Measurements of the electron-phonon interaction in Nb by inelastic neutron scattering

Precise linewidth and frequency measurements of transverse acoustic modes propagating along the [001] and [110] directions were performed on single crystals of niobium in the normal and superconducting phases (Tc=9.2^∘K). For transverse phonons propagating along the [110] direction changes in linewidth are observed when the superconducting gap 2Δ(T) equals the phonon frequency. This behavior agrees with Bobetic's calculation for the attenuation of high-frequency sound waves in superconductors and the magnitude of the change enables us to calculate the electron-phonon interactions. In addition to linewidth changes, anomalous temperature dependence of the peak position of some acoustic modes is also observed. The [001] transverse phonons exhibit a decrease of {~} 15% when T is decreased from 300^∘{}K to Tc. Below Tc there is an additional softening of 3%. This softening extends along the [ζ00] direction to ζ=0.5, the limit of our measurements.