In a scattering experiment, an aluminium foil of thickness L = 10E-6 m is placed in a beam of intensity of 6E12 particles per second. The differential scattering crosss section is known to be of the form.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d\sigma}{d\Omega} = A + Bcos^2 (\theta) [/tex]

where [tex]\theta [/tex] is the scattering angle and [tex]\Omega [/tex] the solid angle.

With a detector area of 0.1x0.1 m^2, placed at a distance of 5m from the foil, it is found that the mean counting rate is 40 Hz when [itex]\theta [/itex] is 30 degrees and 31.5Hz when [itex]\theta [/itex] is 60 degrees. Find the values of A and B.

Clearly I had to set up two simulataneous equations using the different [itex]\theta [/itex] values.

I've found the number of targets which is just

[tex] \frac{N_{A}L\rho}{A}[/tex]

where A is the mass number (27 for Aluminium).

I looked on wiki and the differential cross section is

[tex]\frac{d\sigma}{d\Omega} = \frac{scattered flux / unit of solid angle

}{initial flux / unit of surface}[/tex] but I don't really understand how to relate this to the information I have (I guess the incident flux is just the number of targets x multiplied by the beam intensity per unit area)

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# Homework Help: Hard nuclear physics cross section problem

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