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Questions tagged [scattering]

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, Rayleigh, Mie, geometric).

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172 views

Is the converse of Weinberg's statement on the cluster decomposition principle true?

In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says: We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster decomposition ...
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197 views

How does Weinberg conclude that momentum and angular momentum are unperturbed by interaction terms?

In Weinberg's QFT volume 1, chapter 3.3, just below equation 3.3.19, he says $\vec P=\vec P_0$ and $\vec J=\vec J_0$ can be(easily) concluded from the definition of Møller wave operator or ...
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460 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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1answer
550 views

Continuity of Logarithmic derivative in Scattering theory

I have a problem in understanding why we consider the continuity of the Logarithmic derivative of the wave function at the boundary of the Scattering Potential? I understand that physical arguments ...
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159 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 $H$. ...
5
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1answer
89 views

Can we see stars in day time by making use of a blue notch-filter?

Given on a clear sunny day, the only light that is blocking the star light is the scattered blue light of atmosphere. If we make use of a notch filter, which blocks only the blue light, can we get ...
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96 views

Relativistic scattering off Dirac delta potential

Consider the case of a relativistic electron on a graphene lattice described by the Hamiltonian $$ \mathcal{H} = v\begin{pmatrix} 0 & p_x+ip_y \\ p_x-ip_y & 0 \end{pmatrix}, $$ where $v$ is ...
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315 views

Weinberg's S-matrix and split into free and interacting Hamiltonian

TL;DR: How can states of an interacting QFT asymptotically follow the trajectories governed by the free Hamiltonian, when, say, the free and interacting groundstates are different, and the states look ...
5
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469 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 ...
5
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748 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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1k 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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93 views

Can bound states have zero energy?

Suppose a system is under the influence of a potential which vanishes at $\pm \infty$. Now we know that if the energy of the system is negative ($E<0$) then the system is in a bound state and the ...
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156 views

Scattering, absorption, emission and virtual photons

From reading many questions on this site I have the following conclusions: Interaction of a photon and a free electron is an instantaneous process of scattering (transfer of momentum) between said ...
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228 views

1D Quantum scattering from $V(x) = e^x$

Define $V(x) = e^{x}$, $x \in \mathbb{R}$ and consider the Hamiltonian $H = - \frac{d^2}{dx^2} + V(x)$. The eigenvalue problem is $$ -\psi''(x) + e^{x} \psi(x) = E \psi(x)\,, \quad x \in \mathbb{R}\,. ...
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136 views

What happens to the incident electromagnetic wave in Rayleigh scattering?

In Rayleigh scattering an incident EM wave causes an induced dipole oscillation of an atom/molecule, which in turn causes radiation at the same frequency of the incident wave. But what happens to the ...
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172 views

Why does $U(+\infty,-\infty)|0\rangle= e^{i \theta}|0\rangle$ hold ? i.e. time evolution of vacuum is still a vacuum

In quantum field theory, we always use $U(+\infty,-\infty)|0\rangle= e^{i \theta}|0\rangle$, where $$U(+\infty,-\infty)=\lim_{\epsilon\rightarrow +0} \mathcal{T}\exp\{i \int_{-\infty}^{+\infty} e^{-\...
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193 views

What is the refractive index of an electron?

Consider a free electron or electron bunch, would it have a corresponding refractive index? At low or high energies, the effects are obviously much different. I am curious to know (I haven't found) ...
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281 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 ...
4
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468 views

Convergence of light by light scattering amplitude

Perhaps I'm too exhausted to see the answer of why the photon-photon scattering should contain no divergences. In Peskin and Schroeder page 320 we find that because of the Ward identity the photon-...
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116 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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92 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 ...
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168 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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271 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, ...
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223 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 ...
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1answer
43 views

Thickness of a target bombarded with deuterium

I need to calculate de thickness of a sheet of Zinc that is being bombarded by deuterium nuclei. I'm given that the fraction of nuclei dispersed below $\theta=90º$ with $T=8MeV$ is $0.9999$ and the ...
3
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156 views

QFT cross section: missing information?

