Zeeman quadratic shift

The quadratic shift of the Zeeman components has been calculated for silicon and germanium by a perturbation method [117]8, [139] and by a full calculation [108], The physical interpretation of this second-order effect in terms of the ratio 7 of the transverse and longitudinal effective masses of the donor electron is far from simple. 

We have calculated exactly the Zeeman effect for the levels IS, 3S and 3P. Indeed it is necessary to know the shift for all the hyperfine levels very well. These calculations are very classical and we just present the results in a Zeeman diagram (see Fig. 5). The most important part in the diagram is the crossing between the 38 2 (F=l, mp=-l) and 3P1/2(F=1, mj =0) levels, because the quadratic Stark effect is proportional to the square of the induced electric field and inversely proportional to the difference of energy between the two considered levels. Moreover the selection rules for the quadratic Stark effect in our case (E perpendicular to B) impose Am.F= l. So it is near this crossing that the motional Stark shift is large enough to be measured. In our calculations the Stark effect is introduced by the formalism of the density matrix [4] where the width of the levels are taken into account. The result of the calculation presented on... 

In the Zeeman experiments, two effects can be distinguished the linear one, which produces a splitting of the zero-field lines, and the quadratic Zeeman effect, producing a shift of the Zeeman components. 

The magnetic field and the direction cosines enter quadratically in ( quadratic Zeeman effect contribution ). As a consequence this term will be negligible at low fields, but may play the dominant role at very high fields. The quadratic dependence on the direction cosines leads to a quadratic dependence on the quantum number M and causes a shift of the Af-doublets with respect to each other. Thus, at higher fields the initial sjnnmetry of the Zeeman multi-plets is destroyed. 

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