Rosette orbit

A <1) an elliptic type orbit, cf. the classical case. The latter condition corresponds to a rosette orbit comprising an ellipse with a perihelion motion matching maximum... 

The degeneracy is partly removed by taking into account the relativistic variability of mass, or dependence of the mass of the electron on its velocity. In this case the orbit, according to Som-merfeld, is given by a processing ellipse (rosette) its major axis revolves in the plane of the ellipse round... 

Fig. 7.—Orbit (rosette) of the electron about the nucleus, taking into account the relativistic variability of mass the motion is doubly periodic, the perihelion being displaced by the angle A(f> per revolution.

Since the motion consists of a libration of r, combined with a uniform rotation of the perihelion, the form of the orbit is that of a rosette (cf. fig. 12). 

The form of the orbit is, as in every multiply-pcriodic central motion, a rosette. Its equation is easily found. In order to derive it we again introduce the co-ordinates r, ifs in the orbital plane. By (12), 21, we obtain then for the differential equation of the orbit ... 

Our model, in which the electron under consideration moves in a central field, gives rosettes for the electron paths, and these are determined by two quantum numbers n and k. Orbits with different values of n must in fact occur in the interior of the atom. The behaviour of the Rydberg corrections shows that, for almost all elements, the p-orbiljp penetrate in order that this may be possible the core must at least contain orbits with n=2. Of the orbits in the core those with n— k=l) are nearest to the nucleus, then... 

---