Characterization of Rayleigh Scattering.

Rayleigh scattering can be characterized in terms of the difference between the Rayleigh Amplitude A(E,θ ) and the modified form factor amplitude A^mff(q)=-r_o(ξ_i \cdot ξ_f )g(q), where g(q)= modified form factor, q=momentum transfer, ξ =polarization vectors. This difference is the sum of the real g^' and the imaginary g^' ' anomalous scattering factors for θ =0 while it is described in terms of four anamolous scattering factors at finite angles. Taking the difference between the screened and Coulombic forms of this quantity with the bound state normalization constants factored out (ie (A(E,θ ) -A^mff(q))_s - (N_s/N_c)^2(A(E,θ )-A^mff(q))_c )no more than three multipoles of this difference are required to characterize forward angle Rayleigh scattering at all energies and for any subshell. The highest multipole requirement occurs in the 0.1E_b to 10E_b (E_b=binding energy) range. This is because at high energy A(E,0 ) approaches A^mff(0) in all multipoles and the difference between screened and Coulombic terms gets small. This is consistent with the results of our characterization of photoionization [1] and is due to the fact that g^' ' is proportional to the photoeffect cross section according to the optical theorem while g^' is a function of g^' ' through a dispersion relation. 1. R. H. Pratt and L. LaJohn, Nuc. Instr. Meth. Phys. Res. 99, 136 (1995); also manuscript in preparation.