Paramagnetic Effect in Superconductors. II. Further Theoretical Aspects

An investigation was made to determine how the theory of the paramagnetic effect which was developed in part I, joins the two limiting cases of ${\varphi }_0\to 0$ and ${\varphi }_0\to \infty$, where ${\varphi }_0=\frac{H_{\varphi 0}}{H_{z0\mathrm{}}}$. While the theory joins smoothly to what one would expect for ${\varphi }_0\to 0$ (external magnetic field only) it does not join so smoothly in the limit ${\varphi }_0\to \infty$ (current only). This, however, shows that London's theory is an ideal limit which cannot be practically realized, so that the current density at $r=0\mathrm{}$ will in practice always remain finite. A discussion of Scott's experiments on the current transition of thin wires gives valuable information as to where the present theory has to be amended in order to obtain the—so far empirical—correction factor $1-\frac{I_g}{I}$. This discussion supports on the whole the ideas which were given in this connection in part I. A calculation of the apparent relative permeability ${\tilde{K}}_m$ at points other than the peak provides good agreement with experiment for higher currents, but a large discrepancy for the lowest current. This calculation tests whether the assumption of an intermediate core surrounded by a normal conducting cylinder is correct rather than the theory itself.