Pressure Dependence of the Specific Heat of a Superconductor Derived from Critical-Magnetic-Field Data

The low-temperature variation of the critical magnetic field of a superconductor is related to the normal-state electronic specific-heat coefficient $\gamma$. Measurements of the critical magnetic field at zero and finite pressure are used to obtain a value for the volume $\Omega$ dependence of $\gamma$. We show that strong-coupling corrections must be included in such an analysis. For example, in Pb, ignoring such corrections leads to an error of almost a factor of 2 in $\frac{d\ln \gamma }{d\ln \Omega }$.