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We present a new method for neutrino-matter coupling in multi-dimensionalradiation-hydrodynamic simulations of core-collapse supernova (CCSN) with thefull Boltzmann neutrino transport. The development is motivated by the factthat the accurate conservation of momentum is required for reliable numericalmodelings of CCSN dynamics including a recoil of proto-neutron star (PNS). Thenew method is built on a hybrid approach, in which we use the energy-momentumtensor of neutrinos to compute the momentum feedback from neutrino to matter inthe optically thick region while we employ the collision term in the opticallythin region. In this method we utilize a general relativistic description ofradiation-hydrodynamics with angular moments, which allows us to evaluate themomentum feedback from neutrino to matter without inconsistency with ourBoltzmann solver. We demonstrate that the new method substantially improves theaccuracy of linear momentum conservation in our CCSN simulations underreasonable angular resolutions in momentum space, alleviating the difficulty ingiving the diffusion limit precisely with the discrete ordinate (Sn) method. Itis the first-ever demonstration that the PNS kick can be handled directly andproperly in multi-dimensional radiation-hydrodynamic simulations with the fullBoltzmann neutrino transport.

Three-Dimensional Boltzmann-Hydro Code for core-collapse in massive stars III. A New method for momentum feedback from neutrino to matter