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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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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36 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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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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57 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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20 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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50 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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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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104 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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24 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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78 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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85 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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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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48 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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78 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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25 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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49 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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20 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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66 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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18 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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1answer
55 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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156 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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45 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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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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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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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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189 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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158 views

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, ...
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108 views

Form factor for Proton

To find the charge distribution of proton , we study electron proton scattering and compute the form factor to find the cross section. The form factor comes out to be Fourier transform of charge ...
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31 views

Do exotic states of matter have high fusion cross-sections?

The Lawson criterion suggests that a chain fusion reaction will only occur in a confined plasma. Since it's a product of temperature and pressure (or density) a chain reaction would be virtually ...
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179 views

What determines the probability of creating a particular particle in a collision?

When discussing events at the quantum level, we deal in probabilities and not absolutes. Articles I've read on particle physics state that a particle has a probability of being created in a collision. ...
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Inelastic cross section derivation

I am trying to derive the inelastic cross section (the mass changes). I looked up the elastic derivation on Peskin's book (are there any alternatives?): $$d \sigma = \frac{1}{2 E_a 2 E_b \left| ...
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60 views

Differential cross section $d\sigma/dp^{\gamma}_{T}$?

Why we care about $d\sigma/dp^{\gamma}_{T}$? What the physical meaning of it? Why not plot $\sigma$ follow $p^{\gamma}_{T}$?. As in this picture.
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Total cross section of particle decay

Suppose a particle A travelling along the $z$-axis and decays into particles B and C. The cross section is given by $$\frac{d\sigma}{d\cos\theta^*} = k(1+\cos\theta^*)^2$$ where $k$ is a constant ...
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Scattering amplitude, link between quantum mechanics and QFT

In quantum mechanics, we can define the scattering amplitude $f_k(\theta)$ for two particles as the magnitude of an outgoing spherical wave. More precisely, the asymptotic behaviour (when ...
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colliding point particles

when I draw e.g. the diagram of compton scattering I assume that the electron of given momentum gets 'hit' by a photon and interacts with it. How close does the photon have to get to the electron that ...
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Gamma matrices in Decay Calculations [closed]

I am trying to calculate the transition amplitude, $\lvert M^2\rvert$, for the process where a top quark (momentum p) decays to a bottom quark (momentum q) and a $W^+$ boson (momentum k). I am ...
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1answer
45 views

Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
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Database of experimental cross sections for atomic collisions

Does the atomic-physics community keep a comprehensive database of experimental data (cross sections) for atomic collisions? I am looking for data about Bremsstrahlung, ionization, elastic and ...
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Differential Cross Section

I would like to know what exactly the term differential cross section means. It comes from electron scattering experiments which are used to deduce the charge distribution of a nucleus and the cross ...
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Interaction rates from cross sections in a thermalized gas

Consider a target particle embedded in a gas with a thermal distribution of velocities. If we know the cross section $\sigma$ for interactions between the target particle and a gas particle, how do we ...
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139 views

One dimensional scattering cross section

My quantum mechanics book (http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf, pages 94-95 of the pdf, or 86-87 of the book) considers the one dimensional step potential ...
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Why average incoming spins and sum over outgoing spins? [duplicate]

The book by Griffith on elementary particles reads: A typical experiment starts out with beam of particles whose spin orientations are random, and simple counts the number of particles in a given ...
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89 views

Differential Cross sections from amplitude scattering matrix

How can I get the differential cross sections from the amplitude scattering matrix, $S$ (2x2 matrix)? I've seen this in a Mie solution solver: Parallel Polarized Light: dCsdOp = $\frac{2}{\pi k} ...
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64 views

Units of rutherford singly differentiated cross section for secondary electron production

I have an equation that I have found in several papers which I am currently using for a project, including Waligorski (1986) and this book page 32. 4.2 BUTTS AND KATZ MODEL Butts and Katz ...
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51 views

2-body differential cross section in CM frame discrepancy

The standard equation for the 2-body differential cross section in the CM frame (from several references) seems to be: $$\frac{d\sigma}{d\Omega} = \frac{1}{64\pi^2s}\frac{q}{k}|\mathcal{M}|^2,$$ where ...
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How to write down the Lippmann-Schwinger equation for such a problem? [closed]

Suppose there are three particles, 1, 2, 3. Initially, particle 2 and particle 3 form a bound state. Particle 1 is free. Now we want to study the scattering of particle 1 against the 2-3 bound system. ...
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How to get rid of Dirac deltas in a phase space integration of one final particle procecess?

I was trying to compute a cross section of a process $AB\to{}C$ using formula (4.79) from Peskin $d\sigma=\frac{1}{2E_A2E_B|v_A-v_B|}\frac{d^3p}{2E(2\pi)^3}|M|^2\delta^4(p_A+p_B-p) $ The problem is ...