So I'm having a hard time understanding how the (QM) cross section fits into the general picture, of e.g. collider experiments. So we can calculate cross sections (for one reaction) exactly in QFT ...
3
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112 views

Angle between velocities: Elastic collision question in 3D

I have been given a scenario of a proton (particle 1) travelling with u1 = 3î+ 4j–6k and a Helium-3 nucleus (particle 2) travelling with u2= 3î+ 4j–2k. The two particles collide and the proton (...
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99 views

How can LSZ formalism deal with “glancing blows”?

My recent answer to the question Scattering, Perturbation and asymptotic states in LSZ reduction formula got me thinking again about wave packets and the LSZ reduction formula. In my answer, I claim ...
3
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54 views

What Exactly is the “Optical Limit” in High energy hadronic collisions?

I am a little confused about what "Optical Limit" means in the context of hadronic diffraction. In some text it says that is the case where $A$, $B$ goes to infinity, where $A$ and $B$ are the ...
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73 views

Optical Conductivity and Scattering rate - Physical intuition

Why does the real part of conductivity increase with increase in scattering rate at frequencies much larger than the scattering rate? I understand the mathematical implication, but do not understand ...
3
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414 views

S-matrix for $\phi^3$ theory

In the book Quantum Field Theory for the gifted amateur by Tom Lancaster & Stephen J Blunden, in the chapter about expanding the S matrix they give an example using the $\phi^4$ Langrangian, $$ \...
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62 views

Møller Opeartors and dressing relations: what picture?

Møller operators can be defined as (Urban, 2013;pg70): \[ \newcommand{\ket}[1]{\left|#1\right>} \newcommand{\braket}[2]{\left<#1|#2\right>} \Omega_{\pm}=\underset{t\rightarrow \mp 0}{\...
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56 views

Why do scattered waves vanish when the wavenumber of the incident wave is an eigenvalue of the interior Dirichlet problem. Where has the energy gone?

I normally work with numerical computations for wave scattering, but I am now trying get a better understanding of the physical processes underlying the theory, in particular what happens to the ...
3
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67 views

Topological insulators: What does the scattering matrix at an topological edge tell about the Chern number?

In class we were briefly discussing, that one way to see if the edge of a TI carries a state is to consider the scattering of a lead that is attached to this edge. In fact the argument was more ...
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100 views

Non-relativistic scattering amplitude

For the nonrelativistic scattering in a potential $V$, the scattering amplitude $\vec{p}$ to $\vec{k}$ is proportional to $$<\vec{k}|V|\phi^{+}_\vec{p}>,$$ with $$E(\vec{k})=\frac{\vec{k}^2}{2m}=...
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516 views

Optical Theorem - Imaginary part

The optical theorem in Quantum Mechanics states: $$Im(f(\theta=0))= \frac{k}{4 \pi} \sigma_{out}.$$ Where $f$ is the scattering amplitude, in this case for an angle $\theta = 0$, i.e. in forward ...
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132 views

Inverse Scattering Transform (IST) for the Linear Schrödinger Equation

I know that the Inverse Scattering Transform (IST) has been employed to solve, for instance, the KdV equation and I believe also other nonlinear PDEs, such as the NLS. However, if we consider the ...
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163 views

What picture is the $S$-matrix defined in?

I am looking into the definition of the $S$-matrix, and have found two different cases. Firstly I have seen it derived that (see here, link to Google books p110): $$ S=U_S(\infty,-\infty)$$ But more ...
3
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1answer
255 views

Questions from Srednicki's Introduction to Interacting Field Theory using the LSZ Formula

I have been reading through the chapter on the LSZ Reduction Formula from Srednicki's Quantum Field Theory, and I have a few questions about which I'm sort of confused. The questions are referenced ...
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195 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 ...
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191 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 $\...
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44 views

Please help me understand this simple model for energy loss in backscattering experiments

I'm using Dr. Wei-Kan Chu's book on backscattering spectrometry for self-study. Early on in the book he describes how a projectile entering a material loses energy as it progresses through the ...
3
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1answer
106 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 ...
3
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0answers
288 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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0answers
333 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 ...
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246 views

Metastable bound state in resonance scattering

In resonance scattering, why does the mean lifetime of the "metastable" bound state depend inversely on the width of the resonance?
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666 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 ...
3
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165 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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175 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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1answer
202 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}(...