Questions tagged [scattering-cross-section]
A cross-section is the name given to a hypothetical unit of area (often in units of Barns) for measuring the probability of scattering events in particles collisions. DO NOT USE THIS TAG for a physical non-probabilistic cross-section of a macroscopic object.
536
questions
-2
votes
0
answers
50
views
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
-2
votes
1
answer
59
views
What is the energy of a photon in an electron-muon scattering?
Currently I am reading about this process in an Introduction to Quantum Field Theory by Peskin and Schroeder (pages 153-154). It should be mentioned that they are working in a center-of-mass (CM) ...
- 41
0
votes
1
answer
29
views
Fitting function to compton continuum of data measured by scintillator detector
I have measured the spectrum of $ \:^{60}$Co with an NaI-scintillator detector. Now I want to fit a function to the measured compton continuum. My idea was, that the measured counts are proportional ...
1
vote
1
answer
37
views
Relative speed in unpolarized cross-section
In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
0
votes
0
answers
60
views
How can I calculate the cross-section of a $N+\pi \rightarrow N + \pi$?
In the same theme as my previous question, I have the diffusion process $$N+\pi \rightarrow N + \pi$$ where the Lagrangian for this theory is
$$L = \partial^\mu\psi\partial_\mu\psi^* - M²\psi\psi^*-\...
- 11
0
votes
1
answer
77
views
How can I calculate the cross section in general?
How can I calculate the cross-section of a process with three possible Feynman diagrams? I usually see examples with only the scattering amplitude defined by the $t$ channel, but if the scattering ...
- 11
0
votes
0
answers
34
views
Relation bitween Mandelstam Variables in three-body final state
What is the relation between Mandelstam variables in the three body final state?
There are 5 independent Mandelstam variables. What is the relationship between them?
- 11
0
votes
1
answer
63
views
How to Express the Cross Section of a Three-Body Final State Scattering in Terms of Invariant Masses $s_{ij}$?
I'm working on calculating the cross section for a scattering process that results in three bodies in the final state. My goal is to express the cross section in terms of the invariant masses $s_{ij}$...
- 11
2
votes
1
answer
78
views
Fermi theory cutoff from unitarity bound
Tree-level cross sections for processes described by Fermi theory behave like $\sigma $ $\sim$ $G_{F}^2 \cdot s$, where $G_{F}$ is the Fermi constant and $\sqrt s$ is the energy entering in the ...
- 31
0
votes
0
answers
36
views
How to deal with the divergence in tree-level diagrams? where the propagator momentum is on-shell
Only consider the interaction term between electron Higgs and $Z$ boson
$$
\mathcal{L}_{h ff}=-\frac{Y_f v}{\sqrt{2}} \bar{\psi} \psi\left(1+\frac{h}{v}\right)
=-m_f \bar{\psi} \psi\left(1+\frac{h}{...
- 19
1
vote
0
answers
27
views
Compton cross-section measure, 0 degrees
We are a group of undergraduate students currently doing a lab work to measure the Compton Cross-section, using a radioactive ${}^{22}$Na source.
The setup simply has the ${}^{22}$Na source decaying $\...
1
vote
0
answers
60
views
Spinor-helicity formalism: relationship between 1 and 2 reference vector setups
The spinor-helicity formalism is usually set up so that for a massless vector boson (photon or gluon) with momentum $k$ an arbitrary reference momentum $p$ is introduced and the corresponding ...
- 312
0
votes
0
answers
18
views
Incident flux in a plane wave
As mentioned in Nuclear Structure by Bohr and Mottelson
Flux of incident particles associated with waves normalized per unit energy is
$$(\rho v)_\text{incident channel} = p^2/(2\pi\hbar)^3$$
How does ...
- 1,405
0
votes
0
answers
70
views
Highly relativistic electron scattering in thin plasma
I am curious about how extremely relativistic electrons (10s of GeVs to single TeVs) scatter when going through the interplanetary and interstellar medium, which is a thin plasma. I have read about ...
- 113
0
votes
0
answers
29
views
Reciprocity theorem of reaction cross section
The reciprocity equation for reaction cross section reads
$$ka^{2}\sigma_{ab}=kb^{2}\sigma_{ba}$$
or
$$pa^{2}\sigma_{ab}=pb^{2}\sigma_{ba}$$
Here
$\sigma_{ab}$ is the total reaction cross section for ...
