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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.

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Motivation behind the representation of differential cross sections using histograms

From my lecture notes: In most cases a cross section is represented in a differential way with respect to one or more observables. While it is possible to make a theoretical prediction for a ...
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Rate of reaction of collision in relation to the geometric cross-section

I am reading "Particles and nuclei : an introduction to the physical concepts / Bogdan Povh" and on page 44 of the book there is a section about the geometric cross section in a idealised scattering ...
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Mass dimension of an $n$-particle scattering amplitude in 4D

For the 4-dimensional case, and using the cross-section formula, how can we show that the mass dimensions of an $n$-particle amplitude must be $$[A_n] = 4-n~?\tag{2.99}$$ My understanding is that the ...
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Elementary particles & their reactions: literature

I would like to find a book which contains lot of examples of different reactions with elementary particles (for instance, electron-electron scattering, electron-positron annihilation, electron ...
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Why is number density of atoms taken in reaction cross-section?

When reaction cross-section area corresponding to one target nuclei is given, then to calculate total scattering cross-section that area is simply multiplied by the number of atoms in that slab to ...
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QFT cross section: missing information?

So I'm having a hard time understanding how the (QM) cross section fits into the general picture, of e.g. collider experiments. So we can calculate cross sections (for one reaction) exactly in QFT ...
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Why the nuclear fusion 6Li+D and 7Li+P reactions happens 10 time less than H+11B?

The first two reactions generates 2 alphas and the boron one generates 3, but boron has 2 more protons than lithium so should repels more to hydrogen. I suppose is a question of nuclear states, but ...
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Ratio between neutrino scattering cross-sections

I would like to calculate the ratio between the cross-section of the processes: $$\frac{\nu_\mu+e^- \rightarrow \nu_e+\mu^-}{\bar{\nu}_e+e^- \rightarrow \bar{\nu}_\mu + \mu^-}$$ I found this set of ...
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Theoretical definition and pratical mesurement of differential cross section

In Sakurai's book, the definition of differential cross section is: $$d\sigma/d\Omega= transition \;rate / probability\; flux $$ However this def doesn't contain any information about the thickness ...
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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 ...
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What's the relationship between reduced mass and the total energy of collisions in the lab and center of mass frame?

Is there a relationship between reduced mass and the total energy of collisions in the lab and center of mass frame? If so, could someone explain how it is related?
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What are the axis of collisions in the laboratory and center of mass frame?

This may be a silly question. I was asked, "what are the axis of collisions in the lab and center of mass frame?". My first thought was that that the colliding masses are on the same axis for both ...
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Why is the laboratory frame energy always greater than the center of mass frame energy for collisions? [duplicate]

I looked through lots of sources to answer the question, 'Why is lab frame energy (total energy) always greater than the center of mass frame energy?' Many of them provided lots of mathematical ...
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Why is the laboratory frame energy always greater than the center of mass frame energy?

I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'. A lot of resources provided mathematical explanations....
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Mass vs cross-section studies

Let's assume we have a event generator like "Pythia", and from that I have collected four momentum of a certain lepton production. the leptons are from excited gamma state. And the excited ...
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exchanged momentum in Compton scattering

I am trying to resolve a confusion regarding scattering kinematics. I am considering Compton scattering, i.e. a photon with four-momentum $k$ scatters on an electron with four-momentum $p$, the final ...
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1answer
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At what stage is it necessary to introduce a field theory in the regeon-pomeron-odderon model of hadron interactions?

I've been reading some papers from G.F. Chew and S. C. Frautschi and they do not even bother to introduce the concept of "Field" when they describe hadron interactions. My impression is that they do ...
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What is $\gamma$$\rho$ mixing?

In a previous question, I asked about the apparent universality behaviour in hadron elastic scattering. I was particularly shocked to see that even $\gamma p$ showed that universal behaviour with ...
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1answer
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Do Reggeons-Pomerons-Odderons offer an Universal picture of hadron interactions?

As far as I know, the total cross-sections of the following hadron interactions are well described by a single Reggeon trajectory and a single Pomeron (soft Pomeron) trajectory. It seems to work for ...
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What is the Relative Radiation Absorbtion per unit Mass of the various states of matter?

