Depletion of the nuclear Fermi sea

The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an ab initio description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.

Figure 1

Correlated momentum distribution obtained with the Av18 interaction at $\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$ and two temperatures: $T=5$ MeV (left panel) and $T=10$ MeV (right panel). The dashed line corresponds to the momentum distribution of the free Fermi gas under the same conditions.

Figure 2

Density dependence of the occupation of the lowest momentum state at $T=5$ MeV for Av18 (solid lines), CDBonn (dotted lines), and the FFG (dashed lines). The left (right) panel corresponds to nuclear (neutron) matter results. Note the different vertical scale of the two panels.

Figure 3

Momentum distribution of symmetric (upper panels) and neutron (lower panels) matter obtained with the Av18 interaction at $T=5$ MeV for different densities. The right panels focus on the high-momentum region.

Figure 4

Correlated momentum distribution obtained with the Av18 interaction at $\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$ and $T=5$ MeV (solid line). The $n_{\uparrow }(k)$ and $n_{\downarrow }(k)$ contributions of Eqs. (41) and (43) are shown in dashed and dot-dashed lines, respectively.

Figure 5

Different components to the imaginary (upper panel) and real (lower panel) parts of the self-energy for CDBonn at $\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$ and $T=5$ MeV.

Figure 6

Imaginary part of ${\Sigma }_{\downarrow }$ as a function of energy for the $k=0$ state. Different densities are displayed with different line styles. The upper panels have been obtained with CDBonn, whereas the lower panels correspond to Av18. Symmetric (neutron) matter results are shown in the left (right) panels. Note the difference in scales between the upper and lower panels.

Figure 7

The same as Fig. 6 for the real part of ${\Sigma }_{\downarrow }$. The dots represent the position of the quasiparticle peak.

Figure 8

Partial derivative of ${\Sigma }_{\downarrow }$ as a function of energy for the $k=0$ state at $T=5$ MeV. Different densities are displayed with different line styles. The upper panels show symmetric matter results, while the lower panels correspond to neutron matter. Left (right) panels have been obtained with the Av18 (CDBonn) interaction.

Figure 9

Isospin asymmetry dependence of the free Fermi gas (left panel) and the correlated momentum distribution from Av18 (right panel). The density ($\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$) and temperature ($T=5$ MeV) are fixed and the results for different asymmetries are shown in different line styles. Symmetric matter results correspond to the central solid curve, while curves to its right (left) correspond to neutron (proton) distributions for the corresponding isospin asymmetric cases.

Figure 10

Isospin asymmetry dependence of the neutron (filled circles) and proton (squares) lowest momentum occupation. Correlated results for the Av18 (solid lines) and CDBonn (dotted lines) interactions are compared to the free Fermi gas (dashed lines) predictions.

Figure 11

Difference of neutron and proton occupation of the lowest momentum state as a function of isospin asymmetry for different interactions. The two panels show results at $T=5$ MeV for $\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$ (left) and $\rho =0.32\hspace{0.5em}{\mathrm{fm}}^{-3}$ (right).

Figure 12

The $k=0$ imaginary (left panels) and real (central panels) parts of ${\Sigma }_{\downarrow }$ as a function of the energy for different asymmetries at $\rho =0.16\hspace{0.5em}{\mathrm{fm}}^{-3}$ and $T=5$ MeV. Upper (lower) panels display the results for neutrons (protons) obtained from the Av18 interaction. The right panels display the partial derivatives of the real part with dots representing the location of the self-consistent quasiparticle energy.