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.
538 questions
3
votes
0
answers
153
views
Light by light cross section using equivalent photon approximation (EPA)
I'm trying to understand how to do a numerical calculation of the light by light cross section utilizing the Equivalent photon approximation (EPA). I'm considering two incoming electron beams of ...
- 2,816
1
vote
0
answers
123
views
Interpretation of scattering plane waves in quantum mechanics
When treating scattering theory in (non relativistic) quantum mechanics, one at first considers the simple setup in which a plane wave impinges on a scattering potential, and one considers a scattered ...
- 131
0
votes
1
answer
980
views
What exactly azimuthal symmetry means?
In quantum mechanics, when discussing scattering by a potential, it is written that we are assuming the potential is spherically symmetric so the function cannot depend on $φ$.
Azimuthal symmetry ...
- 117
0
votes
1
answer
456
views
Why we use partial wave analysis for scattering amplitude? [closed]
Why we use partial wave analysis for scattering amplitude?
We can do it by Born approximation also
- 117
2
votes
1
answer
324
views
Classical scattering cross section and attractive potentials
If I want to calculate a scattering cross section $\sigma$ for a classical central potential $V(r)$, the first thing to do is to obtain an expression for the angle
$$
\Theta=\pi-2\int_{r_*(b,E)}^{\...
- 151
3
votes
2
answers
248
views
Why this factor $1/r$ is used in the equation of asymptotic behavior of scattered wave?
Why $1/r$ factor is used?
And in this equation $f_k(\theta,\varphi)$ is scattering amplitude then why plane wave ($e^{ikz}$) amplitude is not used?
- 117
0
votes
1
answer
460
views
How and why the state of free particle in quantum physics is represented by plane wave packet? [closed]
In Quantum Mechanics (Cohen Tannoudji) Topic: "Asymptotic Form Of Stationary Scattering States"
It is written that for large negative values of $t$, the incident particle is free and it's ...
- 117
0
votes
0
answers
118
views
What's the definition of absorption cross section?
I'm now studying quantum scattering theory and I'm confused as to what the word "absorption cross-section" means.
My textbook writes it as
$$
\sigma_\mathrm{abs}=\sigma_\mathrm{total} - \...
0
votes
0
answers
179
views
Relative cross section rates using isospin
There is a step in a solved problem I am not able to make sense of. Such problem finds the relative cross-section rates for the two following reactions using isospin formalism:
\begin{equation*}
R= \...
- 148
5
votes
1
answer
886
views
Trouble deriving expression for differential scattering cross section from $S$-matrix
I am following the derivation of the scattering cross-section from Peskin and Schroeder textbook. On page 105, we get an expression for the differential cross-section:
$$d\sigma = \left(\prod_f \frac{...
- 316
0
votes
1
answer
51
views
Does differential cross section assume no multiple collisions in a material?
The differential cross section definition is often expressed as $\frac{d\sigma}{d\Omega} = \frac{n(\theta,\phi)}{N_{target} j_A}=\frac{n(\theta,\phi)}{p_N \Delta x \space j_A}$
My question concerns ...
- 2,654
0
votes
1
answer
139
views
Vacuum polarization and initial state radiation correction for the cross section
I saw that the experimental Born cross section measured for (e+e- -> Hadrons) for positron-electron particle physics experiments such as the (BESIII or BaBar experiments) is corrected by initial ...
- 215
0
votes
0
answers
29
views
Scattering MC toy model
I would like to make a scattering toy simulation as a computational physics project. I'm having issues visualizing which parameter of the scattering function I need to compare with the randomly ...
- 1
1
vote
1
answer
314
views
What is the meaning of a cross section having "no angular dependence"?
This is in reference to page 112, equation 4.99 of Peskin and Schroeder.
We have just completed the first calculation (to first order) of a differential cross section. Specifically that of 2-particle ...
- 7,008
1
vote
1
answer
746
views
Approximation for the square of a Dirac delta function
I am working in the appendix to Section II.6 in Zee's QFT book, 2nd Ed. I am trying to compute the cross section for a meson to decay to two mesons as $\varphi\to\eta+\xi$ with three respective ...
- 713
2
votes
1
answer
188
views
Absorption cross section for photon with energy less than the necessary to excite the hydrogen atom
Suppose we have a photon with energy less than the necessary to excited the hydrogen atom from ground state to first excited state. Now suppose we make this photon to incise into a hydrogen atom in ...
