A thermal neutron inelastic scattering kernel for polyethylene (PE) of any degree of crystallinity based on a recently proposed dynamic model is suggested. The dynamic model takes proper account of the anisotropic linear chain structure of PE that gives rise to an acoustic phonon frequency distribution function, which is quite different from the usual Debye type, and that has been successful in explaining the observed temperature variation of the specific heat of PE of different degrees of crystallinity. The expressions for zero-phonon and one-phonon neutron scattering cross sections are derived by making use of the frequency distribution function. The kernel incorporates the contribution of two-phonon acoustic modes and also that of optical modes. The kernel has been used to calculate the total scattering cross sections of thermal neutrons from crystalline and noncrystalline PE, including amorphous PE. The calculated values of total scattering cross sections are in reasonable agreement with the experimental results of 60 and 98% crystalline PE. The calculated values for amorphous PE are not very different from those for crystalline PE. Thus the total scattering cross sections are found to be independent of the degree of crystallinity in agreement with the experimental results. The details of the contribution of various scattering processes to the total scattering cross section for crystalline and amorphous PE are reported. The kernel has also been used to study the γij-neutron condensed system energy exchange observable for both crystalline and amorphous PE and has been compared with the equivalent isotropic Debye kernel. The γij values are found to be almost independent of the degree of PE crystallinity. Also, the γij values, as determined using the suggested scattering kernel, are quite different from those calculated using the Debye kernel, showing thereby the importance of the linear chain structure of three-dimensional PE crystal.