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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Scattering of light by light: experimental status

Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
37
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9answers
12k views

Why can't we see gases?

I am not sure what causes gas molecules to be invisible.This question may look silly but I really want to know the story behind it.
29
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4answers
4k views

Why does the sky change color? Why the sky is blue during the day, red during sunrise/set and black during the night?

Why does the sky change color? Why the sky is blue during the day, red during sunrise/set and black during the night?
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3answers
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Why does the moon sometimes appear giant and a orange red color near the horizon?

I've read various ideas about why the moon looks larger on the horizon. The most reasonable one in my opinion is that it is due to how our brain calculates (perceives) distance, with objects high ...
22
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6answers
2k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
21
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2answers
763 views

Covariant Description of Light Scattering at a fastly rotating Cylinder

Let us consider the following Gedankenexperiment: A cylinder rotates symmetric around the $z$ axis with angular velocity $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\...
20
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4answers
3k views

Tree level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
17
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1answer
8k views

Phase shifts in scattering theory

I have been studying scattering theory in Sakurai's quantum mechanics. The phase shift in scattering theory has been a major conceptual and computational stumbling block for me. How (if at all) does ...
16
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4answers
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Why can't I see the blue color scattered by the lower atmosphere of the earth?

I understand that the blue colour of the sky is because of the scattering of blue light by molecules in earth's atmosphere. The scattering appears to be happening from molecules that are far above in ...
16
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2answers
3k views

What is the physical interpretation of the S-matrix in QFT?

A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers. Given a quantum field theory when ...
16
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2answers
822 views

Does the exact string theory $S$-matrix describe all physics there is?

Suppose someone manages to evaluate the string theory $S$-matrix to all orders for any and all vertex operator insertions including non-perturbative contributions from world-sheet instantons and re-...
15
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2answers
1k views

Why Cronin Effect Happens?

I'm looking for explanation on Cronin effect but unfortunately there's no Wikipedia entry or self-contained paper to start from. The statement of this effect is that: "At leading order, multiple ...
13
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3answers
2k views

Center-of-mass frame for massless particles

Given a scattering event where a photon and electron go in and a photon and electron come out, what is the center of mass frame? I'd say, since the photon has no mass, it's the rest frame of the ...
12
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3answers
2k views

What is the capture cross-section of a black hole region for ultra-relativistic particles?

What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is $$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$ for a Schwarzschild BH in the geometric ...
12
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3answers
5k views

Why is it necessary for an object to have a bigger size than the wavelength of light in order for us to see it?

I keep hearing this rule that an object must have a bigger size than the wavelength of light in order for us to see it, and though I don't have any professional relationship with physics, I want to ...
12
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1answer
1k views

When we define the S-matrix, what are “in” and “out” states?

I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} \...
12
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2answers
525 views

Locality in the scattering amplitude

Early in this talk by Nima Arkani-Hamed, he describes what locality means for scattering amplitudes. "Locality tells you that the only poles in the scattering amplitude occur when the sum of a subset ...
12
votes
2answers
967 views

Why can the Euler beta function be interpreted as a scattering amplitude?

The Wikipedia article on the Veneziano Amplitude claims that the Euler beta function can be interpretted as a scattering amplitude. Why is this? In another word, when the Euler beta function is ...
11
votes
1answer
276 views

Why do some sunsets have a green flash?

Some sunsets exhibit a phenomenon called "green flash," where there is a quick flash of green light right as the sun is setting. I have seen this myself several times, and sort of understand it. I am ...
10
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1answer
1k views

Green's function in path integral approach (QFT)

After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with. I have the ...
10
votes
2answers
785 views

Calculation of the cross section

Why, when we calculate the total cross section, we make the average other initial states and the sum over final states?
10
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1answer
3k views

Proof of Yang's theorem

Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
10
votes
1answer
637 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
9
votes
2answers
1k views

Optical theorem and conservation of particle current

The optical theorem $$ \sigma_{tot} = \frac{4\pi}{k} \text{Im}(f(0)) $$ links the total cross section with the imaginary part of the scattering amplitude. My lecture notes say that this is a ...
9
votes
2answers
670 views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
8
votes
4answers
527 views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
8
votes
1answer
792 views

Is the total cross section a Lorentz Invariant?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
8
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1answer
368 views

There are two definitions of S operator (or S matrix) in quantum field theory. Are they equivalent?

