Paramagnetic Effect in Superconductors. I. Theoretical Aspects

A theory for the paramagnetic effect is developed under the assumption that the ratio of the effective length to the effective diameter l/a of the superconducting particles in the transition region is constant. While experiment shows that the relative apparent permeability ̃ \~Kₘ is a function of γ=φ₀(1-IgI), where φ₀=H_φ0Hz0, H_φ0 is the circular and Hz0 the longitudinal component of the field at the surface, Ig is a limiting current, and I the total current through the sample, this theory gives the permeability as a function of φ₀ only. Good agreement with the experimental range of ̃ \~Kₘ, however, is obtained when the theoretical value of φ₀ is replaced by γ. The experiments of the author et al. on solid and hollow mercury cylinders and recent experiments of Thompson and Squire on a solid tin cylinder are discussed. A reason why the theoretical value of φ₀ has to be replaced by γ cannot be given at this time, although it is indicated where the present theory has to be amended.