Quantum Theory of Scattering
[1] Scattering :
- Scattering Is A Process In Which A Beam Of Particles Is
Allowed To Pass Close To A Scattering Material Called Target
And The Energis
And Angular Distribution Are Measured
- In The Process The Target May Remain In It's Orignal
State(Elastic Scattring) Or Brought To A Diffrent State (Inelastic
Scattering).
- Two Diffrent Opproches Are Possible For The Stady Of
Scattering Equation For The Scattring Wave By Obstacles And
Scattring Considered As A Transtion From An Intial State Of
Given Momentum To A Final
State Of Diffrent Momentum.
[2] Scattering Cross Section :
- Consider A Beam Of Partical Of Mass 'M' Travelling Along The Z
Axies With Velocity 'V' And Scatterd By A Scattering Potential
'V'
Centerd The Orgin.
- The Incident Partical In Genual Scatters In All Direction Due To
Interaction Inside A Sphar Of Radius 'ro' Was The Range Of The
Scattaring Potential Is Exparinced.
- After Leaving The Sphaer They Once Again Leavel In Straight
Liness. The Angle Between The Intial And Final Steaight Line
Path In
Called The Scattering Angle (θ)
- Let 'N' Br The Number Of Incident Particles Crossing Unit
Normal The Beam In Unit Time And 'N' Be The Of Particales
Scatterrd Into The Solid Angle'dΩ' In The Direction (θ,φ) In Unit
Time
- The Differential Scattering Cross Scetion (σ (θ,φ)) Is Defined
By
- The Total Cross Section 'σ' Is The Integral Of σ (θ,φ) Over The
Entire Solid Angle
- The Differential Cross Section σ (θ,φ) And The Total
Cros Section 'σ' Have the dimension of area thus callled cross
section.
- Fore A Spharically Symmetric Potential σ (θ,φ) Is Independent
Of φ And Thus
- Scattering Cross Section Is Usally Measured In Barns.
- 1 barn = 10^-24 cm^2
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