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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Cross section normalization in $2 \to 2$ scattering
Consider Compton scattering $$p_1 + p_2 \to p_3 + p_4$$ in the laboratory frame. According to Quantum Field Theory and the Standard Model by Schwartz, the relation between the differential cross ...
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Scattering probability distribution for $2 \rightarrow 2$ scattering
Consider a 2-to-2 particles scattering process (treated in second quantization) of particles with the following $4$-momenta:
$$p_1 + p_2 \rightarrow p_3 + p_4.$$
The probability measure associated ...
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Computation of scattering cross section using Dirac equation
The differential cross section formula of the scattering of an electron on a nucleus are known to coincide when computed using either classical mechanics approach (Rutherford) or the Schroedinger ...
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Understanding derivation of quantum differential scattering cross-section [duplicate]
I've been trying to understand quantum scattering, but I think I am not very clear about the full picture in the derivation of differential cross-section below. In Modern Quantum Mechanics by Sakurai, ...
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Does hydrogen have resonances of photoelectric cross section for photon energies above 13.6 eV?
I am digging a bit into Geant4 physics and its behavior. I am making some plots of the values for the photoelectric cross-section used by ...
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Why do discussions of classical EM scattering use scattering cross-sections instead of scattering amplitudes?
In every discussion of classical electromagnetic scattering that I've read - e.g. Jackson and Wikipedia (1 and 2) - the primary quantity that is used to quantify EM scattering is the differential ...
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Derivation of the density of states for a two-body collision (bosonic particles)
I am studying the problem consisting in the collision of two bosonic particless with initial momentum $k_1$ and $k_2$. The initial quantum state is so defined as $|k_1,k_2>$. After the collision ...
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Usage of total cross sections in different reference frames relavistically
I am currently working on calculating the mean free path length of mild relativistic positrons in thermalized plasmas. For example, I want to calculate the mean free path length considering Rutherford ...
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Effect of the charge of the incident lepton on the two-photon-exchange lepton-proton scattering amplitude
I am studying two-photon exchange (TPE) scattering between an incident lepton and a proton. The sign of the TPE cross-section depends on the charge of the lepton, it is different for an electron and a ...
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Why is the radar cross section $\sigma$ of a sphere in the optical region ($\lambda<<R$) equal to $\pi R^2$?
I have a fundamental misunderstanding concerning the behaviour of radar cross section (RCS) of a sphere in the limit of short wavelengths, $\lambda\ll R$. As I read, RCS behaviour is usually divided ...
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Derivation of Form Factor to Determine Nuclear Charge Distribution
Background
I am following Introductory Nuclear Physics by Kenneth S Krane. The derivation of form factor to determine nuclear charge distribution is given as follows:
Consider an electron with intial ...
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Cross-section of $\pi^0$ mesons in Pythia
I simulated 10,000 events in PYTHIA 8.3 for p-p collisions (14 TeV High Luminosity run). I get the cross-section for 101.512 mb, which seems reasonable (with certain error) as ATLAS cites 104.7 ± 1.1 ...
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What values should be assigned to the fission channel indices $f_1$ and $f_2$ defined in the neutron cross-section equation for U-235 in ENDF-102?
I am currently trying to calculate the neutron cross-section of U-235 using the formulation given in the ENDF-102-2023 Manual. On page 353, the manual defines the cross-section as:
$$
\sigma_{nf}(E) = ...
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Differential Inelastic Cross section and Optical Theorem
Context
For a single channel scattering problem, it is well known that we have to solve the wave function from the Schrodinger equation:
\begin{equation}
\left( -\frac{1}{2m} \nabla^2 + V(r) \right) \...
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An intuitive derivation of cross-section formula in quantum field theory [closed]
I've seen rigorous derivations of using amplitude from Feynman diagram to calculate cross section (e.g. Peskin & Schroeder's book), However, none of the derivation is intuitively clear, and I am ...
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Two-particle phase space integral for a fixed target: No kinematic limit?
I have a fairly basic question concerning a Lorentz Invariant phase space for a 2 particle final state in a fixed-target experiment lab frame. For some reason, in my derivation, I do not see that that ...
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Trouble understanding differential cross section
In Peskin and Schroeder's "An introduction to Quantum Field Theory" in section 4.5 "cross sections and the $S$-matrix" (concretely pages 100-101) it says
Usually, of course, we ...
