Energy scale, magnetic field

As follows from the above treatment for higher values of the scaled energy e which includes both the energy and magnetic field strength the behaviour of the system becomes more chaotic, while for the smaller values regular behaviour is observed. 

Fig. 3. Splitting of atomic energy levels in a scaled magnetic field. The value A = 1 corresponds to the self consistent atomic XC-field. At this value, the exchange splitting of the Ni 3d states ( 0.6 eV) is much larger than the spin-orbit splitting of these states (fti 0.2 eV). Thus, the 3d states in nickel have almost pure spin character (see also Fig. 9 below). On the contrary, the 4p states show a much smaller exchange splitting and thus remain almost pure K-states.

In Figs. l(a)-l(c) the Lyapunov functions are shown for Z = 50, m = 1 and different scaled energies. Fig. 1(a) shows results for v = 0, p = 0, e = 10. Al( ) tends to zero indicating that this trajectory is regular. This figure has the same shape as that for the nonrelativistic hydrogen atom in a uniform magnetic field (Schweizer et.al., 1988). In Fig. 1(b) the Lyapunov function for v = 0, p = 0, e = 50 is shown. It tends to some positive value, which means that this trajectory is chaotic. While for v = 0, p = 0, e = 100 (Fig. 1(c)) we find that the trajectory is unstable. 

The goal of the calculation is, therefore, to compute the strength of the induced magnetic field in space, relative to the strength of the external one. Because one of the main assumptions is that all fields are small on the typical energy scale of atoms or molecules, this calculation can be performed in the framework of perturbation theory. 

Fig. 21. Faraday rotation for a 2- m thick film of Ga Mn.rAs with x = 0.043 measured as a function of the photon energy in a magnetic field of 6 T at 10 and 300 K (a) and as a function of the magnetic field at 10 K, 1.55 eV and at 300 K, 1.49 eV (b). Solid lines show the magnetization determined from magnetotransport measurements at the given temperatures (scaled to match the open symbols) (Kuroiwa et al. 1998).

While the success of scaled energy spectroscopy suggests that the behavior of atoms does become classically chaotic near the ionization limit, higher resolution reveals a surprisingly orderly structure. Iu et alhave studied the odd parity Li m = 0 states in a beam travelling in the direction of the magnetic field. They... 

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