Part II Introduction to Reaction and Scattering Cross-Sections 1. - - PowerPoint PPT Presentation

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Part II Introduction to Reaction and Scattering Cross-Sections 1. - - PowerPoint PPT Presentation

Sep 21, 2023 16 likes •362 views

Part II Introduction to Reaction and Scattering Cross-Sections 1. Reaction Cross-Section Introduction The cross-section, , is the area that one atom presents to a beam of incident particles for initiating a specific interaction The

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Part II Introduction to Reaction and Scattering Cross-Sections

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  • 1. Reaction Cross-Section

Introduction

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The cross-section, σ, is the area that one atom presents to a beam of incident particles for initiating a specific “interaction”

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The impact parameter, b

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Transmutation reactions

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Li transmutation via thermal n capture σ = = ⋅

α −

941 [barns] 941 10 [cm ]

24 2

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How large is 173 fm?

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Reaction Cross-Section(s). Relationship to the Probability of Interaction

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Fluence

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Probability vs. Cross-Section

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3-D

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3-D

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The Total Scattering Cross-Section, σ

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The Differential Scattering Cross-Section, dσ/dΩ

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Solid angle, dΩ, associated with scattering in 3-D, to angles between θ and θ + dθ

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Rutherford backscattering (RBS) detector:

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The Differential Energy Transfer Cross-Section, dσ(E,T)/dT

State (without proof) an important relationship:

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Cross-Sections for a Hard-Sphere Interaction Potential

Figure 13.

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Hard sphere – scattering is isotropic in the CM system

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Hard-sphere Differential energy transfer cross-section

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Cross-Sections for a Rutherford Interaction Potential

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Cross-Sections for a Rutherford Interaction Potential

Next, we require an equation that provides a one- to-one mapping of

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Hyperbolic solution to the equation of motion

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Hyperbolic solution to the equation of motion

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Rutherford cross-section for angular scattering

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Rutherford cross-section for energy transfer

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Rutherford scattering: Differential probability of energy transfer between T and T+dT

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The solution: The Screened Coulomb Potential