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1. I need to be efficient
• It is inherently beneficial to work in spherical
coordinates to lift the kernel singularity since:
dV=dS dr=r2 dΩ dr = r2 sinθ dθ dφ dr j
  
V
dVjh i 1sc, S
jρ
iρ
1scD j i
  

r
sin2r
2r
) exp(
i 1sc, S
jρ
iρ

     dr dd
rb B
• Instead of evaluating ALL directions around a
scerma generating point, I can DISCRETIZE space
using a number M of solid angle elements, ΔΩM,
i
defined by (θ0,φ 0)M, and assume scerma does not
vary with θ within ΔΩ (i.e. on dS for a given r)
   dd b B ) e p( Siρ D
  


 
r b B
r
r
r
j i
dr ) 0 exp(
0 1sc,i S iρ
x
1sc,i
jρ
1sc
 
 
r jρ