Evidence for Two Superconducting Gaps in $MgB_2$

We have measured the Raman spectra of polycrystalline {\mgb} from 25 {\cm} to 1200 {\cm}. When the temperature was decreased below $T_c$, we observed a superconductivity-induced redistribution in the electronic Raman continuum. The low frequency region of the spectrum is completely depleted indicating the absence of nodes in the gap function. Furthermore, two pair-breaking peaks appear in the spectra suggesting the presence of two different superconducting gaps. We have analyzed the measured spectra using a quasi two-dimensional model in which two isotropic s-wave superconducting gaps open on two sheets of Fermi surface. For the gap values we have obtained $\Delta_1 = 22 cm^{-1}$ (2.7 meV) and $\Delta_2 = 50 cm^{-1}$ (6.2 meV). Finally, we conclude that a conventional phonon-mediated pairing mechanism occurring in the planar boron $\sigma$ bands is responsible for the superconductivity of {\mgb}.