Semicontact three-body interaction for nuclear density functional theory

To solve difficulties related to the use of nuclear density functional theory applied in its beyond-mean-field version, we introduce a semicontact three-body effective interaction. We show that this interaction is a good candidate to replace the widely used density-dependent effective interaction. The resulting new functionals are able to describe symmetric, neutron, polarized, and neutron polarized nuclear matter as well as the effective mass properties simultaneously.

Figure 1

${\mathcal{F}}_3\left(k_{F}a\right)$ as a function of $\left(a{k}_F\right)$ obtained by adjusting the $c_1^{\mathrm{SM}}$ and $c_2^{\mathrm{SM}}$ to get a dependence similar to $1/\left(a{k}_F\right)$ ($\alpha =2/3$) [solid (red) line] or $1/{\left(a{k}_F\right)}^2$ ($\alpha =1/3$) [dashed (blue) line]. The reference curves $1/\left(a{k}_F\right)$ [filled (red) circles] and $1/{\left(a{k}_F\right)}^2$ [filled (blue) diamonds] are also shown. The dotted horizontal line indicates the zero-range three-body interaction limit ($\alpha =1$). The fit was made for $\left(a{k}_F\right)\in [1.25,1.75]$; note that in nuclear physics $\left(a{k}_F\right)\simeq 1.5$ at saturation.

Figure 2

(a) Scalar-isoscalar effective mass and (b) equations of state for SM (red), NM (blue), PM (green), and PNM (black) as a function of the density obtained with the SLy5 functional (symbols) and with the Skyrme (two-body) + three-body functional (lines), called ${\text{SLy5}}^{3\mathrm{b}}$. Inset: Contribution of the three-body functional to the energy per particle in symmetric matter. A simple function proportional to ${\rho }^{1+\alpha }$ has been adjusted on it with $\alpha \simeq 1/3$ for an optimal fit in the vicinity of the saturation density.

Figure 3

Same as Fig. 2, except that the Gogny D1M (symbols) and ${\text{D1M}}^{3\mathrm{b}}$ (lines) are shown. Inset: Again, $\alpha \simeq 1/3$ is found to be optimal.