Pairing properties of nucleonic matter employing dressed nucleons

A survey of pairing properties of nucleonic matter is presented that includes the off-shell propagation associated with short-range and tensor correlations. For this purpose, the gap equation has been solved in its most general form employing the complete energy and momentum dependence of the normal self-energy contributions. The latter correlations include the self-consistent calculation of the nucleon self-energy that is generated by the summation of ladder diagrams. This treatment preserves the conservation of particle number unlike approaches in which the self-energy is based on the Brueckner-Hartree-Fock approximation. A huge reduction in the strength as well as temperature and density range of ${}^3{S}_1\text{−}{}^3{D}_1$ pairing is obtained for nuclear matter as compared to the standard BCS treatment. Similar dramatic results pertain to ${}^1{S}_0$ pairing of neutrons in neutron matter.

Figure 1

(Color online) Imaginary part of the retarded self-energy for nucleons with momentum k = 225 MeV/c in symmetric nuclear matter at the empirical saturation density (ρ = 0.16 fm${}^{-3}$). Results for temperatures T larger than or equal to 4 MeV are directly determined by SCGF calculations, while the $T=0$ result originates from an extrapolation. All results were obtained using the CDBonn interaction.

Figure 2

(Color online) Imaginary (upper panel) and real part (lower panel, including the generalized HF contribution) of the retarded self-energy for nucleons with momentum $k=225$ MeV/c in symmetric nuclear matter at the empirical saturation density ($\rho =0.16$ fm${}^{-3}$). Results obtained for CDBonn interaction are compared to those resulting from SCGF calculations using ArV18. Also included are results for neutrons with the same momentum in neutron matter at $\rho =0.08$ fm${}^{-3}$. The temperature in all these calculations was fixed at $T=5$ MeV.

Figure 3

(Color online) Spectral function for nucleons in symmetric nuclear matter at the empirical saturation density. Results of SCGF calculations have been extrapolated to $T=0$. The CDBonn interaction has been used.

Figure 4

(Color online) Results for the gap functions $|{\Delta }_l(k)|$ for symmetric nuclear matter (ρ = 0.16 fm${}^{-3}$, upper panel) and pure neutron matter (ρ = 0.08 fm${}^{-3}$, lower panel) obtained from a solution of the BCS equation (23) using the CDBonn and ArV18 interactions at $T=0$. The dotted line identifies the Fermi momentum $k_F$.

Figure 5

(Color online) Quantity ${\tilde{\chi }}_k$ defined in Eq. (26), which represents the energy denominator for the propagator of two nucleons in the medium. Results are displayed for the quasiparticle (QP) approximation in the limit $T=0$, the QP approximation for finite temperature $T=5$ MeV, and the dressed propagator resulting from SCGF calculations (full prop., $T=5$ MeV). All results displayed in this figure were obtained for symmetric nuclear matter at density $\rho =0.16$ fm${}^{-3}$, using the CDBonn interaction.

Figure 6

(Color online) Effective renormalization constants for the sp strength located in the quasiparticle peak as derived from Eq. (28) are compared to the estimates of Eqs. (29) and (30). Further details as in Fig. 5.

Figure 7

(Color online) Gap parameter $\Delta (k_F)$ in symmetric nuclear matter as a function of temperature T. Results are presented for various densities, with and without taking into account the dressing of the sp propagator due to short-range correlations. The pairing gap disappears at $\rho =0.16$ fm${}^{-3}$ if dressed propagators are considered. All results displayed in this figure were obtained using the CDBonn interaction.

Figure 8

(Color online) Gap parameter $\Delta (k_F)$ in symmetric nuclear matter at $\rho =0.08$ fm${}^{-3}$ as a function of temperature T using the ArV18 and CDBonn interactions.

Figure 9

(Color online) Spectral function for nucleons with momentum $k=193$ MeV/c with (solid line) and without (dashed line) inclusion of pairing correlations. Results are presented for nuclear matter of ρ = 0.08 fm${}^{-3}$ at a temperature $T=0.5$ MeV.

Figure 10

(Color online) Gap parameter $\Delta (k_F)$ in neutron matter as a function of temperature T. Results are presented for the usual BCS approximation (dashed lines) and the solution of the generalized gap equation (20) in the ${}^1{S}_0$ partial wave using the CDBonn interaction.