Density and isospin-asymmetry dependence of high-momentum components

We study the one-body momentum distribution at different densities in nuclear matter, with special emphasis on its components at high momentum. Explicit calculations for finite neutron-proton asymmetry, based on the ladder self-consistent Green's function approach, allow us to access the isospin dependence of momentum distributions and elucidate their role in neutron-rich systems. Comparisons with the deuteron momentum distribution indicate that a substantial proportion of high-momentum components are dominated by tensor correlations. We identify the density dependence of these tensor correlations in the momentum distributions. Further, we find that high-momentum components are determined by the density of each subspecies and we provide a new isospin-asymmetry scaling of these components. We use different realistic nucleon-nucleon interactions to quantify the model dependence of our results.

Figure 1

Momentum distribution for neutrons (top panels) and protons (bottom panels) in asymmetric nuclear matter. Different panels correspond to different $NN$ interactions, from left to right: Argonne v18, CD-Bonn, N3LO, and Av4${}^{\prime }$. Lines represent data obtained at different proton fractions. We also show, for comparison, the momentum distribution of the deuteron (dotted line) associated with each interaction.

Figure 2

Ratio of the nucleon momentum distribution to the corresponding deuteron distribution at high momenta. Different columns correspond to different densities, from $\rho =0.04$ fm${}^{-3}$ (left column) to $\rho =0.16$ fm${}^{-3}$ (right column) in equidistant steps. Vertical panels show different $NN$ interactions: Argonne v18 (top row), CD-Bonn (middle row), and N3LO (bottom row) panels. The dashed horizontal line and gray region represent, respectively, the average and the error bar of the ratio in the tensor-dominated momentum region, depicted by vertical dotted lines.

Figure 3

Density dependence of $a_2$, as defined in Eq. (12). We show values obtained for three $NN$ interactions, with a small horizontal offset for display purposes. Experimental $a_2$ values from Ref. [16] are plotted as a function of a rescaled nuclear density (see text for details). The shaded region corresponds to power laws with exponents $0.4-0.5$.

Figure 4

(Top panels) Ratio of the neutron and proton momentum distribution to the corresponding deuteron distribution at high momenta. Different line styles correspond to different isospin asymmetries. The three different panels correspond to thee $NN$ interactions, from left to right: Argonne v18, CD-Bonn, and N3LO. (Bottom panels) Rescaled neutron and proton momentum distributions, as discussed in the text. After rescaling, all results fall in a narrow band. Gray bands are an error band associated to the maximum deviation in the tensor-dominated region.

Figure 5

Density dependence of the $\gamma$ parameter for the three phase-shift equivalent interactions considered in this work. Data for each $NN$ force have a small horizontal offset for display purposes. Error bars have been calculated as differences between the optimal neutron and proton $\gamma$ parameters. The shaded region corresponds to linear fits with slopes $2.8-3.3$ fm${}^3$.

Figure 6

(Top panels) Ratio of the neutron to the proton momentum distribution for different proton fractions. (Bottom panels) Rescaled ratio of momentum distributions (see text for details). Different columns correspond to different $NN$ interactions: Argonne v18 (left panels), CD-Bonn (middle panels), and N3LO (right panels).

Figure 7

Integrated single-particle strength for neutrons (circles) and protons (squares) in three momentum regions: $k=0-400$ MeV (top panels), $k=400-850$ MeV (middle panels), and $k>850$ MeV (bottom panels). The four columns correspond to different $NN$ interactions. Note the different vertical scales of the different rows.