Coherent and Incoherent Scattering of X-rays by H2and He

An electron density map calculated by Rollett from an accurate function of James and Coolidge has been used to obtain the coherent x-ray scattering from molecular hydrogen. The results given by the Coulson self-consistent field function are also presented, and it is shown that there is excellent agreement with the James-Coolidge results and with earlier calculations of Carter, March and Vincent. In addition a more careful study of the incoherent scattering has been made than has previously been attempted. By considering two correlated wave functions, that of Eckart and Hylleraas for helium and that of Gurnee and Magee for hydrogen, previous approximations are shown to lead to somewhat high estimates of the total scattered intensity. For hydrogen, a maximum reduction of about 4% brings theoretical results to within 1% of the experimental values of Wollan. The momentum distribution and the corresponding shapes of the Compton lines have also been considered for hydrogen and helium. It is suggested from the results obtained for molecular hydrogen that more accurate measurements of the Compton profile might afford a useful method of studying bonding electrons.