Effects of pressure on the superconducting properties of magnesium diboride

We discuss the effects of hydrostatic pressure on the superconducting properties of MgB${}_2$ within the framework of Eliashberg theory. By considering the pressure dependences of all parameters appearing in the McMillan formula, we show that the calculated pressure derivative of $T_c$ as well as the variation of $T_c$ with pressure are in good agreement with recent measurements. The pressure dependences of the energy gap ${\mathrm{\Delta }}_0$, the effective interaction strength $N(E_F)v$, the critical magnetic field $H_c(0)$, and the electronic specific heat coefficient $\gamma$ are also predicted for this system. A comparison of pressure effect in non-transition elements clearly suggests that MgB${}_2$ is an electron-phonon mediated superconductor.