Polarised electrons

An ensemble of electrons is said to be polarised if there is a preferential orientation of the electron spins. If there are N- electrons with spins parallel to a particular direction or axis of quantisation and N[ with spins antiparallel to that direction, then the component of the electron polarisation vector P = (Px,Py,Pz) in that direction is defined by 

The performance characteristics of various sources of polarised electrons have been reviewed extensively (e.g. Kessler, 1985). These sources depend either on the spin dependence of the interaction in the process in which the free electrons are produced, or on the pre-polarisation of one element 

The most widely-used source is the photoemission GaAs source (Gar-win, Pierce and Siegmann, 1974 Pierce et al, 1980), the principle of which is shown in fig. 2.11. The spin—orbit interaction splits the P-valence band at the r point (fe = 0 in the plot of one-electron energy E vs momentum k) into fourfold degenerate P3/2 and twofold degenerate Pl/2 bands with a separation of 0.34 eV. 

The operation of a GaAs source is shown schematically in fig 2.12. Right-hand (or left-hand) circularly-polarised light is incident on a negative-affinity GaAs crystal. The negative affinity is achieved by coating the 

In the rest frame of the electron there appears a magnetic induction 

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An electron donating substituent such as phenyl and methoxy will polarise electron density on the radical-anion of an alkene in favour of more positive charge density on the carbon atom bearing this substituent with more free electron density on the other carbon atom. This promotes dimer formation by linkage through atoms with free electron density. Styrene is oxidised at a graphite anode in methanol... 

Bonner WA, Dort MAV, Yearian MR (1975) Asymmetric degradation of D,L-leucine with longitudinally polarised electrons. Nature 258 419 121... 

Hayashi S (1988) Asymmetry in elastic scattering of polarised electrons by optically active molecules. J Phys B 21 1037... 

In 1960 s, CIDEP was less popular than CIDNP because CIDEP did need much faster measuring techniques than CIDNP. This is due to much faster relaxation times (usually less than 1 /r s) of polarised electron spins than those (usually a few second for protons) of nuclear spins. In 1968, Smaller et al. [2] observed a population inversion for the cyclopentyl radical with a 2-MHz ESR apparatus coupled with a 15 MeV electron beam with pulse duration of 0.5 -4.0 /z s. The response time of the system corresponded to a time constant of 1.6/z s. In 1970, Atkins et al. [3] obtained the photo-CIDEP for the ketyl radical from benzophenone in paraffin solvents with a 2-MHz ESR apparatus coupled with a 20-ns laser flash. Under favorable chemical conditions, Wong and Wan [4] demonstrated that the photo-CIDEP for some semiquinone radicals in alcohol solvents could be observed with a commercial ESR spectrometer having a 100-kHz modulation unit and a custom-designed rotating sector giving light pulses. 

Fig. 2.12. Schematic of a GaAs source of transversely-polarised electrons using photemission from a negative electron affinity GaAs crystal.

Fig. 2.21. Schematic diagram of the apparatus used by Sohn and Hanne (1992) for (e,e y) coincidence measurements on Hg (6 So -> 6 Pi) using polarised electrons.

McClelland, Kelley and Celotta (1986) were the first to measure superelastic scattering in the configuration where the spins of both the incoming electron and target atom were polarised, ensuring that the transitions studied are transitions between well-characterised pure quantum states. In particular they studied the superelastic scattering of spin polarised electrons from the mp = 3 and mp = —3 states of Na 3 P3/2 atoms (or the m/ = +1 and m/ = — 1 states on making the conventional assumption... 

Fig. 2.22. Schematic of the polarised electron—polarised atom scattering apparatus of McClelland et al. (1986, 1989).

In conventional collision experiments the strong Coulomb interaction generally masks the much weaker relativistic spin-dependent interactions. The role of the spin-dependent interactions, such as the exchange and spin—orbit interactions, has also been clarified by sophisticated measurements with spin-polarised electrons and/or spin-polarised targets, sometimes employing spin analysis after the collision process (Kessler, 1985, 1991 Hanne, 1983). 

Such measurements were first applied with considerable success to elastic scattering. Indeed one was able to discuss experiments which would determine all the theoretically calculable amplitudes (Bederson, 1970). For inelastic processes, such measurements necessitate the simultaneous application of spin selection techniques and the alignment and orientation measurements discussed in the previous chapter. The experiments have become feasible with the advancement of experimental techniques. The first successful differential electron impact excitation study with spin-polarised electrons and alignment and orientation measurements was performed by Goeke et al. (1983) for the e—Hg case. McClelland, Kelley and Celotta (1985, 1986) carried out a systematic study for superelastic scattering of polarised electrons from polarised laser-excited Na (3 P) atoms. This system is essentially a two-electron collision system in which spin exchange is the dominant spin-dependent interaction. It thus allows one to obtain... 

A polarised electron beam is one with a preferred orientation of the electron spin direction. If there are electrons with spin components parallel to a given direction and with spins antiparallel to that direction then... 

The role of exchange scattering can be observed most clearly when polarised electrons are scattered from a target of polarised light atoms. If one observes a spin-flip process like... 

The existence of the fine-structure effect has been demonstrated for sodium (Hanne, Szmytkowski and van der Wiel, 1982 McClelland et ai, 1985 Nickich et al, 1990) using the time-reversed arrangement. A polarised electron beam is superelastically scattered from sodium atoms excited to 3 P /2 or 3 3/2 states by a single-frequency laser. McClelland et al. (1985) measured the spin asymmetry of polarised electrons that de-excite unpolarised atoms from the 3> P3/2 fine-structure state over the angular range —35° < 6 < 35°. As expected from reflection symmetry, the... 

Generalised formalism for the scattering of polarised electrons by unpolarised targets... 

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. 

Fig. 9.7. Schematic of the angular dependence of a charge-cloud distribution of an atomic state excited by polarised electrons. The tilt (e) out of the scattering plane must by parity conservation be zero if = 0.

It can be seen that electron—photon coincidence experiments with polarised electrons permit the investigation of spin effects in electron impact excitation of atoms at the most fundamental level. It can lead to direct information on both exchange effects and spin—orbit effects in the excitation mechanism. The information on the population of the magnetic sublevels can be visualised by charge-cloud distributions. These can tilt significantly out of the scattering plane for incident electrons transversely polarised in the scattering plane. 

It has been measured for hydrogen (Fletcher et al, 1985 Crowe et al, 1990) and for lithium, sodium and potassium (Baum et ai, 1985) at incident energies from threshold to several hundred electron volts. The data were obtained by ionisation of polarised target atoms by polarised electrons. The relative total ionisation cross sections for parallel and antiparallel spins were determined by counting the ions, regardless of the kinematics of the final-state electrons. 

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