Ultrasonic Investigation of the Isolated-Vortex State nearHc1in Vanadium

Ultrasonic attenuation in the mixed state of vanadium has been investigated near $H_{c1\mathrm{}}$, where the vortex density is low. The expected rise toward the normal-state value of attenuation at $H_{c2\mathrm{}}$ is preceded by an initial absorption decrease as the vortices penetrate. The unexpected dip is interpreted in terms of a reduction in the quasiparticle mean free path, a result of the scattering of quasiparticles by vortices. The scattering width of a vortex was found to be (2.4±0.4)×${10}^{-6\mathrm{}}$ cm for temperatures near $T_c$, in good agreement with the theoretical determination 2.1×${10}^{-6\mathrm{}}$ cm. The apparent width decreases at lower temperatures. Similar measurements have been made in niobium. The scattering width is found to be considerably greater in vanadium, and its temperature dependence is in the opposite direction. A further feature of the present results observed even at rather low fields was the faster-than-linear dependence of the reciprocal attenuation on the internal field.