I am trying to find information on the relative merits of using a gas, liquid, solid or even a plasma as a radiation shield. Examples Ice, water and water vapour. Iron, molten Iron, Iron ...
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What is the procedure to get the scattering cross-section expression?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
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What is interaction cross section of a photon and how to find it?

I encountered this term while reading about photon interaction with metal electrons. Is this equal to the scattering cross section or is it different? How to find it mathematically?
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Why are the elastic and total cross-section of $pp$ collisions increasing as the C.O.M. energy grows?

Well, that's about it. I don't find any reasonable explanation for this fact. Are they transversally expanding as the energy increases? Please, remember that strong interactions are short ranged and ...
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Use of Cutkosky rule, the Optical Theorem and Regge trajectories in pp scattering total cross-section calculation

Cutkosky rule states that: $$2Im \big(A_{ab}\big)=(2\pi)^4\sum_c \delta\Big(\sum_c p^{\mu}_{c}-\sum_a p^{\mu}_{a}\Big)|A_{cb}|^2\hspace{0.5cm} (1)$$ putting $a=b=p$ in Cutkosky rule we deduce the ...
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Rigorous-ish mathematical meaning of having two total differentials in the denominator

When I'm doing, say, $\pi^0 \rightarrow \gamma \gamma$ decay, and I want to find the angular distribution for the number of photons with energy $E$, $N(E, \Omega)$. To get the probability I then need ...
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233 views

$pp$ and $p\bar p$ scattering energy scaling exponents and 3d directed percolation model critical exponents similarity/equality, why?

$pp$ and $p\bar p$ scattering can be approximately described (in the Regge limit, that is, when $s \gg m \gt |t|$) by the exchange of Reggeons defined by the following Regge trajectory (low $s$): $$\...
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1answer
92 views

How is the cross section related to the probability of a process?

The question is in the title: How is the cross section related to the probability of a process? If I have the total cross section $\sigma$ of a process how is this related to the probability of this ...
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1answer
130 views

Proton-proton and proton-antiproton elastic scattering symmetry

Is $A_{pp}(s,t)=A_{p\bar p}(t,s)$ true based on crossing symmetry? Consider $pp$ and $p\bar p$ elastic colissions ($p + p \rightarrow p + p$ and $p + \bar p \rightarrow p + \bar p$). The scattering ...
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Computing hadronic cross sections with PDFs

I am trying to estimate the cross section for a BSM process at the LHC, and I would like to ask if anyone knows what is the simplest way to integrate over the PDFs, for example with Mathematica. I ...
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33 views

Scattering angle for induced ion-dipole interaction (inverse-5th power force)

I've been trying to work out the relationship between impact parameter and scattering angle for the case where an ion travels near an uncharged atom at non-relativistic speed, near enough such that ...
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How to derive the Klein-Nishina formula from the Dirac equation?

I'm looking for the simplest demonstration of the Klein-Nishina formula, from the Dirac equation without the field described as a quantum operator: https://en.wikipedia.org/wiki/Klein%E2%80%...
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1answer
149 views

Møller scattering amplitudes

In order to compute the scattering cross section for Møller scattering, one needs the amplitudes for both the $t$- and the $u$-channel. Since the cross section is proportional to $|\mathcal{M}|^2$, ...
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Are resonances formed in scattering between a baryon and meson?

Consider the following reaction of strong interaction (in a scattering process) $$n+\pi^+\to \Lambda_0+K^+\tag{1}$$ Then the particle $\Lambda_0$ formed decays with weak interaction $$\Lambda_0\to ...
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Probability density in Fermi golden rule

Consider Fermi golden rule $$\Gamma _{{i\rightarrow f}}={\frac {2\pi }{\hbar }}\left|\langle f|H'|i\rangle \right|^{{2}}\rho $$ I don't understand why $\left|\langle f|H'|i\rangle \right|^{{2}}$ is ...
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Measuring characteristic time of strong and weak interaction using cross section

Consider a scattering between two particles a and b that produces two particles c and d: d is stable, while c decays in two other different particles e and f. The first interaction is by strong ...
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What are the higher order Feynman diagrams I have to consider in muon neutrino-electron scattering?

