Electron Compton scattering from methane and methane-d4

Quasi-elastic electron scattering at high-momentum transfer was measured for CH₄ and CD₄ in the gas phase. At high-momentum transfer, two scattering peaks are observed in each molecule. We interpret the splitting as due to independent Compton scattering from each nucleus, such that, at an impact energy of 2 keV and 100° scattering angle, the peaks for the C and H in CH₄ are split by 2.1 eV while those associated with the C and D in CD₄ are split by 1.1 eV. These splittings are in agreement with those predicted from Rutherford scattering of electrons from single atoms. The widths of the C, H, and D peaks are very different, and reflect the distribution of their momentum. The lineshapes of the H(D) peaks are in agreement with the momentum space vibrational wavefunction. Detailed peak area analysis reveals anomalously low intensities for the hydrogen and deuterium peaks relative to the carbon peak-the theoretical Rutherford C-H ratio is 9.0, compared with 9.8(2) (C-H) and 9.7(2) (C-D) measured in our experiments. Two possible explanations for this discrepancy, one due to deviations of the actual cross section from the Rutherford values, the other due to short lived quantum entanglement, are discussed. The Rutherford scattering interpretation is compared to that for vibrational Compton-like scattering predicted by Bonham and de Souza [R.A. Bonham, G.G.B. de Souza, J. Chem. Phys., 79 (1983) 134].