Scattering is a general term for several physical processes in which radiation of some sort changes direction due to an interaction with a particle. Scattering can be classified by the type of radiation (ie, electromagnetic, x-ray, neutron), or by the relative sizes of the wave and the particle (ie, ...

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110 views

What is the physical interpretation of the automorphism on bounded operators induced by an S matrix?

In a QFT, the S-matrix $S$ is a unitary operator, that fixes the vacuum and commutes with the unitary operators implementing the action of the Poincare group on an appropriate Hilbert space $H$. ...
6
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88 views

$WW\to t\bar{t}$ growth

I was told recently that "it is well known that processes like $WW\to t\bar{t}$ ($t$ being a top, or any massive fermion) grows linearly with the energy in the absence of an Higgs boson." Does anyone ...
4
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0answers
133 views

What is the rigorous description of scattering in relativistic QFT?

The first conundrum is what picture of QM to choose, in order to describe such a scattering. Unlike in non-relativistic QM, in RQFT the three all-known pictures are not at all equivalent. The ...
4
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130 views

Pole in reflection/transmission coefficient and bound states

I was working on a scattering problem in a quantum mechanical system with Hamiltonian $$H_1=A^{\dagger}A=(-\partial_x+W(x))((\partial_x+W(x))).$$ One can show that a 'supersymmetric' partner to this ...
4
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150 views

Will a black hole cause scattering of a gravitational wave?

In my GR textbook, it states that gravitational waves can undergo interference but not scattering. I am just starting the chapter on linearised gravity concepts (weak field approximation) and my ...
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222 views

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 $r\...
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90 views

How to prove that identical particles are attracted or repelled in a given spin-s interaction theory?

Let's assume that we have integer spin interaction theory (EM field, linearized gravity, arbitrary gauge spin s theory). How to prove the consequence that in interaction theory with spin $s = 2n$ two ...
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85 views

Is it necessary to use decay width calculated at the same order as the scattering process?

I would like to calculate higher order corrections to a process for which there is an intermediate resonance which subsequently decays into lighter states. I am confused about how to treat the width ...
4
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128 views

Can $\langle\Omega|f|\Omega \rangle$ always be reduced to $\langle0|f|0\rangle$?

I've not come across any expression involving $\langle\Omega|f|\Omega\rangle$ in Srednicki's QFT book (please correct me if these exist there). On the other hand, they are abound in Chapter 7 of ...
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166 views

Delta normalization and density of states in the Golden rule of Fermi

In the text-book derivation of first order inelastic scattering amplitude, box normalization is usually used to calculate the result. This leads to a correct result through the Golden Rule of Fermi, ...
4
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163 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
4
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813 views

Raman Scattering and the Kramers-Heisenberg Formula

Using the words of the wikipedia article Raman Scattering: The Raman effect corresponds, in perturbation theory, to the absorption and subsequent emission of a photon via an intermediate ...
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52 views

How to correctly calculate the colour of the sky?

It is well-known that the sky is blue due to Rayleigh-scattering. What bothers me though is the question how to actually calculate the spectrum of the scattered sunlight. Yes, use one of the ...
3
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16 views

On the right-angled fork track of alpha particles

In high school we were told that the idea "alpha particles are actually helium nuclei" came from observing the right-angled fork track, produced by placing an alpha source in a diffusion cloud chamber ...
3
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71 views

S-matrix and derivative interaction

I just read in some lecture notes that formally we can write the S Matrix as: $$S=T(e^{-\int_{-\infty}^{+\infty} H_{int}dt}) $$ Where $T$ is the normal product and $H_{int}$ is in the interaction ...
3
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50 views

Physical poles in QFT scattering amplitudes?

In QFT, for instance in $\phi^3$ theory, the scattering amplitudes are said to be constrained to feature so called "physical poles" only. Consider generalized Mandelstam variables $$s_{ij},s_{ijk},s_{...
3
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105 views

False sunset and false sunrise time estimation

False sunset and false sunrise are described . Here is a sample day rise and set time according to AccuWheather site and calculated value of sunrise and sunset in my country. Could you please help ...
3
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105 views

How exactly analyticity of S-matrix comes from causality principle?

