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 ($T_c=9.2\mathrm{}°$K). For transverse phonons propagating along the [110] direction changes in linewidth are observed when the superconducting gap $2\Delta \mathrm{}\left(T\right)\mathrm{}$ 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 $T_c$. Below $T_c$ there is an additional softening of 3%. This softening extends along the $\left[\zeta 00\right]$ direction to $\zeta =0.5\mathrm{}$, the limit of our measurements.