Constraining the in-medium nucleon-nucleon cross section from the width of nuclear giant dipole resonance

We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of ${}^{208}\mathrm{P}\mathrm{b}$ shows a strong dependence on the in-medium nucleon-nucleon cross section ${\sigma }_{\mathrm{N}\mathrm{N}}^{\ast }$. A very large medium reduction of ${\sigma }_{\mathrm{N}\mathrm{N}}^{\ast }$ is needed to reproduce the measured value of the GDR width of ${}^{208}\mathrm{P}\mathrm{b}$ at the Research Center for Nuclear Physics in Osaka, Japan.