Screening of nuclear pairing in nuclear and neutron matter

The screening potential in the ${}^1{S}_0$ and ${}^3{S}_1$ pairing channels in neutron and nuclear matter in different approximations is discussed. It is found that the vertex corrections to the potential are much stronger in nuclear matter than in neutron matter.

Figure 1

Pairing interaction with screening in the RPA approximation. The dashed lines represent the Gogny interaction, the wiggly line the p-h residual interaction resummed to all orders. All vertices are to be understood as antisymmetrized (not shown explicitly).

Figure 2

Splitting of the ${}^1{S}_0$ pairing screening potential ${\mathcal{V}}_{k_F{k}^{\text{'}}}(\omega )$ in nuclear matter. Left (right) panel is for the neutron (proton) p-h one-bubble insertion. The Fermi momentum is fixed to 1.0 fm${}^{-1}$.

Figure 3

Diagonal part of the sum of the neutron and proton bubble insertions for ${}^1{S}_0$ channel in nuclear matter with $k_F$ ranging from 0.6 to 1.4 fm${}^{-1}$.

Figure 4

Nuclear matter screening potential ${\mathcal{V}}_{k_F{k}^{\text{'}}}(\omega )$ in the ${}^3{S}_1$ channel in the one-bubble approximation. The Fermi momentum $k_F$ is fixed to 1.0 fm${}^{-1}$.

Figure 5

Landau parameters from the Gogny force D1. Left panel is for nuclear matter and the right one for neutron matter.

Figure 6

The same as in Fig. 5 but in the induced interaction approximation. Only the values at the Fermi surface are depicted.

Figure 7

Energy ($\hslash \omega$) and momentum-transfer (q) dependence of the induced Landau parameters [see Appendix 5, Eq. (E2)]. The upper two panels are for neutron matter and the lower four for nuclear matter. The Fermi momentum $k_F$ is fixed to 1.0 fm${}^{-1}$.

Figure 8

Diagonal matrix elements ($k=k^{\text{'}}=k_F$) of the interaction at $\hslash \omega =0$: Born term with Gogny force (solid lines), Born term with one bubble insertion (dashed lines), and full pairing potential including one and higher bubble insertion (IIA) (dash-dotted line). The baryon density corresponds to $k_F=1.0$ fm${}^{-1}$. The Born term with the Gogny force (solid line) in the ${}^1{S}_0$ channel is density independent, whereas it is density dependent in the ${}^3{S}_1$ channel.