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How was the unit for two-photon absorption cross section, the Goeppert-Mayer (GM), derived?
The unit for the two-photon absorption cross section, named in honor of Maria Goeppert-Mayer, is $10^{-50}\,\mathrm{cm}^{4}\cdot\,\mathrm{s}\,\cdot{\rm photon}^{-1}$. How did they come up with this? ...
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Differential cross section in electron-positron annihilation
Suppose we have the annihilation reaction $e^{+}e^{-}\to\mu^{+}\mu^{-}$, with the lepton $\mu^{-}$ being produced into a solid angle. In Peskin&Schroeder's intro to QFT book, they state that it is ...
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Predicting scattering cross-sections
I realized that I do not really understand the way we define and calculate scattering cross-sections starting from transition probabilities in QM. I will explain my reasoning in a moment but the TLDR ...
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Potential of Neutron scattering by crystal
According to Ashcroft and Mermin, the neutron-ion interaction is given by $V(r)=\frac{1}{V}\sum_Rv(r-r(R))=\sum_{k,R}v_ke^{ik.(r-r(R))}$. They mentioned that the range of $v$ is the order of $10^{-13}...
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Simplification of the Differential Cross Section in Peskin and Schroeder
I am reading p. 107 in Peskin and Schroeder's QFT, and I am stucked on one of the steps they took while calculation $2\rightarrow 2$ cross section. For $A+B\rightarrow 1+2$ differential cross section ...
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Origin of $1/v$ region of neutron capture cross section and different Breit-Wigner formula formulations
I'm studying neutron radiative capture reactions and was wondering about the origin of the so called "$1/v$ region".
Here's the region I'm referring to:
Apart from being an experimental ...
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Cross Section Formula and Delta Function Identity (Eq 4.77 in Peskin & Schroeder QFT)
In the book, while deriving the cross section formula for particles A and B, a Dirac delta appears in Eq 4.77:
\begin{align}
\int d\bar{k}^z_A \, \delta\left.
\left(
\sqrt{(\bar{k}^\perp_A)^2+(\bar{k}^...
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Verifying Center of Mass to Lab frame transformation for Yukawa cross section
I have computed the Yukawa-potential cross section for two spinless particles with mass ration $\lambda \equiv m_P/m_T$; where $m_P$ is the projectile mass and $m_T$ is the target mass. I want to ...
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Can the Froissart bound be improved?
The Froissart bound is a fundamental result in (axiomatic) quantum field theory, an introduction to which from Froissart himself can be found here.
Given a reaction of scalar particles $1 + 2 \...
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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 ...
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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 ...
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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^*-\...
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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 ...
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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?
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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 $s_{ij}$...
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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 ...
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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 $\...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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{...
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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 ...
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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 ...
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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:
$$ \sum_{\lambda}^{} \epsilon^{\mu} (\...
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Maximum number of partial waves and matching point
I have read that a large number of partial waves, around 200, are required in a situation such as ${}^{16}$O incident on ${}^{152}$Sm at c.m. 65 MeV in Coulomb excitation
Anybody familiar with ...
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Coulomb excitation [closed]
I have read that a very large number of partial waves around 200 and a large matching radius of 300 fm is required to obtain the cross section in Coulomb excitation. This is certainly far greater ...
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$e^+e^- \rightarrow \mu^+ \mu^-$ cross section with circular polarization?
I'm trying to work through problem 5.4 of Schwartz (QFT and the Standard Model), which involves calculating the spin components of the matrix corresponding to the $e^+e^- \rightarrow \mu^+ \mu^-$ ...
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$hh \to hh$ scattering
I'm trying to compute the double Higgs scatter in QFT framework. Is it correct if I use the scalar propagator for this process?
Also I've found that I've four possible diagrams: the three $s,t,u$ ...
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Calculating Scattering matrix of a nuclear fusion reaction using Fortran
I am trying to find out the $S$-matrix elements for the reaction:
$${}^{19}\textrm{F} + {}^{208}\textrm{Pb}. $$
The model followed is Direct reaction model where the optical potential is:
$$ V_{op}(r) ...
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What is the difference between the center of mass energy of partons, and the invariant mass of the particles after a collision?
In a paper about the Atlas experiment (https://arxiv.org/abs/2103.01918) differential cross sections of $pp→ZZ→4\ell$
are being presented. However these cross-sections are functions of the invariant ...
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