Quenching of Weak Interactions in Nucleon Matter

Abstract

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 fm${}^{-3}$ 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 to 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 quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which 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 $\ge$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.

submitted to PRC

References in corpus (6)

• Measurement of the rate of nu_e + d --> p + p + e^- interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory
• Realistic models of pion-exchange three-nucleon interactions
• Spin susceptibility of neutron matter at zero temperature
• Measurements of Charged Current Reactions of ${\nu }_e$ on ${}^{12}C$
• Neutrino Propagation in Dense Astrophysical Systems
• Weak Transitions in A=6 and 7 Nuclei

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• Neutral current interactions of low-energy neutrinos in dense neutron matter
• Perturbation Theory of Nuclear Matter with a Microscopic Effective Interaction
• Weak response of neutron matter at low momentum transfer
• Linear Response Theory with finite-range interactions
• Modeling Neutron Star Matter in the Age of Multimessenger Astrophysics
• Ab initio calculations on nuclear matter properties including the effects of three-nucleons interaction
• Relativistic Corrections to the CBF Effective Nuclear Hamiltonian
• Inadequacy of Scaling Arguments for Neutrino Cross Sections
• The hard-sphere model of strongly interacting fermion systems