Theory of the Effect of Temperature on the Electron Diffraction Patterns of Diatomic Molecules

The effect of temperature on the electron diffraction pattern of a diatomic molecule is considered from the standpoint of the simple kinematic scattering theory utilizing a quartic vibrational potential. The potential is obtained by an expansion of ${\hslash }^2{\text{J(J+1)/2μr}}^2\mathrm{+D}\exp {\text{[−2a(r−r}}_e\text{)]−2D}\exp {\mathrm{[-a(r-r}}_e\mathrm{)]}$ about its minimum value r₀. The second‐order wavefunction for the nth vibrational and Jth rotational state of the system has been obtained, and expressions for the electron diffraction quantities r_g, l_e², and M (s) have been computed. General results for the quantity M (s) utilizing the approximate eigenfunctions of the complete Morse potential and incorporating an approximate treatment of the effect of centrifugal stretching are also presented. Explicit expressions for M (s) for the first three vibrational states as derived by this treatment are given. Appropriate sums over all the vibrational and rotational states have been carried out to obtain the temperature dependence for the above quantities. Estimates of the effect of temperature on the parameters r_g and l_e² at 300° and 1500°K for representative diatomic molecules are given.