Motional Stark effect

To observe a 7s — 9 transition requires that there be a 9p admixture in the 9 state. For odd this admixture is provided by the diamagnetic interaction alone, which couples states of and 2, as described in Chapter 9. For even states the diamagnetic coupling spreads the 9p state to all the odd 9( states and the motional Stark effect mixes states of even and odd (. Due to the random velocities of the He atoms, the motional Stark effect and the Doppler effect also broaden the transitions. Together these two effects produce asymmetric lines for the transitions to the odd 9t states, and double peaked lines for the transitions to even 9( states. The difference between the lineshapes of transitions to the even and odd 9i states comes from the fact that the motional Stark shift enters the transitions to the odd 9( states once, in the frequency shift. However, it enters the transitions to the even 9( states twice, once in the frequency shift and once in the transition matrix element. Although peculiar, the line shapes of the observed transitions can be analyzed well enough to determine the energies of the 9( states of >2 quite accurately.25... 

So the aim of our current experiment is to measure precisely the motional Stark effect and then deduce the velocity distribution. This measure has been made in two steps. 

Although the resonance Is shifted by Zeeman- and motional Stark-effects due to a residual magnetic field of about 75 G in the transition region, the results are promising and lead to the expectation of improved precision in future excited state experiments. 

In the -mixing region, Li has the peculiarity that the p electrons have a rather low quantum defect (pp 0.053). Care is needed to exclude nonhydrogenic effects. In particular, they can intrude in the presence of electric fields because the pe are not all hydrogenic. In an important experiment [569], the -mixed manifold was observed with no motional Stark effect, and the result is shown in fig. 10.13. 

V(t ) occurs at lower energy for larger values of Z2. As t] —> the Stark effect dominates both potentials, so that the motion is always bounded. 

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... 

The first term of (3.289) represents a translational Stark effect. A molecule with a permanent dipole moment experiences a moving magnetic field as an electric field and hence shows an interaction the term could equally well be interpreted as a Zeeman effect. The second term represents the nuclear rotation and vibration Zeeman interactions we shall deal with this more fully below. The fourth term gives the interaction of the field with the orbital motion of the electrons and its small polarisation correction. The other terms are probably not important but are retained to preserve the gauge invariance of the Hamiltonian. For an ionic species (q 0) we have the additional translational term... 

As a consequence of the collective motion of the neutral system across the homogeneous magnetic field, a motional Stark term with a constant electric field arises. This Stark term inherently couples the center of mass and internal degrees of freedom and hence any change of the internal dynamics leaves its fingerprints on the dynamics of the center of mass. In particular the transition from regularity to chaos in the classical dynamics of the internal motion is accompanied in the center of mass motion by a transition from bounded oscillations to an unbounded diffusional motion. Since these observations are based on classical dynamics, it is a priori not clear whether the observed classical diffusion will survive quantization. From both the theoretical as well as experimental point of view a challenging question is therefore whether quantum interference effects will lead to a suppression of the diffusional motion, i.e. to quantum localization, or not. 

The purpose of the present communication is to resolve this contradiction. From the analogy with Kramers work on the Stark effect, it seemed probable that the discrepancy was due to the omission on Jones part of considering the relativity terms in the motion of the electron. For this reason the problem was studied in its completeness, taking into account the effect produced by the relativistic chauge of mass, as well as the effect due to the presence of the electric field. 

Fig. 10.9. The Ba spectrum in a high magnetic field with the motional Stark field compensated. The data are obtained in atomic beam experiments, and the relative intensities do not suffer from opacity or saturation effects. Both circular polarisations are separated experimentally, and are found to have the same structure (shown by presenting them as though reflected in the axis) when displaced in energy by the linear Zeeman splitting.

The next example of the action of an external field which we shall consider is that of the Stark effect for the hydrogen atom, i.e. the influence of a homogeneous electric field E on the motion in the hydrogen atom (more generally in an atom with only one electron). We shall treat this problem in considerable detail, in order to illustrate the various methods employed for its solution. 

For E =0 the motion of the Stark effect passes over into the simple Kepler motion. This is separable in polar co-ordinates as well as in parabolic co-ordinates. From the separation in polar co-ordinates ( 22) we obtain the action variables Jr, Je, J0, and the quantum condition... 

The parabolic co-ordinates used in the separation method to determine the motion of an electron in the hydrogen atom under the influence of an electric field are a special case of elliptic co-ordinates. The latter are the appropriate separation variables for the more general problem of the motion of a particle attracted to two fixed centres of force by forces obeying Coulomb s law. If one centre of force be displaced to an infinite distance, with an appropriate simultaneous increase in the intensity of its field, we get the case of the Stark effect at the same time the elliptic eo-ordinates become parabolic. 

The Stark Eppect por the Hydrogen Atom 36. The Intensities of Lines in the Stark Effect op Hydrogen. 37. The Seculab Motions of the Hydrogen Atom in an Electric... 

In this way Dexter showed how the quadratic (normal) Stark effect can produce an exponential edge at hcj < Eg if the field distribution is Gaussian. Dexter considers the ionic motion to be the source of the fields. The field intensity is proportional to the relative ion displacement q. Their distribution in thermal equilibrium is Gaussian. is determined by Eq. (4.13). It follows that F y T. By comparison of Eq. (4.20) with... 

The Stark effect An electric field only affects the relative motion of an exciton and has no affect on the centre-of-mass motion. Thus, the total potential experienced by the electron-hole pair, Viot r), is... 

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