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The method
Let us take a closer look at q
scat
:
Ed d Er
E Ers
Er scat
q
→
=
ˆ )ˆ, ,( )ˆ ˆ,
,(
04
)ˆ, ,(
The probability of a photon scattering from Ω’ to Ω (for a given energy)
depends only on cosθ [-1,1], where θ is the scattering angle
and
the number of photons scattered in a given direction (for a given energy)
depends on the solid angle element around the direction: sinθdθdφ
or
the area on the unit sphere defined by the solid angle around the direction
Hence, I can expand q
scat
in an infinite series of spherical harmonics.