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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How do funnels hinder (help?) detection of dark matter?

I came across some a new (to me) bit of terminology at a seminar recently. In the context of dark matter scattering off of atomic nuclei (but I think it may apply more generally for any particle ...
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Exercise: Calculating Q-value for $D_0 \to \chi_s^-e^+\nu_e$

Question Is the following methodology correct in calculating the Q-value (change in kinetic energy) for the $D^0 \to \chi_s^-e^+\nu_e$ decay process? Steps The change in kinetic energy is ...
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Semileptonic decay amplitude

I'm trying to do past exam papers and I am absolutely failing understand some things. I would very much appreciate any insights/intuition you have. The part I'm struggling is here: In the first ...
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Momentum conserving delta-function in the transfer matrix of quantum-field-theoretic scattering theory

The $S$-matrix vanishes unless the initial and final states have the same total $4$-momentum, so it is helpful to factor an overall momentum-conserving $\delta$-function: ...
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62 views

Issues of normalization & differential final state momenta in analysis of normalized differential quantum-field-theoretic probability of scattering

The normalized differential quantum-field-theoretic probability $dP$ of scattering is given by $$dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,$$ where $|i\rangle$ ...
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61 views

How do I calculate the differential cross section with respect to the transversal momentum?

First of all, sorry for my English, my first language is German. My problem is: I calculated the matrix element of the quark-gluon-Compton process (q+g -> gamma + q). With the kinematics of ...
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34 views

Differential cross-section for a 2-particle process in the LAB frame

This should really be a straightforward calculation, but somehow, I keep confusing myself and failing over and over again. I did the calculation so many times that I don't even know what I'm looking ...
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1answer
42 views

$e^-e^-\rightarrow e^-e^-$ scattering relative negative sign quick computation

In the QED scattering process $e^-e^-\rightarrow e^-e^-$ there are two possible diagrams in the tree level. If I label the momenta I have, $$e^-(k_1)\quad e^-(k_2)\quad \longrightarrow \quad ...
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136 views

Thomson scattering cross section: free electrons vs atoms

I am trying to find a reference for the Thomson scattering cross section difference between free electrons and atoms. I have always assumed that free electrons have a higher cross sections, but I can ...
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70 views

Interpreting the Cross Section Ratio R

Below is experimental data for the ratio $$R=\frac{\sigma(e^+e^-\rightarrow hadrons)}{\sigma(e^+e^-\rightarrow\mu^+\mu^-)}$$ as a function of the centre of mass energy $\sqrt s$. I am interested in ...
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131 views

Why the cross section can be obtained directly from the stationary scattering states?

I'm currently studying scattering theory in the book Quantum Mechanics, Vol. 2 by Cohen-Tannoudji. In the book the author deduces that to find the number of particles detected far from the target at a ...
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67 views

Question about Quantum Scattering and the Born Approximation in Griffiths Intro to QM

I am trying to follow Griffiths Intro to Quantum Mechanics 2nd edition, chapter 11 Section 4 on the Born approximation of scattering. My question is what exactly are the definitions of $\vec{r}$ and ...
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29 views

Area of cross section for atomic chain

I want to calculate the resistivity (rho = R*A/l)) of an atomic chain, for that I need to calculate area of cross section first. I am really confused, on how to calculate the area of cross section ...
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1answer
18 views

The basic probabilistic relation of collision theory

In "Classical Mechanics", John R. Taylor gives this basic relation of collision theory $$N_{sc}=N_{inc}n_{tar}\sigma$$ for firing projectiles into targets. $N_{sc}$ is the number of projectiles ...
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57 views

Derivation of exponential charge distribution and form factor from the normalized yukawa charge distribution and form factor

For a problem solving class I need to derive the normalized exponential charge distribution $\rho_e \propto e^{-\mu r}$ and corresponding form factor $F_e$, from the normalized Yukawa distribution ...
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25 views

How to calculate the decay rate of Higgs to lepton pair?