Recently I've read that analyticity of S-matrix ($S(k)$, where $k$ corresponds to momentum, may be analytically extended into complex values of momentum) comes from causality principle. How to prove ...
3
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305 views

Derivation of the Lippmann-Schwinger equation

I was trying to understand the derivation of the Lippmann-Schwinger equation in Sakurai's Modern Quantum Mechanics, Section 6.1. Our teacher presented a much simpler derivation, similar to that on ...
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124 views

Clarification about Bragg's law explanation

The Wikipedia has this illustration of Bragg's law and then says The two separate waves will arrive at a point with the same phase, and hence undergo constructive interference, if and only if ...
3
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92 views

String Vertex Operators in Light Cone Gauge

I have a basic confusion about how to compute string scattering amplitudes in light cone gauge, using the operator formalism reviewed in GSW. I am familiar with the covariant gauge formalism, where I ...
3
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0answers
98 views

Conversion of QCD cross section formula

I'm writing a program to calculate NLO cross sections for semi-inclusive high-$p_T$ pion production in proton-proton-collisions for my bachelor thesis. I've got a paper describing the production ...
3
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0answers
165 views

Partial waves and the velocity expansion of a scattering cross section

I'm confused about the relation between the velocity expansion of a scattering cross section and the angular momentum (partial wave) expansion. For example, for dark matter annihilation, we write $\...
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50 views

Scattering theory on Schrodinger and Feynman languages

Recently I heard that both of "languages" of scattering theory (formal solution by method of classical scattering theory and its reworking by Feynman with his rules) predict virtual particles. But for ...
3
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0answers
165 views

Møller scattering: twisted?

I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?
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39 views

What are the differences (if any) between the Dyson's series definition and the “in/out” definition of the $S$-matrix

So long, in my QFT courses, I've seen two definitions of the $S$-matrix: The first, more elementary, definition is given in the interaction picture: $$S=\text T \lbrace \exp [-i\intop \text d ^4 x \,...
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30 views

Why do vortices scatter at right-angles

I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him. In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ...
2
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54 views

Question on in and out states in chapter 10 of Weinberg's QFT volume 1

In chapter 10 section 2 (on pomology) of Weinberg's QFT volume 1, he shows $G$ has a pole when the external line goes on shell. In the proof, he inserted a complete set of single-particle states $\...
2
votes
0answers
35 views

How to calculate material depth at which penetrating radiation direction becomes randomized?

Consider a very light particle impinging on a material composed of atoms which are effectively infinitely heavy (e.g., because they are bound together and stiff). If the scattering with nuclei is ...
2
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46 views

X-rays scattered at righ angles of the incident ones: are they polarised?

Basic books dealing with the interaction of X-rays with matter ussually don't mention anything about the polarisation, but I read somewhere that X-rays scattered in matter are linearly polarized, ...
2
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181 views

What is the relation of scattering, extinction and absorption cross sctions with scattering parameters?

In optics and electromagnetics, they frequently calculate the extinction, scattering or absorption cross sections of a single particle (e.g. a sphere). Scattering cross section which is the ratio of ...
2
votes
0answers
22 views

Main differences between elastodynamic and light scattering when using S-matrix to find bound states

What are the main differences (top 5 if question is too broad), for using the S-matrix to find bound states, between elastodynamic and light scattering? (if it facilitates a higher quality question/...
2
votes
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141 views

Optical Theorem ,how can experiment distinguish the unscattered wave from the forward scattered wave?

How can experiment distinguish the unscattered wave from the forward scattered wave? The Optical Theorem says the imaginary part of the forward wave determines the cross section for an initial two-...
2
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111 views

How do I determine resistivity from electron defects of high purity gold?

