In this paper we give a complete and hopefully straightforward analysis of the n = 2 Zeeman structure which is intrinsically accurate to 1 ppm for determining the Lamb shift from present experiments. This analysis takes into account the current experimental and theoretical knowledge of the atomic Hamiltonian. It is shown that the magnetic part of this Hamiltonian can be taken as that of a free electron and a free nucleus. Radiative corrections to this assumption are shown to be negligible. The total Hamiltonian can then be diagonalized in the 1 F, j, 1, mF> representation. Matrix representations of the Hamiltonian are given for all n = 2 states of hydrogen and deuterium. We give theoretical predictions for the Q = 1 hyperfine intervals in hydrogen and deuterium which are accurate to 10 ppm. Values of the Lamb shift calculated from the recent Zeeman level crossings of Robiscoe and Cosens are tabulated.

Today nobody really worries about the spectra of Alkaliatoms. Modern methods of solving many electron problems allow calculations of the spectrum and of any other properties to any desired accuracy. Still, there is a desire in many minds for a simple and clear insight in what are the essential reasons for the phenomena. In the case of the alkalis the question is to formulate in a simple way the essential reason for the difference between the spectrum of the alkali-atoms and the hydrogen atom.The usual answer to this question refers to the so called penetrating orbits, -the German term is much more romantic, Tauchbahnen, -One says, that the valence electron finds itself in an n S orbit, -the lowest, which the Pauli-principle admits, n being 2, 3, 4, etc., for lithium sodium, potassium, etc. -but, the energy is depressed compared to the corresponding hydrogen values -Ry/n 2 on account of the fact that the orbit dives into the internal region of the core, where the effective strength of the Coulomb field is much stronger. This picture has its weak points. The valence electron is mostly outside the core, first because of the large size of the orbit, and second because of the fact that inside the core it has very large kinetic energies. As long as the valence electron is outside, the core acts like a charge of unity. There is no reason for the electron to avoid orbits with low values of n, excluded by the Pauli principle. This point has been considered, of course, in the more accurate variational calculations. The additional nodes, which the Pauli-principle imposes upon the wave function of the valence electron, are all inside the core so that the wave-function outside resembles closely to a one electron problem which is not inhibited by an exclusion principle. In fact, if one forgets about this principle and ascribes main quantum numbers n to the levels, by starting with n= 1 for S-states, n=2 for P-states, etc. in the same way for all Alkalis, the quantum defects c5 are all smaller and mostly negative. We define fi by the expression E~=-Ry/(n-~5) 2. This is seen in Table 1. A negative value of 6 indicates that the core has a repulsive effect and not an attractive one.

No abstract