I think in a $\nu_\mu + e^{-}$ scattering can happen: $\nu_\mu + e^{-} \rightarrow \mu^{-} + \nu_e$ and $\nu_\mu + e^{-} \rightarrow \nu_\mu + e^{-}$ With two Feynman diagrams (CC and NC). My ...
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Shape of partons from differential cross section as function of $Q^2$: is it valid, despite the $\theta$ dependence?

For deep inelastic scattering of electron on a nucleon the following graph represent the ratio $$\frac{\frac{d^2 \sigma}{d \Omega d E'}}{(\frac{d \sigma}{d \Omega})|_{Mott}} $$ as a function of $Q^2$,...
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Parton model: relation between $F_2(x)$ at fixed $Q^2$ and differential cross section as function of $x$

Consider deep inelastic scattering of electron on proton and parton model: $F_2(x)$ as a function of Bjorken $x$ at fixed $Q^2$ goes as in the following graph. The differential cross section is: $$\...
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1answer
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Trace from Casimir's trick (muon neutrino- electron inelastic scattering)

Griffiths defines Feynman amplitude for the CC process $\nu_\mu + e \rightarrow \mu + \nu_e$ as $$\mathscr{M} = \frac{ g_w^2}{8M_W^2} \left[\bar \nu_e \gamma^\mu (\mathbb{1} -\gamma^5) e\right] \...
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Feynman amplitude and tensor 4-vector multiplication (muon neutrino-electron scattering)

In the calculation of the Feynman Amplitude for the muon neutrino-electron scattering (in the Charged Current way from W boson), or $e + \nu_\mu \rightarrow \nu_e + \mu$ (considering the 4-momentum ...
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1answer
38 views

Spherically symmetric potentials

I'm trying to calculate differential cross sections for a certain scattering problem. I want to use the approximate formula for the scattering amplitude in a spherically symmetric potential. Is any ...
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1answer
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Deep Inelastic Scattering cross section: Smearing of the $F_2(x)$ graph and relation of form factors with Fourier Trasform of nucleon distibutions

Consider Deep Inelastic Scattering cross section $$\frac{d^2 \sigma}{d \Omega d \nu}=(\frac{d \sigma}{d \Omega})|_{Mott} \{ W_2(Q^2,\nu)+2 W_1(Q^2,\nu) \tan^2(\theta/2) \}$$ It is said that the ...
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Are there cross sections with an energy threshold? ($\sigma\sim \Theta(E-E_0)$ )

Is it in principle possible to have a cross section $\sigma$ of a process, say $a \bar{a}\to b \bar{b}$, which is proportional to the Heaviside function $\Theta(E-E_0)$, so this particular process ...
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Exclusion limits on particle dark matter

I'm trying to make sense on how the upper limits of the cross section of particle dark matter (WIMPs) are computed, like in the figure below. This is taken from an article on dark matter searches. ...
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Does scattering cross-section of a large number of scatterers tend to sum of their cross-sections?

Suppose we know differential cross-section for some type of scatterer particle. Now, consider a large number of such scatterers distributed randomly in some volume. If there's much space between these ...
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Flux of particles not uniformly distributed

I am puzzled by this issue. When introducing the cross section, the flux F is defined as the number of particles over unit area and over unit time. The flux is then used to obtain the cross section ...
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Bhabha Scattering and its differential cross section

I worked out the differential cross section for Bhabha Scattering in the center of mass frame and I obtained the following: $$\left(\dfrac{d\sigma}{d\Omega}\right)_{CM} = \dfrac{\alpha^2}{2s} \left[\...
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connection between scattering absorption cross sections and plasmon resonance in nano particles

I'm working on systems with plasmonic nano particles and I'm quite new to this area. I would highly appreciate if someone can please explain the connection between scattering absorption cross sections ...
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67 views

Born Approximation at Low Energies

According to Griffiths, in a typical scattering scenario, we have $$\psi(r, \theta) = A\left(e^{ikz} + f(\theta, \phi) \frac{e^{ikr}}{r}\right)$$ Where $k = \frac{\sqrt{2mE}}{\hbar}$. I.e an incident ...
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Does total cross section in high energy physics only depend on s?

I am very confused why people draw pictures of total cross section with respect to s. For example Does cross section only depends on s? Can anyone explain this a bit, or provide any references?