response function at $k_F^{}=1.68{\text{fm}}^{-3}$ and $q/k_F=0.5$ in the $S=1$ channel calculated at $l_{\max }=3$ with and without the different contributions of the tensor terms. The chiral nuclear potential with a cutoff of $\Lambda =450$ MeV is employed. See text for additional details.

Figure 4

Response function in the various ($S,M$) channels at $\rho =0.16{\text{fm}}^{-3}$. In the left column [panels (a), (c), (e)], we used the complete Landau parameters, while in the right column [panels (b), (d), (f)] we discarded the three-body terms.