Magnetic substate scattering

The target part of the entrance-channel state Ovoko) is a coherent superposition of magnetic substates defined by an arbitrary choice of coordinate frame. It is transferred into another fully-coherent superposition of states in the exit channel ivjkj). The scattering amplitude is defined as a generalisation of (4.46), so that its absolute square is the corresponding... 

The scattering amplitude may be considered as a matrix in the space of magnetic substates of the target and projectile the scattering matrix. The excitation process is coherent since the collision time is much shorter than any characteristic time associated with the excited state. 

The least ambiguous and most appropriate description of the atom after the collision is in terms of the density matrix (Blum, 1981), whose elements are bilinear combinations of scattering amplitudes for different magnetic substates. For the sake of simplicity we restrict ourselves to the most common case, in which the target is initially in an S state and the excitation involves the transfer of one electron from an s orbital to a p orbital in the independent-particle approximation. In atoms with one active electron the transition is — P. If there are two active electrons it is — P. We use the LS-coupling scheme. 

If the photons and scattered electrons are detected independently of each other, the incident-electron-beam direction is an axis of symmetry, and the excited ensemble must also have this axial symmetry. Then all the off-diagonal terms of p are zero (Blum, 1981). Coherently-excited magnetic substates can only be produced by excitation processes, such as (8.2), which are not axially symmetric. The determination of these off-diagonal elements of p has been the main goal of electron—photon coincidence experiments. 

Fig. 8.6. The magnetic substate parameters A, R and I (8.17) for 54.4 eV electron scattering to the 2p state of hydrogen. Squares, Weigold, Frost and Nygaard (1979) and Hood, Weigold and Dixon (1979) circles, Williams (1981,1986). The theoretical curves are as for fig. 8.3.

Sodium has another advantage as a test for scattering and structure calculations. A very wide range of experimental data is available. This includes spin-dependent measurements of scattering and magnetic substate data, which will be described in chapter 9. In this section we consider only differential, integrated and total cross sections. 

The investigation of sodium as a critical test of the theoretical treatment of scattering is given a new dimension by the spin-dependent measurements of Kelley et al. (1992) in elastic and superelastic scattering experiments with polarised electrons on the polarised 3s and laser-excited 3p states. Not only have asymmetries been measured for these states, but spin-dependent observations of the magnetic substate parameter L have been made for the 3p state. 

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