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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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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Averaging over initial spins and summing over final spins
Consider the term $S\cdot J$ in matrix element $\mathcal{M}$, which is related to the cross section. S corresponds to a spin-1/2 particle. J is the angular momentum operator corresponding to a nucleus ...
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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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Collisional Association Cross-section
Suppose I have a free proton and a free hydrogen atom that collide. How would I go about determining the cross-section for the collision to result in an $H_2^+$ molecule in a particular vibrational ...
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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
$$L = \partial^\mu\psi\partial_\mu\psi^* - M²\psi\psi^*-\...
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How can I calculate the cross section in general?
How can I calculate the cross-section of a process with three possible Feynman diagrams? I usually see examples with only the scattering amplitude defined by the $t$ channel, but if the scattering ...
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Relation bitween Mandelstam Variables in three-body final state
What is the relation between Mandelstam variables in the three body final state?
There are 5 independent Mandelstam variables. What is the relationship between them?
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How to Express the Cross Section of a Three-Body Final State Scattering in Terms of Invariant Masses $s_{ij}$?
I'm working on calculating the cross section for a scattering process that results in three bodies in the final state. My goal is to express the cross section in terms of the invariant masses $s_{ij}$...
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Fermi theory cutoff from unitarity bound
Tree-level cross sections for processes described by Fermi theory behave like $\sigma $ $\sim$ $G_{F}^2 \cdot s$, where $G_{F}$ is the Fermi constant and $\sqrt s$ is the energy entering in the ...
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How to deal with the divergence in tree-level diagrams? where the propagator momentum is on-shell
Only consider the interaction term between electron Higgs and $Z$ boson
$$
\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}{...
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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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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 ...
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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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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 ...
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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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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 ...
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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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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,...
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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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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 ...
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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:
$$ \sum_{\lambda}^{} \epsilon^{\mu} (\...
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Maximum number of partial waves and matching point
I have read that a large number of partial waves, around 200, are required in a situation such as ${}^{16}$O incident on ${}^{152}$Sm at c.m. 65 MeV in Coulomb excitation
Anybody familiar with ...
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Coulomb excitation [closed]
I have read that a very large number of partial waves around 200 and a large matching radius of 300 fm is required to obtain the cross section in Coulomb excitation. This is certainly far greater ...
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$e^+e^- \rightarrow \mu^+ \mu^-$ cross section with circular polarization?
I'm trying to work through problem 5.4 of Schwartz (QFT and the Standard Model), which involves calculating the spin components of the matrix corresponding to the $e^+e^- \rightarrow \mu^+ \mu^-$ ...
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Definition of (Differential) Scattering Cross Section in QED
In QED we like to define the (differential) cross section for a scattering process as follows:
$$d\sigma \ \dot= \ \frac{w_{fi}dN_f}{|j_{inc}|}\tag{1}$$
where $w_fi$ is the probability of transition ...
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$hh \to hh$ scattering
I'm trying to compute the double Higgs scatter in QFT framework. Is it correct if I use the scalar propagator for this process?
Also I've found that I've four possible diagrams: the three $s,t,u$ ...
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Neutron double differential capture cross section
Can one define what is the double differential capture cross section for a neutron, and how one would construct an experiment to calculate the double differential cross section as a function of energy ...
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Calculating Scattering matrix of a nuclear fusion reaction using Fortran
I am trying to find out the $S$-matrix elements for the reaction:
$${}^{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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feynman scalar integral with on-shell condition
There are many integration written down in the standard QFT textbooks for scalar integrals in the computation of matrix elements. For example, in Peskin and Schroeder, we see
$$\int \frac{d^d \ell_E}{(...
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Differential Cross Section and Factor of $\pi$
I hope this is not a double-post, but the other threads couldn't help me:
In my calculations of the differential cross section $\frac{d\sigma}{d\Omega}$, I am always a factor $\pi$ lower than the ...
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What is a cross section, really? [closed]
Upon looking at different resources, there is a common definition of a cross section (in the context of QFT) to be the probability that some scattering process occurs. For example, here is a ...
user310742
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Physical mechanism of $s$-wave neutron resonances in nuclear physics
In this answer by Arturo don Juan, and also, in section $7.8$ of Sakurai's Modern Quantum Mechanics, it is argued that resonances in the scattering cross-section at certain energies are due to the ...
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Inverse muon decay on Mandl shaw- Help on $W$ boson propagator
Hello, I cannot understand why here the other term of the propagator of $W$ boson $k^{\alpha} k^{\beta}/m_{W}^{2}$ is not present, and how/if this absence is linked to the fact that we neglect terms ...
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Reducing Inelastic Electron-Proton's Scattering Cross Section to Rosenbluth's Formula
I'm currently studying electron-proton scattering from Halzen & Martin's book (Quarks & Leptons : An Introductory Course in Modern Particle Physics). I found that the cross section for the ...
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Scattering cross section for distinguishable particles
I am reading Quantum Mechanics book by N. Zettili (2nd ed.) and encountered something confusing in the chapter of scattering theory, section 11.5: scattering of identical particles.
This is the ...
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Can the Moller cross-section be calculated using a two-particle potential?
Can the Moller scattering cross section be calculated with a two-particle potential?
The Feynman prescription for scattering two electrons, using perturbation theory (Weinberg QTF Vol1) involves ...
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Another "real vs virtual particle" one: calculate the full diagram or $\sigma \times \mathrm{BR}$?
I have recently been forced to think about something I always thought that I understood but that, in reality, I could not be more confused about.
Suppose I want to study the LHC prospects for ...
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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 ...
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