Potential of a wire bent into a circular shape Application to Saturn’s Rings

In this article, we develop the calculation of the potential generated by a homogeneous wire bent into a circular shape [1]. In a second time we develop a new method of perturbation. It gives an expression of the potential in terms of R, the radius of the circle. The potential is expressed as a sum of the Newtonian and a small term. The former will be considered as a perturbation. We give the orbits of a test particle in accordance with the initial conditions. Precession of perihelia or chaotic cases is proved [2]. In an accurate way, we must use a juxtaposition of such circular wires, in order to built a two dimensional disc.In this article, we develop the calculation of the potential generated by a homogeneous wire bent into a circular shape [1]. In a second time we develop a new method of perturbation. It gives an expression of the potential in terms of R, the radius of the circle. The potential is expressed as a sum of the Newtonian and a small term. The former will be considered as a perturbation. We give the orbits of a test particle in accordance with the initial conditions. Precession of perihelia or chaotic cases is proved [2]. In an accurate way, we must use a juxtaposition of such circular wires, in order to built a two dimensional disc

Anharmonic double-phonon excitations in the interacting boson model

Double-$\gamma$ vibrations in deformed nuclei are analyzed in the context of the interacting boson model. A simple extension of the original version of the model towards higher-order interactions is required to explain the observed anharmonicities of nuclear vibrations. The influence of three- and four-body interactions on the moments of inertia of ground- and $\gamma$-bands, and on the relative position of single-$\gamma$ and double-$\gamma$ bands is studied in detail. As an example of a realistic calculation, spectra and transitions of the highly $\gamma$-anharmonic nuclei $^{164}$Dy, $^{166}$Er, and $^{168}$Er are interpreted in this approach.Comment: 38 pages, TeX (ReVTeX). 15 ps figures. Submitted to Phys. Rev.