Debye-Waller factor of sodium: A comparison of theory and experiment

We have compared the Debye-Waller factor of sodium calculated by three different theoretical methods with the recent measured values in the temperature range 80–295 K, using the Mo¨ssbauer γ-ray-scattering technique. The Mo¨ssbauer results are also compared with the two sets of earlier x-ray measurements, one of which extends to 365 K. The three theoretical methods are the following: the lowest-order anharmonic perturbation theory, a Green’s-function method that includes anharmonic contributions of the lowest-order perturbation theory summed to infinity, and the molecular-dynamics method, which includes the anharmonic contributions to all orders. In all three methods the Ashcroft pseudopotential with the Vashishta-Singwi screening function is employed to generate the real-space two-body potential function whose range is cut off at the sixth-neighbor distance. Excellent agreement is found between the results of these three methods and the Mo¨ssbauer experimental results. The x-ray results are also in very good agreement with the Mo¨ssbauer data where the temperatures overlap in the measurements.