I am trying to create a plot for the electrical resistivity of high purity gold from 1 K to 1000 K. I found gold's resistivity at 300 K using the Wiedemann-Franz Law based on thermal conductivity data ...
2
votes
0answers
48 views

Difference between positron and electron scattering in Coulomb field

In first order of perturbation theory the S-matrix amplitude for electron scattering in the Coulomb field will be (up to normalization factors) $$ S_{fi} = \frac{iZ q^2}{\sqrt{2E_{f}2E_{i}}}\bar {u}(...
2
votes
0answers
82 views

How to prove the equivalence of two definitions of the scattering cross section

I have noticed that there are two definitions of differential scattering cross section in non-relativistic quantum mechanics. One of them is the most popular, particularly it is used in the book of ...
2
votes
0answers
764 views

Radial Wave Function for Spherical Squared Well Potential and $S$-Matrix

I have a problem with this exercise because I really don't know how to proceed. It's related with the "S-matrix". In class we saw this example: Consider the spherically symmetric potential: $$V(r)=\...
2
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60 views

How common is compromised reference data for physical properties of materials and elements?

This question concerns Monte Carlo simulation of electron scattering in complex material structures, especially the reliability of publicly available source codes and reference data for physical ...
2
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0answers
474 views

QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...
2
votes
0answers
95 views

Mie Scattering for spheres with constant dipole moment

I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a ...
2
votes
0answers
68 views

Origin of crossing relations in relativistic scattering amplitudes

What is the origin of crossing relations in relativistic scattering amplitudes? At first I thought it was CPT, but then it turned out that was not correct. That is, what is the formal reason that ...
2
votes
0answers
174 views

Parton Distribution Functions, average cross section of the nucleon

Say we are given the scattering cross section for neutrinos from $d$ and $\bar{u}$ quarks as $\frac{d\sigma^{d}}{dQ^2}=\frac{G_F^2}{\pi}$, $\frac{d\sigma^{\bar{u}}}{dQ^2}=\frac{G_F^2}{\pi} (1-y)^2$, ...
2
votes
0answers
58 views

How to write down the detailed balance (microreversed) amplitude

I know that time-reversal of a reaction and the detailed balance (microreversed, or reciprocal) reaction are different. Textbooks on scattering theory explain how to relate the S-matrix elements of a ...
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vote
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15 views

How can tree level amplitudes have poles? And how can amplitudes have dimensions?

Consider the $\phi^{3}$ theory, whose lagrangian is $\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}-\frac{\lambda}{3!}\phi^{3}$ The amplitude for tree level (2->1) process is simply ...
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0answers
28 views

Doubt regarding scattering and bound states in quantum mechanics

I just started studying quantum mechanics from Introduction to Quantum Mechanics by D. J. Griffiths. At the beginning of the second chapter, he proves that we cannot have negative energies in the time-...
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53 views

Decoherence: What is the spectral density of a bath of gaseous particles?

I am studying the decoherence theory of a two-level system in interaction with a background gas. Caldira and Leggett (1987) showed that any environment can be modeled by a bath of harmonic oscillators....
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16 views

Generic Rayleigh effect experiment - nothing happens for water

On youtube, a bunch of Rayleigh scattering experiments (e.g this one are set up with some compound being added to water in order to invoke the effect. Why is there no Rayleigh effect for "pure" water?...
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20 views

Difference between 'merging' and 'matching' procedure

For combining scattering processes with different jet-multiplicities in the final state, higher order corrections and parton shower, merging/matching procedures need to be applied to avoid double-...
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31 views

Bremsstrahlung in body tissue

As far as I know, the intensity of the produced radiation from bremsstrahlung is proportional to: $$I \propto \frac{Z^2}{m^2},$$ where $Z$ is the atomic number, and $m$ is the mass of the particle. ...
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39 views

Lippmann-Schwinger equation and time dependence

Consider the Lippmann-Schwinger equation (LSE) $$ |\psi\rangle = |\phi\rangle + \hat{G}_0(\epsilon) \hat{V} |\psi\rangle \tag{1}$$ where $\hat{G}_0(\epsilon) = \frac{1}{\epsilon - \hat{H}_0 + i\eta}$...