- 1,405
0
votes
0
answers
23
views
Extending Quantum Treatment of Attentuation Coefficient
I was reading this document to understand the links between the attenuation coefficient and quantum scattering. Consider a beam of number density $\rho$ and velocity $v$ in the z direction. $I = \rho ...
- 199
1
vote
0
answers
47
views
How to interpret the scattering cross section in quantum mechanics? [closed]
I am following Sakurai's Modern Quantum Mechanics, 3ed.
Define the scattering, or S-matrix elements as
$$S_{ni} \equiv \delta_{ni} - 2\pi i\delta(E_n - E_i)T_{ni}.$$
We can then derive the ...
- 2,676
0
votes
0
answers
16
views
Hydrogen and deuterium reaction with neutrons
In my book "Introduction to nuclear engineering" by John R.Lamarsh and Anthony J.Baratta,
(4th edition), they explain
"The nuclei 1H and 2H, which are present in large amounts in many ...
- 51
2
votes
0
answers
25
views
Modelling Mie Theory: Resources
I am currently working on simulating the scattering of light from nanoparticles. Are there any resources like books/ handouts/ videos that explain Mie Theory in depth?
1
vote
0
answers
30
views
How much gas is needed to produce absorption lines?
I am trying to know whether it would be possible to do an undergraduate laboratory experiment to measure absorption lines produced by a gas. The idea is to have a background source of light with a ...
- 636
0
votes
0
answers
13
views
How does the cross section of bound state look like in scattering process?
I am studying the non-relativistic scattering theory. I know when the incident particle is in the bound state the scattering amplitude diverges. Then does it mean the cross section also diverge? If so,...
- 388
1
vote
1
answer
42
views
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
2
votes
0
answers
154
views
Mathematical explanation of the extinction paradox
I am trying to learn properly about scattering. For this I was pointed to Wave Propagation and Scattering in Random Media by Ishimaru.
I got a bit stuck in section 2-2 General properties of the Cross ...
- 91
0
votes
0
answers
66
views
Phase shift in hard sphere scattering
Consider scattering towards a hard sphere with radius a and potential (Assume ka=1):
$$ V(r) =\begin{cases}
\infty , &r<a\\
0 , &r>a \\
\end{cases} $$
So first I ...
- 189
0
votes
0
answers
63
views
Commutation behavior of spinors in Feynman diagrams
I am currently playing around with computing cross sections of several simple interactions in QED like Bhabha and Compton Scattering and I have stumbled upon a question which I havent yet managed to ...
- 101
1
vote
0
answers
65
views
Why do I find different polarization vector completeness relations?
I am currently working on computing the cross section of Compton scattering in QED and in the process need to evaluate an expression of the following form:
$$ \sum_{\lambda}^{} \epsilon^{\mu} (\...
- 101
1
vote
1
answer
40
views
Maximum number of partial waves and matching point
I have read that a large number of partial waves, around 200, are required in a situation such as ${}^{16}$O incident on ${}^{152}$Sm at c.m. 65 MeV in Coulomb excitation
Anybody familiar with ...
- 1,405
1
vote
1
answer
34
views
Coulomb excitation [closed]
I have read that a very large number of partial waves around 200 and a large matching radius of 300 fm is required to obtain the cross section in Coulomb excitation. This is certainly far greater ...
- 1,405
0
votes
0
answers
42
views
$e^+e^- \rightarrow \mu^+ \mu^-$ cross section with circular polarization?
I'm trying to work through problem 5.4 of Schwartz (QFT and the Standard Model), which involves calculating the spin components of the matrix corresponding to the $e^+e^- \rightarrow \mu^+ \mu^-$ ...
- 9
0
votes
0
answers
46
views
Definition of (Differential) Scattering Cross Section in QED
In QED we like to define the (differential) cross section for a scattering process as follows:
$$d\sigma \ \dot= \ \frac{w_{fi}dN_f}{|j_{inc}|}\tag{1}$$
where $w_fi$ is the probability of transition ...
- 4,577