The Bardeen, Cooper, and Schrieffer theory of superconductivity has shown remarkably good agreement with most experiments considering that a single isotropic energy gap has been used. 1 However, there are disagreements, particularly with respect to specific heats, as was emphasized by Boorse in a recent Letter. 2 A likely explanation of such discrepancies is that the energy gap in most superconductors is appreciably anisotropic. 3 Thus the specific heat variation with T would be determined near the transition temperature (T c ) by some average value of the gap, while at low temperatures the smaller values would dominate.In order to demonstrate whether or not the energy gap depends upon the electron's position on the Fermi surface, an experiment must select electrons from a fairly limited region of the surface. Such is the case with the ultrasonic attenuation. If the electronic mean free path (I) is large compared to the wavelength (X), then a sound wave having vector q scatters electrons from state k to k', where k' =k±q. In addition, a phonon is absorbed or emitted; i.e., E(k') =E(k)±#a>, where w is the angular frequency of the sound wave. These conditions of momentum and energy conservation are satisfied only by a particular group (or groups) of electrons on the energy surface. Since Hw is small, then AE =(Ak)« (V^E), or flu) =q-(V^E), where V^ is the gradient operator in k space. Since the electronic group velocity is % -h~l s7 k&> the required electrons are those for which v 0 cos6 =v s , where v s is the velocity of sound and 6 is the angle between q and v 0 . Thus the scattered electrons are ones which drift in the direction of the wave with the speed of sound and so remain in a constant phase of the wave. For a spherical energy surface these electrons lie on a ring perpendicular to the direction of the sound propagation, and since v 0 »v s , this ring of electrons is nearly an equatorial one. 4 As has been shown previously, 5 the temperature dependence of the longitudinal wave attenuation in superconductors is determined in the Bardeen-Cooper-Schrieffer theory by the energygap temperature variation. By this theory the ratio of the superconducting attenuation coefficient (a s ) to that in the normal state (a n , 2L constant) is given by (1) a /a =2(e e/kT + l)-x , s n where 2e is the temperature-dependent energy gap. Thus measurements of & s / a n as a function of T for waves in various directions in a single crystal, by selecting different groups of electrons, should show up any significant anisotropy of €. We have made measurements of longitudinal wave attenuation at frequencies up to 80 Mc/sec in oriented single crystals of tin at temperatures down to 1.00°K. From these observations it appears that 2e 0 , the energy gap as T-*0, varies at least between 3.2kT c and 4t.ZkT c . The samples were oriented such that propagation was along [001], [100], and [110]. Figure 1 shows the measurements along two of these directions and displays the extreme behaviors. Observations T •i.o 0^%/a^n. hO.8 ho.6 \~0A -0.2 q...
