Doppler broadening solutions

To illustrate how the preceding formalism is generally used, we apply it to the solution of a well-known problem. Let. us derive an analytic expression for the Doppler broadening in the dipole approximation. The Hamiltonian which describes the interaction between radiation of polarization, e, and matter in the dipole approximation was discussed in the first section of this review article. 

In 1974, O.E. Mogensen and V.P. Shantarovich concluded from ACAR measurements on aqueous solutions of sodium chloride [15] that in this system a fourth positron state (in addition to p-Ps, free positrons and o-Ps) was formed, which they identified as an e+Cl bound state. The existence of such a bound state found support in several Doppler broadening and ACAR investigations on aqueous and non-aqueous solutions of halides and pseudohalides [16-20]. Since the commonly used expression bound state of positrons may lead to confusion with positrons bound in Ps, we refer to this fourth state as positron molecules and characterize it by the subscript M. 

The linewidth of annihilation from the free-positron state is Doppler-broadening measurements. In lifetime measurements the PsF component hides beneath the o-Ps component which has a similar lifetime. This is a case where the two-dimensional data analysis shows its great advantage As the Doppler broadening of each positron state is determined in its own time regime even positron states with similar features may be seperated from each other. Moreover, a tentative fitting procedure with only the three positron states as in pure water did not come to a satisfactory result with the AMOC histogram of the NaF solution. 

Solute content PA coincidence Coincidence Doppler broadening... 

The first age-momentum correlation (AMOC) measmements were performed more than 20 years ago (McKenzie and McKee 1976 Kishimoto et al. 1982a, b). Those measurements applied Na sources and measured, in fact, the energy dependence of lifetime spectra. The electronics of those days resulted in a much worse resolution of these age-momentum correlation spectrometers than that of individual lifetime and Doppler-broadening spectrometers. In spite of the bad resolution, these measmements provided valuable information about, for example, the structure of certain solutions (Kishimoto et al. 1982b). 

The DLS technique involves measurement of the Doppler broadening of the Rayleigh-scattered light as a result of Brownian motion (translational diffusion) of the particles. This thermal motion causes time fluctuations in the scattering intensity and a broadening of the Rayleigh line. The Rayleigh line has a Lorentzian line shape. In macromolecular solutions, concentration... 

Dynamic light scattering (DLS), also called photon correlation spectroscopy (PCS) or laser light scattering (LLS) is a technique based on the principle that moving objects cause a frequency shift due to the Doppler effect. If a solution of macromolecules with random Brownian motion is illuminated with monochromatic laser light, the scattered light should contain a distribution of frequencies about the incident frequency the spectral line is virtually broadened. The width of the distribution is related to the MMD. 

In a QELS experiment, a monochromatic beam of light from a laser is focused on to a dilute suspension of particles and the scattering intensity is measured at some angle 0 by a detector. The phase and the polarization of the scattered light depend on the position and orientation of each scatterer. Because molecules or particles in solution are in constant Brownian motion, scattered light will result that is spectrally broadened by the Doppler effect. The key parameter determined by QELS is the diffusion coefficient, D, or particle di sivity which can be related to particle diameter, d, via the Stokes-Einstein equation ... 

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