  We have measured the temperature dependence of the microwave surface
impedance Zs = Rs + i\Omega\mu_0 \Lamda of two c-axis oriented MgB2 films at a
frequency \Omega /(2\pi) of 17.9 GHz employing a dielectric (sapphire)
resonator technique. The temperature dependence of the magnetic field
penetration depth \Lamda can be well fitted from 5 K close to Tc by the
standard BCS integral expression assuming the reduced energy gap Delta(0)/kTc
to be as low as 1.13 and 1.03 for the two samples. For the penetration depth at
zero temperatures, values of 110 nm and 115 nm were determined from the fit.
Our results clearly indicates the s-wave character of the order parameter. The
temperature dependence of the surface resistance Rs below Tc/2 is consistent
with the low value of the energy gap. The surface resistance below 8 K was
found to be below the resolution limit of 100 microOhm of our measurement
technique.
