Ultrasonic Attenuation of Transverse Waves in V, Nb, and Ta forql<1

Abstract

The temperature dependence of the ultrasonic attenuation coefficient of transverse waves with a wave vector parallel to $〈110〉$ was measured in superconducting V, Nb, and Ta. The product of the wave vector times the mean free path $\mathrm{ql}$ was smaller than one during these measurements. The sharp drop in the attenuation coefficient below the transition temperature, which is found when $\mathrm{ql}>\mathrm{}1\mathrm{}$, was not present. The zero-temperature energy gap was found to be $3.6\pm 0.2 k{T}_c$ for V, $3.5\pm 0.3k{T}_c$ for Nb, and $3.5\pm 0.2k{T}_c$ for Ta.