Search

A new set of periodic orbits is found in the irregular region for the hydrogen atom in a magnetic field. The quantisation of these orbits is discussed and new level spacings near the zero-field threshold are predicted.

In the irregular region for the hydrogen atom in a uniform magnetic field a set of periodic orbits are found to bifurcate from the same periodic orbit along the field at various values of the energy. These values are determined numerically by studying the stability of this particular orbit. A repeated pattern of stability and instability of these orbits exists over decreasing intervals of energy until the escape energy is reached. All these orbits are unstable beyond the ionisation limit.

There have been many new developments in the analysis of the quadratic Zeeman effect, both in theory and experiment since the last meeting (Nayfeh and Clark.1New high resolution experiments on hydrogen have revealed a dense series of sharp lines near and above the ionization threshold by Holle et al.,2 and Main et al.3 showing that the lower resolution quasi-Landau modulations of Garton and Tomkins4 are full of structure. A Fourier transform of the absorbtion spectrum also revealed new modulations. Theoretically the large basis set calcultions for hydrogen by Clark and Taylor5 harve been taken higher in energy towards threshold by Wintgen and Freidrich,6 Delande and Gay,7 and Wunner et al.8 There has followed a parallel development in the semi-classical treatment of the problem by Al-Laithy et al.,9 and Wintgen and Freidrich.10 The quadratic Zeeman effect for atoms has proved to be a physically realizable quantum system whose classical Hamiltonian exhibits chaotic motion. The consequences of this will be discussed in detail in Section 3, but initially in Section 2 we will describe a new approach which extends the basis set methods to non-hydrogenic systems O’Mahony and Taylor.11