

Paper: 
The KramersHeisenberg Coherency Matrix 
Volume: 
526, Solar Polarization Workshop 8 
Page: 
49 
Authors: 
Stenflo, J. O. 
Abstract: 
Scattering of light is governed by the KramersHeisenberg formula,
which is an expression for the scattering probability amplitude. While it
provides a well established foundation for scattering theory, its
application to the derivation of observable quantities in
the case of multilevel atomic systems is not
straightforward. One has to sum over all the possible bilinear
products of the scattering amplitudes for all the combinations of
sublevels in the ground state and the excited state and then do
ensemble averaging to construct the
coherency matrix that directly relates to observable quantities like
the Stokes parameters. Previous applications of density
matrix theory to radiative scattering have from the outset
excluded valid interference effects by doing ensemble averaging of
the atomic system before the scattering processes and thereby
(in the absence of optical pumping) prohibited the possibility of
any phase relations between the
initial atomic states. However, the concept of partial
polarization or of an unpolarized state always refers to ensembles
of individual quantum entities (like
photons or atoms). The ensemble is unpolarized if its entities are
uncorrelated, although each entity is always fully polarized
(i.e., contains definite phase relations). The
averaging must be done over the ensemble of Mueller matrices from
the individual scattering processes. The definite (but random)
phase relations between the initial ground states give nonzero
contributions to the ensemble average when a phase closure
condition with the final substates of the scattering process is
satisfied. We show how the resulting, previously overlooked
interference terms, can be
included in a physically consistent way for any quantum system, and
how these new effects provide an explanation
of the decadelong D_{1} enigma from laboratory scattering at
potassium gas, at the same time as explaining how a symmetric
polarization peak can exist in the solar line of sodium D_{1}. 



