TPDSci Scattering vector and phase delay

Scattering vector and phase delay for a dilute dispersion

Fig. 1. Scattering vector and phase delay for a dilute dispersion of "point" scattering centers in a medium with a refractive index, m'. The assumption of the dispersion being dilute allows one to neglect complications due to multiple scattering. Consider scattering of a plane wave with the wavelength λ₀ in vacuum, incident horizontally from the left, by two arbitrarily selected scattering centers P and P '. Unit vectors u_i and u_s represent the directions of the incident and scattered waves respectively. The vector diagram on the right illustrates the relationship, k_s = k_i + q, between the wave vector, k_i, of the incident wave, that of the scattered wave, k_s, and the scattering vector q. Angle θ is the scattering angle. We consider elastic scattering, hence | k_s | = | k_i |.
The phase delay, Δφ, between the waves scattered by centers P and P' is a product kΔr of the magnitude, k, of the wave vector, k_i, i.e. 2πm' / λ₀, and the geometrical path difference Δr = dr₁ + dr₂ between paths APB and A'P'B'. In vector notation, Δr = -r • u_s + r • u_i = -r • ( u_s - u_i ). Since, k = ku, it follows that Δφ = -r • q.

CITATION:
Jonasz M. 2006. Scattering vector significance (www.tpdsci.com/Tpc/ScaVctSgnf.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 30-Jan-2008
Modified: 18-Feb-2008
Peer-reviewed: PENDING

Topics in Particle and Dispersion Science