Nonlocality in the nucleon-nucleon interaction and nuclear matter saturation

We study the possible relationship between the saturation properties of nuclear matter and the inclusion of nonlocality in the nucleon-nucleon interaction. To this purpose we compute the saturation curve of nuclear matter within the Bethe-Brueckner-Goldstone theory using a recently proposed realistic nonlocal potential, and compare it with the corresponding curves obtained with a purely local realistic interaction (Argonne $v_{18}$) and the most recent version of the one-boson exchange potential (CD Bonn). We find that the inclusion of nonlocality in the two-nucleon bare interaction strongly affects saturation, but it is unable to provide a consistent description of few-body nuclear systems and nuclear matter.

Figure 1

Diagonal matrix elements of the $v_{18}$ (solid line), CD Bonn (dotted) potentials, and Doleshall's IS potential of Ref. 6 (dot-dashed, labeled as NL) for the np interaction in the ${}^1{S}_0$ (upper panel), ${}^3{S}_1$ (middle), and in the coupling ${}^3{S}_1-{}^3{D}_1$ (lower panel) channels. The on-shell $R(q_0,q_0;E)$ R-matrix elements are also shown (symbols), for laboratory energies ranging from 50 to 350 MeV in steps of 50 MeV.

Figure 2

(Left panels) Off-diagonal ${}^1{S}_0$ np matrix elements of the $v_{18}$, CD Bonn, and NL potentials for three fixed momenta $q_0$ corresponding to laboratory energies $E_{\mathrm{lab}}=2E=25$ (upper panel), 150 (middle) and 350 (lower) MeV. (Right panels) Corresponding half off-shell R-matrix elements. The solid dot marks the on-shell values of the R-matrix.

Figure 3

As in Fig. 2 but for the ${}^3{S}_1$ matrix elements.

Figure 4

As in Fig. 2 but for the ${}^3{S}_1-{}^3{D}_1$ matrix elements.

Figure 5

Potential energy per particle for symmetric nuclear matter calculated with the nonlocal potentials NL1 (squares), which includes the nonlocality in the ${}^1{S}_0$ channel only, and NL2 (triangles), which has the nonlocality both in the ${}^1{S}_0$ and in the ${}^{3}S-D_1$ channels. Empty symbols correspond to the two hole-line calcu- lations, whereas full symbols represent the full two + three hole-line results.

Figure 6

Contributions of the different channels to the potential binding energy per particle (in MeV) vs. the Fermi momentum $k_F$. The upper panel corresponds to the ${}^1{S}_0$ channel, the middle panel to the ${}^3{S}_1+{}^3{D}_1$ channels, whereas the lower panel shows the total potential binding energy. All curves are calculated at the two-hole-line level.

Figure 7

Potential $U(k)$ (MeV) of Eq. (4) for $k_F=1.4$ (upper panel), $1.6$ (middle), and $1.8\hspace{1em}{\mathrm{fm}}^{-1}$ (lower) and for the $v_{18}$ (solid line), nonlocal (dot-dashed), and CD Bonn (dashed) potentials.

Figure 8

Energy per particle (in MeV) for symmetric nuclear matter calculated for the $v_{18}$ and CD Bonn potentials and for the nonlocal interactions NL1, which includes the nonlocality in the ${}^1{S}_0$ channel only, and NL2, where the nonlocality is included both in the ${}^1{S}_0$ and in the ${}^{3}S-D_1$ channels. The upper panel shows results at the two-hole-line level, whereas in the lower panel three hole-line contributions are included.