Analytic Solution for the Critical State in Superconducting Elliptic Films

A thin superconductor platelet with elliptic shape in a perpendicular magnetic field is considered. Using a method originally applied to circular disks, we obtain an approximate analytic solution for the two-dimensional critical state of this ellipse. In the limits of the circular disk and the long strip this solution is exact, i.e. the current density is constant in the region penetrated by flux. For ellipses with arbitrary axis ratio the obtained current density is constant to typically 0.001, and the magnetic moment deviates by less than 0.001 from the exact value. This analytic solution is thus very accurate. In increasing applied magnetic field, the penetrating flux fronts are approximately concentric ellipses whose axis ratio b/a < 1 decreases and shrinks to zero when the flux front reaches the center, the long axis staying finite in the fully penetrated state. Analytic expressions for these axes, the sheet current, the magnetic moment, and the perpendicular magnetic field are presented and discussed. This solution applies also to superconductors with anisotropic critical current if the anisotropy has a particular, rather realistic form.Comment: Revtex file and 13 postscript figures, gives 10 pages of text with figures built i

Coherent Description for Hitherto Unexplained Radioactivities by Super- and Hyperdeformed Isomeric States

Recently long-lived high spin super- and hyperdeformed isomeric states with unusual radioactive decay properties have been discovered. Based on these newly observed modes of radioactive decay, consistent interpretations are suggested for previously unexplained phenomena seen in nature. These are the Po halos, the low-energy enhanced 4.5 MeV alpha-particle group proposed to be due to an isotope of a superheavy element with Z = 108, and the giant halos.Comment: 8 pages, 2 figures, 1 table, to be published in Int. J. Mod. Phys.

Super- and Hyperdeformed Isomeric States and Long-Lived Superheavy Elements

The recent discoveries of the long-lived high spin super- and hyperdeformed isomeric states and their unusual radioactive decay properties are described. Based on their existence a consistent interpretation is given to the production of the long-lived superheavy element with Z = 112, via secondary reactions in CERN W targets, and to the low energy and very enhanced alpha-particle groups seen in various actinide fractions separated from the same W target. In addition, consistent interpretations are suggested for previously unexplained phenomena seen in nature. These are the Po halos, the low-energy enhanced 4.5 MeV alpha-particle group proposed to be due to an isotope of a superheavy element with Z = 108, and the giant halos.Comment: 4 pages. Contribution to the 2nd Int. Conf. on the Chemistry and Physics of the Transactinide Elements (TAN 03) Napa California, November 200

Theory of Type-II Superconductors with Finite London Penetration Depth

Previous continuum theory of type-II superconductors of various shapes with and without vortex pinning in an applied magnetic field and with transport current, is generalized to account for a finite London penetration depth lambda. This extension is particularly important at low inductions B, where the transition to the Meissner state is now described correctly, and for films with thickness comparable to or smaller than lambda. The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow naturally from an equation of motion for the current density in which the integral kernel now accounts for finite lambda. New geometries considered here are thick and thin strips with applied current, and `washers', i.e. thin film squares with a slot and central hole as used for SQUIDs.Comment: 14 pages, including 15 high-resolution figure