Polarized light scattering from large quantum systems with zero initial and final angular momentum

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Abstract
We consider the scattering of light from a molecule or a cluster. The scattering may be elastic or inelastic, but we limit ourselves to the special case of transitions from initial states having total angular momentum number J=0 to final states also having J=0. In practice, this covers elastic scattering from clusters as the rotational temperature drops toward absolute zero. This hypothesis allows us to do the orientation average at the amplitude level, a method fundamentally incorrect in the general case. Without approximation, we are able to deduce the pattern of the observable Mueller matrix M of the scattering. We find a new symmetry that reflects the spherical nature of the J=0 states: M11+M33=M22+M44. This result includes all multipole orders of the scattered light, and is therefore valid for clusters large compared to wavelength, as well as for small clusters. In an Appendix, we discuss a new generating function for orientation averages, which allows one to make exact tensor averages weighted by two plane waves (for scattering, one incoming and one outgoing).