Complex wave vectors in the energy gap find an expression for the imaginary part of the wave vector in the energy gap at the boundary of the first Brillouin zone, in the approximation that led to Eq. (46). Give the result for the Im (k) at the center of the energy gap. The result for small Im (k) is (h2/2m)[Im(k)]2 ≈ 2mU2/h2G2.