The neutrino mean free paths (NMFP) for scattering and absorption in cold symmetric nuclear matter (SNM) are calculated using two-body effective interactions and one-body effective weak operators obtained from realistic models of nuclear forces using correlated basis theory. The infinite system is modeled in a box with periodic boundary conditions and the one particle-hole $\left(p\text{−}h\right)$ response functions are calculated using the Tamm-Dancoff approximation (TDA). For the densities $\rho =\frac{1}{2}$, 1, $\frac{3}{2}{\rho }_0$, where ${\rho }_0$ is the equilibrium density of SNM, the strength of the response is shifted to higher energy transfers when compared to a noninteracting Fermi gas (FG). This and the weakness of effective operators compared to the bare operators, significantly reduces the cross sections, enhancing the NMFP by factors of $\sim 2.5–3.5$ at the densities considered. The NMFP at the equilibrium density ${\rho }_0$ are also calculated using the TDA and random phase approximation (RPA) using zero range Skyrme-like effective interactions with parameters chosen to reproduce the equation of state and spin-isospin susceptibilities of matter. Their results indicate that RPA corrections to correlated TDA may further increase the NMFP by $\sim 25\%$ to $3–4$ times those in a noninteracting FG. Finally, the sums and the energy weighted sums of the Fermi and Gamow-Teller responses obtained from the correlated ground state are compared with those of the 1 $p\text{−}h$ response functions to extract the sum and mean energies of multi $p\text{−}h$ contributions to the weak response. The relatively large mean energy of the multi $p\text{−}h$ excitations suggests that they may not contribute significantly to low energy NMFP.

• Received 23 April 2004

DOI:https://doi.org/10.1103/PhysRevC.70.035801