Neutron matter in the hole-line expansion

We calculate the binding energy of pure neutron matter up to third order in the Brueckner-Bethe-Goldstone hole-line expansion, employing various modern nucleon-nucleon potentials. At that order all results appear well converged to within a few percent up to a density of $0.8{\mathrm{fm}}^{-3}$. We analyze the potentials in terms of the strength of their hard core. Comparison with results of other theoretical methods is made.

Figure 1

Different Goldstone diagrams contributing to the binding energy of nuclear matter: Diagrams (a) and (b) correspond to the 2HL (BHF) calculation. The sum of the other diagrams, (c), (d) bubble, (e) ring, (f) higher, gives the 3HL contribution. $T^{\left(3\right)}$ is the three-body in-medium scattering matrix. For a detailed discussion, see Refs. [4, 6, 15].

Figure 2

Diagonal matrix element $V_{{}^1{S}_0}(k,k)$ and $V_{{}^{3}P{F}_2}(k,k)$ for various NN potentials. Note the different energy scales.

Figure 3

Deviation of the momentum distribution in PNM from the bare Fermi distribution $n_0\left(k\right)=\theta (k_F-k)$ for all potentials at different densities (${\rho }_0=0.17{\mathrm{fm}}^{-3}$). The bottom panels are weighted with a factor $k^2$ in order to emphasize the long-range tail of the distributions.

Figure 4

${}^{1}S_0$ and ${}^{3}PF_2$ defect functions in PNM at different densities (${\rho }_0=0.17{\mathrm{fm}}^{-3}$) for all potentials. The vertical dashed lines indicate the interparticle distance $d\equiv {\rho }^{-1/3}$.

Figure 5

Correlation parameter $\kappa$, Eq. (2), in PNM for all potentials. The N4LO550 calculations do not converge well for $\rho \gtrsim 0.5{\mathrm{fm}}^{-3}$.

Figure 6

Energy per particle of PNM for different NN potentials in 2HL (left panel) and 2HL+3HL (right panel) approximation with continuous- (thick curves) or gap-choice (thin curves) s.p. potentials. The N4LO550 calculations do not converge well for $\rho \gtrsim 0.5{\mathrm{fm}}^{-3}$.

Figure 7

Comparison of continuous-choice BHF results with N4LO EM and EGM potentials. The relation between $r$-space regulator and chiral cutoff is $\mathrm{\Lambda }=2/R$ [27, 28].

Figure 8

Energy per particle of PNM in continuous-choice 2HL+3HL approximation for different NN potentials without 3N forces (thin curves) in comparison with other calculations, all using chiral 2N+3N forces (bold curves): many-body perturbation theory [30, 31]; BHF including $\mathrm{\Delta }$ degrees of freedom [32]; diffusion Monte Carlo [33]; quantum Monte Carlo [34].