All Questions
Tagged with scattering-cross-section classical-mechanics
15
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-2
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How does total cross section converge? [closed]
I am reading Statistical Mechanics by Reif, and when discussing collisions he brings up the notion of cross sections. He defines it by $d\mathcal{H}=F\sigma \mathrm{d}\Omega$, where $\mathcal{H}$ ($\...
- 125
1
vote
1
answer
42
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Numerically Stable form of Scattering Angle
I'm working through the problems in Chapter 3 of the 3rd edition of Goldstein's Classical Mechanics and I'm stuck on Derivation 4. This problem asks the reader to rewrite the scattering angle
\begin{...
- 373
1
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1
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164
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Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics".
The problem states that suppose there is a particle of mass $m$ moving under the ...
- 11
1
vote
1
answer
257
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Scattering Differential Cross Section Laboratory Frame
Let the differential cross section of a scattering experiment given by $\frac{\text{d}\sigma_{c}}{\text{d}\Omega_{c}}(\vartheta_{c})$, where $\vartheta_{c}$ describes the scattering angle in the ...
- 66
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0
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61
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Infinite total cross-section in Rutherford scattering [duplicate]
In Greiner's Classical Mechanics, vol. 2 (Springer 2010, p. 59), he mentions that differential cross-section in Rutherford scattering diverges as scattering angle goes to 0, i.e. when impact parameter ...
- 23
2
votes
1
answer
107
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What accounts for the difference in factor of 4 between quantum cross section and classical cross section?
In classical mechanics, we could calculate the total cross section of scattering from hard sphere to be $$\pi a^2$$
where $a$ is the radius of sphere.
Recently in quantum mechanics we calculated the ...
- 301
1
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1
answer
259
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Calculating classical scattering angle using Gauss-Legendre quadrature
In Goldstein problem 3.5, We have to calculate the scattering angle, $\Phi(s)$, given as a function of input parameter, using Gauss-Legendre Quadrature. The full question is as follows;
Compute ...
- 173
1
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1
answer
109
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Can’t find the right impact parameter - flux of particles scattered by surface of revolution [closed]
I’ll be so happy to understand what am I doing wrong.
There is no potential in the question so I assumed this is solvable by geometry alone. The question ask for the impact parameter while
$$\rho=\...
- 60
3
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0
answers
123
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The idea of scattering cross-section in classical mechanics, quantum mechanics, and high energy physics
I am very confused about the idea of the cross-section in classical mechanics, quantum mechanics, and high energy physics. It seems like in classical and quantum mechanics, scattering cross-section is ...
- 157
1
vote
1
answer
92
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Dependence Of A Cross-Section
I am trying to understand the dependence of a differential cross-section on $$\sigma(\theta) = \left(\frac{s}{ \sin \theta}\right)\left|\frac{ds}{d\theta}\right|,$$ where $s$ is the impact parameter ...
- 65
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2
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287
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Why does the scattering cross section equal to the sum over all differential cross section; including the incident angle?
According to Beer Lambert's law, the intensity of light passing through a homogeneous medium diminishes at a rate proportional to the incident intensity; i.e.
$$
\frac{dI(s)}{ds} = -I(s)\sigma\, ,
$$
...
- 310
0
votes
1
answer
388
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Clarification for the formulae for Differential Cross Section in Scattering theory [duplicate]
I am trying to study scattering theory using "Quantum Mechanics Concepts and Applications" by "Nouredine Zettili" .
He starts from the formula
$${d \sigma( \theta,\phi) \over d \Omega } = {1 \over ...
- 545
3
votes
1
answer
835
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How can I calculate scattering cross section of Yukawa potential classically?
https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential
Here is classical form of Yukawa potential.
I want to calculate classical scattering cross section of this potential ...
4
votes
2
answers
518
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The Relationship between coulomb collision, inverse square law and Rutherford scattering
I was reviewing the following question.
"A key result of the α particle scattering experiment of Geiger and Marsden was that the number of particles scattered into a given angle was proportional to ...
- 39
4
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2
answers
164
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Particle number vs time in collisional N-body problem
I have created a crude N-body simulator which allows N bodies of equal masses to interact gravitationally in 2 dimensions.
Each body is modeled as a circle with a radius as a function of its mass, ...
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