- 485
2
votes
2
answers
963
views
Dimension of matrix elements in scattering cross section
This question is probably going to be somewhat trivial, but I am a little confused about the dimension of the matrix element that appears in the formula for the cross section of a scattering process.
...
- 71
1
vote
3
answers
890
views
In particle physics what is the derivation of the mean free path length: $\ell=\frac{1}{n \sigma}$?
From my lecture notes (ICL, dept. of Physics) it is written:
Consider a thin piece of material with thickness $d$ containing target particles with number density $n$, as illustrated in Figure $\bf{2....
- 2,520
3
votes
1
answer
116
views
From 1PI function to cross section
The full propagator in QFT is the inverse of this two-point 1PI function defined as $$
\tilde{\Gamma}^{(2)}(p)=p^{2}-m^{2}-\Sigma(p)
$$
where $\Sigma(p)$ is the self-energy. I am have calculated the ...
1
vote
0
answers
32
views
Cross section for Hydrogen molecule formation
I have been searching for theoretical articles that calculate the hydrogen formation cross section $\sigma(H+H \rightarrow H_2)$, but I found nothing. Can anyone suggest me articles or computer ...
3
votes
1
answer
281
views
Goldstone bosons in soft limit
There's interesting statement about amplitude of Goldstone bosons:
I wanna to understand simple argument for statement of vanishing of amplitudes in the single scalar soft limit. In principle, it is ...
- 5,737
1
vote
1
answer
41
views
Number of Ionization event estimation
First of all, I am new in this field and therefore if I ask a silly question please forgive me.
I have a gas-cell (say 3$\times$3$\times$3 mm$^3$ volume) filled with a N$_2$ gas. The number density is ...
- 13
2
votes
0
answers
326
views
$2 \to 2$ scattering cross section in arbitrary theory
What is the general method to compute the $2 \to 2$ scattering cross section given an arbitrary Lagrangian ? I would like a step by step recipe that can be easily implemented in Mathematica.
For ...
- 169
1
vote
0
answers
59
views
Unitarity and Legendre polynomials
Zohar Komargodski in these lecture notes claims:
I don't understand the requirement about unitarity.
Why must residues be expressed in terms of Legendre polynomials?
How does this statement follow ...
- 5,737
1
vote
1
answer
196
views
Cross section in Coulomb scattering of relativistic electrons
i'm currently reading about electron scattering and i cant understand the following statement of the book im reading. I quote the book(translated by me):
Many scattering experiments are done with ...
1
vote
1
answer
825
views
Unitarity and amplitudes
In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
In a local theory of ...
- 5,737
6
votes
2
answers
455
views
Why amplitudes are rational functions?
In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
Tree amplitudes must ...
- 5,737
1
vote
2
answers
293
views
Do electron-electron collisions have an associated scattering cross section?
Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an ...
- 579
6
votes
1
answer
614
views
The Ward-Takahashi identity in Peskin and Schroeder (page 311)
I'm working on the Ward-Takahashi identity in Peskin (page 311), but I canʻt obtain Eq.(9.105) from Eq.(9.103)
According to Eq.(9.103)
\begin{align}
&i \partial_{\mu}\left\langle 0\left|T j^{\mu}(...
- 169
1
vote
0
answers
90
views
Cross section from transition rate, finite and infinite volume normalization
In scattering theory, the transition rate is expressed in terms of the transition operator
$$\frac{2\pi}{\hbar}\rho_f|T_{fi}|^2 \,,$$
and the cross section is obtained by dividing the transition rate ...
- 36
2
votes
2
answers
918
views
Why do we refer the cross section ratios to muons?
For electron-positron interactions, we have different cross sections, depending on the available reaction energy. To get an overview how many particles of a certain type have been created, we can ...
- 65
2
votes
1
answer
231
views
Wrong application of optical theorem
I am trying to use optical theorem* ( given in box 24.2 in Quantum Field Theory and the Standard Model, M. Schwartz ). I am trying to calculate the imaginary part of this diagram for the scalar field:
...
- 542
31
votes
4
answers
4k
views
How do photons affect each other gravitationally?
Photons are energy. According to general relativity they should bend space.
Assuming two photons pass one another in a large void of empty space how would they gravitationaly affect each other ...
- 630
2
votes
2
answers
225
views
A photon scatters an electron at an angle... Does it imply electron having an area greater then the photon's?
Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral ...
- 2,275
1
vote
1
answer
243
views
Why does the scattering wave vector and reciprocal lattice vector have to be the same?
