Effective Interaction Strength in Superconductors

A semiempirical extension of the BCS model to intermediate- and strong-coupling superconductors is used to derive a set of simple rules by which the following thermodynamic quantities can be related to one another: the absolute-zero energy gap $2{\Delta }_0$; the critical field $H_0$; the critical temperature $T_c$; the jump $\Delta \mathrm{C}$ in specific heat at $T_c$; and the slope at $T_c$ of the critical-field curve, ${\left(\frac{\mathrm{dh}}{\mathrm{dt}}\right)}_1$. The procedure determines an "effective interaction strength" $N_0{V}^{*}$ (larger than the value of $N_{0}V$ obtained from $\frac{T_c}{{\Theta }_D}$) for each superconductor. A "temperature-variation" of this $N_0{V}^{*}$ is the major departure from the original BCS model. $N_0{V}^{*}$ is obtained for 9 superconductors from their specific-heat jumps, and used to predict values of the ratios ${\left(\frac{\mathrm{dh}}{\mathrm{dt}}\right)}_1$, $\frac{{\Delta }_0}{k{T}_c}$, and $\frac{\gamma {T_c}^2}{V_m{H_0}^2}$ which agree well with experiment. The resulting values for the "effective cutoff" ${\Theta }_c$ lie close to $\frac{{\Theta }_D}{9}$.