Scattering Note - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

86

Pages:

2
Author:

Jabin F.

Scattering Peye-4M Prob. (iv) Soln f(θ,φ) = a + ib sinθ dσ/dΩ = |f(θ,φ)|² = a² + b²sin²θ σ = ∫∫(dσ/dΩ) sinθdθdφ 0 2π = ∫∫(a² + b²sin²θ) sinθdθdφ 0 2π = 2π ∫(a²sinθ + b²sin³θ) dθ 0 π = 2π [(-a²cosθ) + b²(sinθ - (1/3)sin³θ)] 0 π :: sin^3θ = 3sinθ - 4sin^3θ ==> 4sin^3θ = 3sinθ - sin^3θ ==> sin^3θ = (3/4)sinθ - (1/4)sin^3θ σ = 2π ∫(a²sinθ + b²(3/4)sinθ - (1/4)sin^3θ) dθ 0 π = 2π [(-a²cosθ) + b²(3/4)(-cosθ) + (1/4)(cosθ - (1/3)cos^3θ)] 0 π = 2π [(2a² + b²(3/2 + 1/12))π] = 2π [(2a² + b²(19/6))π] σT = 2π(2a² + b² 8/6) σT = 4π(a² + b² 4/6) σT = 4π(a² + 2b²/3) Arg. Ques. 14 page-99 2 = |R - r| V(r) = C/r^2 f(θ) = (-2mc/ħ^2q) * ∫(sin(qr)/(2r)) dr let 2qr = y 2q dr = dy dr = dy/2 = (-2mc/ħ^2q) * ∫(siny/y) dy = (2mc/ħ^2q) * π/2 dσ/dΩ = |f(θ)|^2 α 1/q^2 (option-a)

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