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phys documents (dragged) 62

# phys documents (dragged) 62 - 56 Physics Formulary by ir...

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56 Physics Formulary by ir. J.C.A. Wevers 11.3.2 The Coulomb interaction For the Coulomb interaction holds: 2 b 0 = q 1 q 2 / 2 πε 0 mv 2 0 , so W ( r ) = 2 b 0 /r . This gives b = b 0 cot( 1 2 χ ) and I ( Ω = b sin( χ ) b ∂χ = b 2 0 4 sin 2 ( 1 2 χ ) Because the influence of a particle vanishes at r = λ D holds: σ = π ( λ 2 D - b 2 0 ) . Because dp = d ( mv ) = mv 0 (1 - cos χ ) a cross section related to momentum transfer σ m is given by: σ m = (1 - cos χ ) I ( Ω ) d Ω = 4 π b 2 0 ln 1 sin( 1 2 χ min ) = 4 π b 2 0 ln λ D b 0 := 4 π b 2 0 ln( Λ C ) ln( v 4 ) v 4 where ln( Λ C ) is the Coulomb-logarithm . For this quantity holds: Λ C = λ D /b 0 = 9 n ( λ D ) . 11.3.3 The induced dipole interaction The induced dipole interaction, with p = α E , gives a potential V and an energy W in a dipole field given by: V ( r ) = p · e r 4 πε 0 r 2 , W ( r ) = - | e | p 8 πε 0 r 2 = - α e 2 2(4 πε 0 ) 2 r 4 with b a = 4 2 e 2 α (4 πε 0 ) 2 1 2 mv 2 0 holds: χ = π - 2 b r a dr r 2 1 - b 2 r 2 + b 4 a 4 r 4 If b b a the charge would hit the atom. Repulsing nuclear forces prevent this to happen. If the scattering angle is a lot times 2
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