Scattering cross section, Lecture notes of Physics

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Scattering Cross-section

M o h a m m a d Z a h e e r A n s a r i M. P h i l & P h. D ( A p p l i e d P h y s i c s )

Scattering Cross-section

Consider a uniform beam of mono-energetic particles containing n particles per unit volume moving with a velocity v, with respect to a stationary target. Let, F (= 𝐀𦰀) is the flux of the incident beam which can be estimated as 𝐀𦰀 = 𝐀𠐀𝐀𨠀𝐀𦠀 𝐀𧀀 𝐀𧐀𦠀𣠀𝐀𧰀𝐀𝐀𝐀 𦰀𝐀𝐀𠐀𝐀𝐀

×

𝐀𝐀𝐀𝐀𝐀𧐀𧰀𝐀𝐀𝐀𝐀𣠀 𝐀𧀀 𣠀ℎ𝐀 𝐀𧐀𦠀𣠀𝐀𧰀𝐀𝐀 𣠀𝐀𝐀𝐀 = 𝐀𠐀𝐀𨠀𝐀𦠀 𝐀𧀀 𝐀𧐀𦠀𣠀𝐀𧰀𝐀𝐀𝐀 𧐀𦠀𝐀𧐀×𣠀𝐀𝐀𝐀 = 𧀀𝐀𠐀𦐀 𝐀𝐀𦠀 𠐀𝐀𝐀𣠀 𣠀𝐀𝐀𝐀 The detector detects all the particles scattered through angle 𝐀, into the solid angle dΩ. Therefore, the number of particles d𝐀^ detected per unit time depends on the following factors: (a) Flux of incident beam (F) (b) Solid angle dΩ (c) Number of Scattering centers in the target (N)

Now from equation (2) and (3), we can calculate a

N

Fa

FN

N

N (^) Tot Tot incedent

scattered^ ^ 

Therefore,  (^) Tot = Total Scattering cross section  

N

a N

N

incedent scattered  Tot