Abstract
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 $\Delta_{0}$, 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.
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