Self-Consistent Green’s Function Calculation of the Nucleon Mean Free Path

The extension of Green’s functions techniques to the complex energy plane provides access to fully dressed quasiparticle properties from a microscopic perspective. Using self-consistent ladder self-energies, we find both spectra and lifetimes of such quasiparticles in nuclear matter. With a consistent choice of the group velocity, the nucleon mean-free path can be computed. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 fm.

Figure 1

Imaginary part of the propagator in the complex energy plane, $z=E+i\Gamma$, at zero momentum for a CD-Bonn self-energy at $\rho =0.16{\mathrm{fm}}^{-3}$ and $T=5\mathrm{MeV}$. The left plot corresponds to the usual propagator, $\mathcal{G}(k,z)$, while the right plot represents its analytic continuation, $\tilde{\mathcal{G}}(k,z)$. Solid lines show the imaginary part of the propagator just above and below the real axis, $\pm \mathcal{A}(k,\omega )/2$.

Figure 2

Upper panels: spectral function at $\rho =0.16{\mathrm{fm}}^{-3}$ and $T=0\mathrm{MeV}$ for the CD-Bonn interaction. Lower panels: absolute value of $\tilde{G}$ in the same conditions. The fully dressed pole is indicated by a cross, while the circle (square) show the position of the first (second) renormalization quasiparticle.

Figure 3

Quasiparticle properties at $\rho =0.16{\mathrm{fm}}^{-3}$ and $T=5\mathrm{MeV}$ for different approximations and two $N\mathrm{\text{−}}N$ potentials: CD-Bonn (left) and Av18 (right panels). Upper panels correspond to the qp spectrum, central panels to inverse qp lifetimes, and lower panels to effective masses. The different approximations are explained in the text.

Figure 4

Mean-free path of a nucleon in nuclear matter as a function of energy. Upper panel: results obtained with a $\mathrm{CD}\mathrm{\text{−}}\mathrm{Bonn}+3\mathrm{BF}$ self-energy at $T=0\mathrm{MeV}$. The different approximations are commented on the text. Lower panel: results obtained mean-free path from the fully dressed pole for different $N\mathrm{\text{−}}N$ forces and two different temperatures. The shaded band and solid dots correspond to the experimental results of Refs. 1, 26, respectively.