Energy dependent total thermal neutron scattering cross-section and transport of a neutron pulse in Fullerite at 300 K

摘要

Crystalline fullerene-fullerite- is a molecular crystal and therefore possesses a number of dynamical modes: librational, orientational diffusive, tunneling and optical, in addition to the usual anisotropic translational modes. Making use of these dynamical modes a thermal neutron scattering kernel for fullerite has been developed. The total scattering cross-sections of thermal neutrons have been computed in the energy range 10~(-4) - 0.3 eV. For inelastic scattering while one phonon and two phonon processes are sufficient, for libron exchanges as many as thirteen libron quanta exchanges have to be considered. Using the thermal neutron scattering kernel the multigroup Boltzmann transport equation has been diagonalized, to obtain the eigenvalues and the corresponding eigenfunctions of a neutron pulse propagating in the medium. The variation of lowest eigenvalue with the size of the assembly is compared with the corresponding measured values in graphite and it turns out to be slower in smaller assemblies of fullerite. The time dependent thermalization of the neutron pulse, introduced in the assembly at time t=0, has also been computed. While in large assemblies (B~2=0.0006 cm~(-2)) the high energy neutron pulse gets thermalised in about 1500 μs, it takes as long as 5000 μs in smaller assemblies (B~2=0.005 cm~(-2)).