THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

458 16. Ultrasonicsinitial of their surnames) that predicts a temperature-dependent energy gap 2ε widearound the Fermi level at the critical temperatures of T c and less (Bardeen et al.,1957). As the temperature is reduced, the gap increases toward a maximum at zeroabsolute temperature, where the predicted value of ε is equal to 1.75 × κ T c , whereκ is the Boltzmann constant. In the realm of l e >λ/2π, the B.C.S. theory predictsthatα s 2=α n e ε/κT + 1where l e denotes the mean-free path of an electron, α s and α n represent the valuesof absorption in the super-conducting and normal state, respectively, at absolutetemperature T . This variation was confirmed experimentally by Morse (1959) andBohm for indium at 28.5 MHz. Gibbons and Benton measured the velocities oflongitudinal waves in both normal and superconducting tin; they found a verysmall reduction in velocity (about 1/500,000th) for the superconducting state.Application of a magnetic field to a metal at low temperatures affects the meanfreepath and thus affects acoustic attenuation. For l e