Quenching of weak interactions in nucleon matter

We have calculated the one-body Fermi and Gamow-Teller charge-current and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16, and $0.24{\mathrm{fm}}^{\ensuremath{-}3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne-v18 and Urbana-IX two- and three-nucleon interactions. The squares of the charge- current matrix elements are found to be quenched by 20\char21{}25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin-up proton quasiparticle to be a bare spin-up/down proton/neutron. Within the interval considered, the charge-current matrix elements do not have significant dependence on the matter density, proton fraction, and magnitudes of nucleon momenta; however, they do depend on momentum transfer. The neutral-current matrix elements have a significant dependence on the proton fraction. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions that give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However terms greater than or equal to three-body terms are necessary to reproduce the compressibility. Realistic calculations of weak interaction rates in nucleon matter can presumably be carried out using the effective operators and interactions studied here. All presented results use the simple two-body cluster approximation to calculate the correlated basis matrix elements. This allows for a clear discussion of the physical effects in the effective operators and interactions.