In class, the generic formula we've been given for calculating scattering amplitudes for the weak decay (at low energies so that the interaction is effectively point-like) is $$ M= ...
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35 views

Decay rate and differential cross-section

If I have a $pp-$beam producing an on-shell particle $A$, which then decays into particle $B+C$, then I can find the total cross-section $pp \to A \to B+C+Y$ ($Y$ being inclusive particle which should ...
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169 views

Resonant Scattering and the Breit-Wigner Formula

Most of what I ask relates to the derivation found here: https://farside.ph.utexas.edu/teaching/qm/lectures/node91.html The basic idea is that we first consider zero energy s wave scattering from a ...
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19 views

Grazing angle in a nuclear collision

How is the grazing angle calculated theoretically? Also, experimentally, the quarter point angle of elastic scattering angular distribution is taken as the grazing angle in accordance with ...
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164 views

Intensity of inelastic neutron scattering: analitycal expressions

I am currently working with experimental results of magnon spectrum (in antiferromagnet with many atoms per unit cell), which was obtained by inelastic neutron scattering method, but some spectral ...
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74 views

Understanding scattering cross section

I think I might have a serious misunderstanding of some concepts to do with scattering cross sections and would really appreciate any help. As far as I can tell the differential cross section is ...
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77 views

Green's Function in the Lippmann Schwinger Equation

When deriving the scattering cross section using the Lippmann-Schwinger equation we need to calculate the Green's function defined by ...
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32 views

Energy dependency of the total cross section for different species

Comparing the plots for the total (inelastic) cross sections as a function of the centre of mass energy for $pp$ and $e^+e^-$ collisions: one notes that the trend at high energy is opposite: the ...
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82 views

Scattering Theory

In non-relativistic quantum mechanical scattering theory you can derive an expression for the differential scattering cross section under the first order Born approximation as ...
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41 views

Neutron activation time for Boron, Silver, and possibly other materials

How do i justify/explain that the time needed to activate Boron is 2 hours and the time needed to activate Silver in water is 45 minutes? Response to comment: In a neutron cross section experiment, ...
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Assigning values of angular momentum transfer

How do the shapes of the experimentally measured differential scattering or transfer cross sections help in assigning reliable angular momentum transfer values?
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60 views

Relativistic Scattering

When we work out the relativistic general two-body scattering in the CM frame (like two elementary particles producing two other P1 +P2 -P3 -P4) , the cross section is proportional to absolute final ...
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28 views

Scattering cross section in terms of current density

I was struggling to understand what a scattering cross section is (in a classical setting), and I found this document: ...
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122 views

Analyzing electron-positron scattering cross section in detail

It can be found in any quantum electrodynamics book that the cross section for electron-positron scattering in the high energy limit is \begin{equation} \dfrac{\mathrm{d} \sigma}{\sin \theta \, ...
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40 views

What does it mean that the Rutherford's cross section is infinite?

I'm studying elastic scattering and I read that the Rutherford's differential cross section is defined as: $$\left( \frac{d \sigma}{d \Omega} \right)_R = \frac{Z^2}{4} r_o^2 z^2 \frac{(m_ec / \beta ...
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82 views

Baryons annihilation

I was wondering if there is a way of calculate the annihilation cross section for two baryons, say $p\bar p\to\pi\pi$ or $p\bar p\to\gamma\gamma$. The problem here is that we cannot use the usual ...
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131 views

Integrating the differential scattering cross section

In classical scattering theory, the differential scattering cross section, σ(Ω), is defined such that σ(Ω)dΩ is the number of particles scattered into the differential solid angle dΩ in the direction ...
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52 views

Relationships between optical depth, $\tau$, and probability of being scattered

The optical depth is given by many as: $$ \tau=n_e\sigma_{cs}L $$ Where $n_e$ is the number density of the medium, $\sigma_{cs}$ is the scattering cross section and L is the linear extent of the ...
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49 views

How to integrate over a circle in sperical coordinates

I have an angular distribution $\frac{s \sigma}{d\Omega} = \frac{d\sigma}{d \left(\cos\theta\right) d\phi}$. How can I calculate it over a circle which lies on the plane $X = dist$, has radius $r$ and ...
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120 views

How to calculate scattering amplitude from lagrangian? (quantum field theory)

I'm doing a question in Mark Srednicki's Quantum Field Theory. (Question 10.5) Which says that, when one changes a free field $\phi$ to $\phi + \lambda\phi^2$, the Lagrangian density would include an ...
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27 views

How to intergate the cross section over the surface of a detector?

