Linear Attenuation Coef.

Define Compton

f[E_] := 0.597 * (10^-24)* Exp[-0.0028 (E - 30)];

Plot[f[E], {E, 10, 200}, {PlotRange -> All}]

E is in keV

NA  =  6.02 * 10^23;

μcompton[E_, ρ_, Z_,  A_] :=  ρ NA (Z/A) f[E];

ρ is density
Z is atomic number
A is atomic mass

Define photoelectric

μphoto[E_,  ρ_,  Z_,  A_] :=        ρ NA (Z/A) 9.8 * 10^-24 (Z^3.8 /E^3.2);

Example water

\(Zwater\  = \ 7.54; 
Awater\  = \ 16; \)

\(p1 =
       Plot[μcompton[E, 1, 7.54, 16], {E, 10, 200}, \ 

         										{PlotRange -> {0, 3}, 
											
           PlotStyle -> {{Thickness[0.01], RGBColor[1, 0, 0]}}}]\)

\(p2 =
       Plot[μphoto[E, 1, 7.54, \ 16], \ {E, \ 10, 200}, \ 

         											{PlotRange\  -> \ {0, 3}, \ 

           												
           PlotStyle -> {{Thickness[0.01], \ RGBColor[0, 0, 1]}}}]\)

\(p3 =
       Plot[μphoto[E, 1, 7.54, \ 16] + μcompton[E, 1, 7.54, 16],
         \ {E, \ 10, 200}, \ 

         											{PlotRange\  -> \ {0, 3}, \ 

           												
           PlotStyle -> {{Thickness[0.01], \ RGBColor[0, 1, 0]}}}]\)

Show[p1, p2, p3]

Show[p1, p2, p3,  {PlotRange -> {0, 0.5}}]

Example Hexane

\(Zhexane = 5.51; 
Ahexane\  = \ 11; 
ρhexane\  = \ 0.66; \)

\(p4 =
       Plot[μcompton[E, ρhexane, Zhexane, \ Ahexane], {E, 10, 200},          
										{PlotRange -> {0, 3}, 
											
           PlotStyle -> {{Thickness[0.01], RGBColor[0, 1, 0]}}}]\)

\(p5 =
       Plot[μphoto[E, ρhexane, Zhexane, \ Ahexane], {E, 10, 200}, \ 

         										{PlotRange -> {0, 3}, 
											
           PlotStyle -> {{Thickness[0.01], RGBColor[1, 0, 0]}}}]\)

Show[p4, p5, {PlotRange -> {0, 0.5}}]

Example Calcium Carbonate

\(Zcalc = 14.2; 
Acalc = 21.4; 
ρcalc = 2.93; \)

\(p6 =
       Plot[μcompton[E, ρcalc, Zcalc, \ Acalc], {E, 10, 200}, \ 

         										{PlotRange -> {0, 3}, 
											
           PlotStyle -> {{Thickness[0.01], RGBColor[0, 0, 1]}}}]\)

\(p7 =
       Plot[μphoto[E, ρcalc, Zcalc, \ Acalc], {E, 10, 200}, \ 

         										{PlotRange -> {0, 3}, 
											
           PlotStyle -> {{Thickness[0.01], RGBColor[0, 1, 0]}}}]\)

Show[p6, p7]

Comparison (Compton)

Show[p1, p4, p6,  {PlotRange -> {0, 1}}]

blue - calcium carbonate
red - water
green - hexane

Comparison (photoelectric)

Show[p2,  p5,  p7]

Show[p2,  p5,  p7,  {PlotRange -> {0, 1}}]

green - calcium carbonate
blue - water
red - hexane