Polarisation vector

Frequencies m and polarisation vectors are determined by the diago-nalisation of the dynamical matrix... 

The spin is an inherent property of an electron. Since the photo- or Auger electrons are ejected in a certain direction in space, for an ensemble of these electrons a spin polarisation vector P can be defined which gives the excess of individual spin components measured in three orthogonal directions (see Section 9.2.1). In Fig. 1.5 the components of P are shown for a convenient decomposition into one longitudinal, Plong, and two transverse components, P,ranS and PtransX, respectively. The measurement of these components requires an electron detector which is sensitive to spin. An example of the spectrometry of photoelectrons with spin-analysis will be described in Section 5.4. 

The true molecular field F acting both on the segment and on molecules of solvent differs from the average field E because the scale of the dimensions of the segments is molecular. Each solvent molecule makes an isotropic contribution to the polarisability vector the contribution of each segment of the macromolecule is anisotropic and is expressed by the formula... 

The written set of equations has a simple solution for the components of the polarisation vector. We use them to write, in accordance to equation (10.1), the relative permittivity tensor... 

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 magnetic coil shown in figs. 2.15 and 2.16 was used to orient the electron polarisation vector P parallel to the axis of the analysing target—Mott detector system. The deflection system is part of the differential pumping stage which is necessary for the maintenance of the required ultra-high vacuum in the source chamber. 

Fig. 2.16. The behaviour of the polarisation vector in the experiment of Berger and Kessler (1986).

Fig. 8.1. Schematic representation of the collisionally-induced charge cloud in a P-state atom. The collision plane is determined by the ingoing and outgoing electron momenta ko and k,. The excited atom is characterised by the alignment angle y, its inherent angular momentum (Z, ) = L , and the shape of the charge cloud P/. The direction of emission of the photon and its polarisation vectors are also shown.

We now consider the radiative decay of the excited ensemble of atoms. The angular distribution and polarisation of the emitted photons can be conveniently described in terms of the Stokes parameters I, t]i, t]2, and (Born and Wolf, 1970). The emitted photons can be observed in the direction n making polar angles 6 and azimuthal angles with respect to the collision frame (fig. 8.1). It is convenient to choose the coordinate system in which the direction of observation n of the radiation is chosen as the z axis. The polarisation vector of the photons is restricted to the plane perpendicular to n by the two unit vectors i = (0 + 90°, 0) and 2 = (0,light emitted in the direction n and I y) the intensity transmitted by a linear polariser oriented at an angle y with respect to the i-axis, then the Stokes parameters are defined by... 

Fig. 21. Resonance Raman spectra of oxyhaemoglobin (bottom pair of curves) and ferrocyto-chrome c (top pair). The scattering geometry is shown schematically in the diagram at the top. Both the direction and the polarisation vector of the incident laser radiation are perpendicular to the scattering direction. The scattered radiation is analysed into components perpendicular (Ij ) and parallel (I ) to the incident polarisation vector. The exciting wavelength was 568.2 nm for oxyhaemoglobin and 514.5 nm for cytochrome c. The slit width was about 10 cm". The concentrations were about 0.5 mM for each. The anomalously polarised, polarised and depolarised bands, are indicated by ip, p, and dp respectively. [From Spiro and Strekas, Ref. (42) ...

This is an example of LO-TO splitting of the vibrational modes according to their direction of motion at the gamma point ( 2.6.1.3, 4.2.6). For any general direction the polarisation of the waves is not strictly longitudinal or transverse and the polarisation vectors are dependent on k as well as k. Similarly, the acoustic modes split into a longitudinal and two transverse modes. These modes vary in frequency along different directions in the unit cell [16]. 

New apparent surface charges will be produced at the surface of the spherical hole. The normal to any small surface element of the sphere makes an angle 6 with the polarisation vector, so that the apparent charge per unit area on this element is a cos 6 = P cos 6. The electric field produced at the centre of the sphere by all these surface elements can be shown by... 

Let the absorption and emission axes of a particular fluorescent molecule have direction cosines ft and ft, respectively with respect to O—t. V2. X3, where 1 = 1,2,3, and let the direction cosines of the polarisation vectors of the incident and observed scattered light be / and If, respectively. It follows from eqn. (1) that the observed intensity from an aggregate of molecules is then given by... 

It must be noted when considering the geometrical form of the specimen and the directions of the incident and fluorescent light beams that it is the direction of polarisation inside the specimen which is important. The use of certain geometries may necessitate corrections for refraction effects. It is also important for any type of system to correct for any sensitivity of the illuminating or detection systems to the polarisation vectors. 

In this work uniaxially oriented specimens of polyethylene terephthalate were studied, most of which were from the first series used in the work of Nobbs et al. described in Section 5.3.1. The Raman intensity measurements were made using a Coderg PHO spectrometer and a CRL 52A argon ion laser tuned to 488 nm. The tape samples were mounted parallel to the spectrometer slit. The partially focused laser beam was incident normally on them and the scattered light was collected in directions making approximately 180° with the incident light direction. The incident and scattered light polarisation vectors could be chosen parallel or... 

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