In Introduction to Solid state physics 8th edition by Charles Kittel. The scattering amplitude is defined as, $$F=\int dV n_G exp[i(\bf{G-\Delta k}).\bf{r}]$$ where G is the reciprocal lattice vector ...
1
vote
1
answer
637
views
How could the collision cross section be a probability?
I am new to learning about the concept about the collision cross section. I am having a hard time understanding the collision cross section (defined as $\sigma_{AB}=\pi(r_A+r_B)^2$ in this link ).
But ...
- 199
0
votes
1
answer
74
views
Where is expressed the distance between particles for the formula of cross-section in an accelerator?
Let's consider the so-called Master formula, which expresses the cross-section of interaction between two protons, taking into account the parton density function and the intrinsic cross-sections ...
0
votes
1
answer
162
views
Mistake in Walter Greiner's "Quantum Mechanics" Special chapters
I am going through section 2.4 and 2.5 of Walter Greiner's book "Quantum Mechanics: Special Chapters". In section 2.4, there is a detailed analysis of the elastic scattering of a free ...
- 11
2
votes
2
answers
440
views
Why is the plane wave ansatz appropriate for scattering cross sections of a localized particle beam?
This question is a spin-off from this related question: Why does the Born approximation for the scattering amplitude depend on the potential $V$ everywhere in space, unlike classical scattering? This ...
- 171
0
votes
2
answers
432
views
How is strong coupling constant related to cross section?
I've been looking through different Pdfs /articles on strong coupling constant and nearly all of them involve cross section, I've understood what cross section is but not how is it connected to ...
- 151
1
vote
1
answer
289
views
What is a structure function (or proton structure function)?
Can someone explain structure functions (proton structure functions)? I know they are used to study or understand the structure of protons , but does there exist a particular formula to calculate ...
- 151
1
vote
1
answer
91
views
Why there are "messy" areas in ENDF neutron cross section (barn)/neutron energy plots for different elements?
I was looking in ENDF for neutron cross section (barn)/neutron energy plots in different elements. As I looked through many elements, I realized that there is always an area at specific energies where ...
- 557
2
votes
1
answer
330
views
How to determine the sign of coupling constant in quantum field theory?
Experimentally, we determine the value of the coupling constant by measuring the scattering cross-section and compare it with the results calculated by the scattering amplitude.
However, in the ...
- 547
2
votes
2
answers
434
views
Suppression of $W$ boson propagator by its mass
In my experimental particle physics introductory class it was often said that quantum electrodynamics (QED) is very predictive for sufficiently small center of mass energys since the $W^\pm$-...
- 2,236
1
vote
1
answer
2k
views
The differential cross section and cross section
As we know the total cross section can always be obtained from the differential cross section:
$$\sigma = \int_0 ^{2 \pi } \int_{0}^{\pi } \frac{d \sigma}{ d \Omega} d \Omega $$
I understand how the ...
user12906
4
votes
1
answer
2k
views
Derivation of Thermally averaged cross sections
In many sources discussing neutrino decoupling I find the following claim:
"The thermally averaged rate of weak interactions is given by:
$\Gamma = n \langle\sigma |v|\rangle$,
where $\langle\...
- 375
3
votes
2
answers
350
views
Crossing Symmetry between tree-level diagrams of $e^+ e^- \rightarrow \mu^+ \mu^-$ and $e^- \mu^- \rightarrow e^- \mu^-$
According to Peskin and Schroeder (P&S)'s book, on pp. 156-157, the two processes $e^+ e^- \rightarrow \mu^+ \mu^-$ and $e^- \mu^- \rightarrow e^- \mu^-$ are connected via $s \leftrightarrow t$ ...
- 373
3
votes
3
answers
486
views
Understanding quantum cross sections as areas
In scattering cross sections we deal with $d\sigma/d\Omega$, incident area per scattered solid angle. When a particle scatters into a small finite $\Delta\Omega$, the incident particle was in a small ...
- 654
1
vote
2
answers
446
views
Partial waves method in scattering problems
One way of deal with scattering problems is to use partial wave analysis.
This is the procedure I've found in my notes:
It's assumed that the observer is in the center-of-mass reference frame and the ...
- 1,978
2
votes
0
answers
50
views
Cross-section in unitary gauge $e^-e^+\rightarrow ZZ$ process
I've been trying to calculate the cross-section for the process $e^-e^+\rightarrow ZZ$ in unitary gauge with vanishing electron mass $m_e=0$. I've obtained the following:
I've only determined the ...
- 484