I read several textbooks of QFT and found that there are two kinds of definition of $S$ operator (or S matrix). First kind: Define $\hat{S}$ is map from out space to in space $$\hat{S}\left|\beta,\...
8
votes
1answer
388 views

Setting of renormalization scale in field theory calculations

In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
8
votes
2answers
338 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
8
votes
1answer
279 views

Significance of Poles of Correlation Function in QFT

In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
7
votes
3answers
282 views

Contradictory result for scalar-field propagator from Feynman rules and LSZ formula

I am trying to learn how to calculate scattering amplitudes in a Klein-Gordon theory. I am getting stuck with the simplest of the examples: $\phi\to\phi$ in a free scalar-field theory. If I calculate ...
7
votes
3answers
887 views

Physical interpretation of infinite total cross section

What does it tell us about a process, say A+B->C+D, if the calculated total cross section is infinite?
7
votes
2answers
669 views

Why are neutrino and antineutrino cross sections different?

Particularly in the case of Majorana neutrinos, it seems a little odd that the particle and antiparticle would have differing cross sections. Perhaps the answer is in here, but I've missed it: http://...
7
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4answers
1k views

Is forward scattering = no scattering?

What is forward scattering? If it is equivalent to no scattering, then why not call it "no scattering"?
7
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2answers
635 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' |...
7
votes
2answers
988 views

Infinite and Finite Square Wells

For the infinite square well in the first region, outside the well: $$\frac{-\hbar^2}{2m}\frac{d^2 \psi}{dx^2} + V(x) \psi (x) = E \psi (x),$$ where you set $V = 0$. Rearranging gives $$\frac{d^2 \...
7
votes
1answer
770 views

Charge Renormalization and Photon Propagator

I'm trying to understand charge renormalization in QED. I know that one can write the full photon propagator as $$\frac{-i\eta_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ where $\Pi$ is regular at $0$. Obviously ...
7
votes
1answer
203 views

Importance of MHV amplitudes

Why are MHV amplitudes so important? How/where are they used and why do people keep trying to rederive them in many different ways?
7
votes
1answer
362 views

How do ideas of leading singularities and Grassmanian help in curing infrared divergences when calculating N=4 scattering amplitudes?

Broadly speaking how do ideas of leading singularities and Grassmanian help in curing infrared divergences when calculating N=4 scattering amplitudes? My understanding is that one gets infra red ...
7
votes
1answer
390 views

Why does the conductivity $\sigma$ decrease with the temperature $T$ in a semi-conductor?

We performed an undergrad experiment where we looked at the resistance $\rho$ and Hall constant $R_\text H$ of a doped InAs semiconductor with the van der Pauw method. Then we cooled it down to around ...
7
votes
1answer
366 views

Are the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ from field theory?

When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and $\...
7
votes
1answer
246 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 ...
7
votes
2answers
364 views

Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson $\psi(p_1)\psi(p_2)\rightarrow\psi(p_1')\psi(...
7
votes
1answer
207 views

Do small-angle coherent scattering experiments really see coherent effects over arbitrarily large distances?

Short version After integrating over all possible outgoing angles, the total cross-section of coherent elastic scattering from a fixed target of characteristic length $L$ scales like $L^4$. Does ...
7
votes
1answer
126 views

Some more questions about the BCFW reduction

This question is a continuation of this previous question of mine and I am continuing with the same notation. One claims that one can actually split this $n$-gluon amplitude such that there is just ...
7
votes
1answer
163 views

Does QED provide a closed form for Coulomb logarithms?

The classical models for the integrand as well as the cut-offs in computing the Coulomb logarithm are pretty rough. Does quantum electrodynamics have definite expressions for the quantity $\...
6
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5answers
7k views

Why is the sky of the moon always dark?

Why is the sky of the moon always dark compared to the sky of the earth, doesn't it have day and night like earth?
6
votes
4answers
824 views

Why is the sky blue: For a 3-year old [duplicate]

My nephew asked me yesterday why the sky was blue. I tried to explain it to him as best and as dumbly I could, but I failed. I tried to explain the concept of scattering of light using an analogy of ...
6
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4answers
13k views

What is the difference between Raman scattering and fluorescence?

What is the difference between Raman scattering and fluorescence? Both phenomena involve the emission of photons shifted in frequency relative to the incident light, because of some energetic ...