My beam moves along the $X$ axis. I know the cross section $\frac{d \sigma}{d \Omega}$. My rectangular detector is perpendicular to the $XY$ plane and its surface is perpendicular to the line ...
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57 views

Why does cross-section decrease with density?

I read on the wikipedia page for cross-section, that cross-section is related to the reciprocal of a material's density. This seems entirely counter-intuitive. Is there an intuitive reason for this? ...
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21 views

FESR: Relation Between Total Cross Section and Spectral Function

In the papers I am reading the total cross section of electrons, positron scattering into hadrons can always be written in terms of an integral of a weight function w(s) and the spectral function ...
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148 views

Rutherford scattering: Alpha particle scattering angle probability

An alpha particle (charge $q$) of energy $E$ is normally-incident upon a flat surface made of material with atomic number Z, number density n, and thickness d. What is the probability that it will ...
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19 views

Evaluation of width function; thermal neutron scattering cross section

I am attempting to perform some molecular dynamics simulation, based off of this paper, and do not have the slightest clue how they evaluate the width function (Eq. 4). My attempt at figuring it ...
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81 views

Spin sums in cross sections. Summing amplitudes or probabilities?

The context: I'm calculating the cross section for a scalar particle to decay into a fermion-antifermion pair in Yukawa theory, at tree level. In doing this, when calculating the amplitude from ...
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174 views

Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
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58 views

Intuitive explanation of differential scattering cross-section

I'm looking for a conceptual, intuitive understanding of the differential cross section (classical scattering). Its origin, its use, the general process for derivation (conceptually, rather than the ...
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244 views

Converting between $\frac{d \sigma}{d t}$ and $\frac{d \sigma}{d \Omega}$

I'm performing some simulation where I require the integration of a cross section of the form $$\sigma = \int_{-s}^{0}dt \frac{1}{(t-\mu^2)^2} f(\theta,\phi)$$ where $s$ and $t$ are the usual ...
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143 views

Why does an interaction see the proton instead the quark mass?

When an interaction goes deep in the nucleus, should we have some way to interpolate between the proton mass and the quark mass which is going to be the ultimate destination of the interaction? For ...
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Bound state of $\mu^- \mu^+$ . Why non-relativistic muon states?

Peskin & Schroeber page 148 discuss the creation of a $ \mu^+ \mu^-$ resonance state . Equation (5.44) describes the creation of a Spin Up bound $ \mu^+ \mu^-$: $$ \mathcal{M} = \sqrt{2M} \int ...
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65 views

Is this possible to determine exactly the scattering angle for inverse-cube force?

I am trying to determine the scattering cross section for the potential $$ V= \frac{a}{r} + \frac{b}{r^2}$$ As I am completely stuck while determining the scattering angle (I don't see a way to ...
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66 views

Rate of interaction of free electron with photons from sunlight

How many photons does a free electron (in sunlight say) interact with per second? I did a rough calculation assuming the electron interacts with any photon that enters through an area the size of ...
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213 views

Is this statement correct or incorrect: Moving objects undergo length contraction because they appear in space-time cross-section

Why or why not? This is closely related to another question I posited here, Does it make sense to say that objects moving at relativistic velocities appear in space-time cross-section? What I mean ...
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Does it make sense to say that objects moving at relativistic velocities appear in space-time cross-section?

Let object A move at relativistic velocity relative to a frame O. In 4D space-time (Minkowski diagram) the space view of O at any given moment of its own time is a space-like hypersurface (hyperplane, ...