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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Potential step and exponential decay?

Let us say we have a wave going from a region ($x<0$) where the potential is $U_1$ to a region ($x>0$) where the potential is $U_2$. The wave function in the second region takes the form: ...
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1answer
20 views

Complex scaling method for solving resonance states

I am now reading about the complex scaling method for solving resonance states. As far as I understand, the procedure goes like this: Let us take the 1d potential $V(x) = A e^{-x^2} x^2 $ as an ...
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2answers
103 views

Is the plane wave model always valid in reflection and transmission?

my question is related to another one I asked, but I foolishly made that question about several things (experiment, computation, theory) at once so it was confused. I was talking to my boss about ...
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1answer
93 views

Forward-scattering off a potential well

In his book, James Binney writes the following: My question is what is the meaning of this expansion as $1+T$? I say this because you don't tend to consider the possible "paths" that a particle ...
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1answer
129 views

What is the most accurate experimental confirmation of Rutherford's $\sin^{-4}\phi/2$ law?

What is the most accurate experimental confirmation to date of Rutherford's $\sin^{-4}\phi/2$ law, where $\phi$ is the scattering angle?
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1answer
264 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 ...
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15 views

Why don't we see a totally circular rainbow in the sky [duplicate]

We know that the rainbow is formed due to the scattering of light. We always see the rainbow in a semicircular style. Does it is possible that we can ever see a totally circular Rainbow.
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0answers
23 views

Rayleigh scattering equation for optical frequencies

I would like to know if there is an empirical/generic equation for Rayleigh scattering at optical frequencies in the atmosphere, similar to the Mie scattering model from Kim and Kruse which states ...
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0answers
21 views

Metastable $E=0$ s-wave bound state in a spherical potential well

I am currently dealing with scattering theory. I looked up the scattering on a spherical well potential. $$V(r) = \begin{cases} -V_0 & , r \leq R\\ 0 & ,r > R \end{cases} $$ where ...
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2answers
694 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 ...
2
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0answers
20 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 ...
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32 views

$e^- e^+ \to \mu^+ \mu^-$ scattering in a general $R_\xi$-gauge [closed]

I am working out the scattering cross section at tree level of the process: $$e^- e^+ \to \mu^+ \mu^-$$ in general $R_\xi$-gauge, namely: $$\mathcal{L}=-\frac{1}{4}F_{\mu \nu }^2 ...
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45 views

Quantum Physics - Step Potential? Don't understand it and how it relates to debroglie wavelength

Ok so I posted a question in the wrong format so it got closed, I hope this one is formatted better. I have a revision question that gives me the total energy of the electron, it then states that the ...
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0answers
18 views

Inhomogeneous scattering from a dielectric box in 2D?

I wrote an E&M simulator and need to verify the accuracy. My simulator evaluates a 2D grid (which is what my camera measures), and would like to test an object that is minimally perturbed by ...
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1answer
48 views

Scalar Yukawa theory derivation

I am using Tong's notes for QFT, and on page 59 there is a derivation for the scattering amplitude of $\psi\psi \rightarrow \psi\psi$ in Scalar Yukawa theory. It goes from here: $$\langle ...
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2answers
199 views

Quantum theory of light

What's the scattering matrix for a PBS (polarization beam splitter)? Is it just unitary? If one polarization never couples into another polarization (then there's a lot of zeroes in that 4x4 matrix) - ...
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3answers
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Does the Breit Wigner formula apply to intermediate virtual particles?

Breit Wigner Formula describes the cross section for interactions that proceed dominantly via a intermediate particle (O*) A+B → O* → C + D: $$σ = \frac{2\Pi}{k^{2}}\frac{Γ_{i}Γ_{f}}{(E-E_{o})^{2} + ...
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1answer
170 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
2
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1answer
74 views

Why does not Bhabha scattering contain u-channel diagram?

$e^+e^-\rightarrow e^+e^-$ is called Bhabha scattering. Let us only consider the tree level Feynman diagrams of this process. Apparantly, there are s-channel and t-channel diagrams as shown in the ...
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1answer
48 views

Scattering of slow neutrons

I've here a spectrum which was obtained from the scattering of slow neutrons on uran. But I'm not sure what I'm actually see there. Can someone explain the "scattering of slow neutrons"? Edit: ...
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0answers
12 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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2answers
281 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 $B$: ...
2
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1answer
38 views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as ...
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1answer
76 views

Increase contrast on the image taken by CCD camera

I project a pattern on a reflecting object and I capture the reflected pattern (reflected via the object) using a CCD camera. However, the reflected pattern has a very low contrast (due to volume ...
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0answers
38 views

Free particle scattering in 2D using polar coordinates

The free particle hamiltonian commutes with the angular momentum operator L and Lz, so we can use a spherical wave basis instead of the regular plane-wave basis |k>, using spherical Bessel function ...
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3answers
60 views

Why stars are white? According to Rayleigh Scattering

According to Rayleigh Scattering, the red waves are capable of travelling a long distance, so that only we are seeing the Sun as reddish during Sunset and Sunrise. If this was true then all other ...
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1answer
26 views

What is the charge/matter distribution?

I am a mathematics student who is doing an introductory course in nuclear physics and since the course is rather elementary a lot of the definitions/derivations are skipped which makes it quite tough ...
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23 views

Correlation function and scattering amplitude in critical phenomena

When we use scattering radiation to probe critical phenomena, we have the usual Bragg relation for constructive interference $$|\vec{k}|=\frac{4\pi}{\lambda}sin\frac{\theta}{2}$$ where $\vec{k}$ is ...
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89 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 $H$. ...
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40 views

The interaction between waves and particles according to their wavelength [duplicate]

Why do EM waves with a large wavelength like those in the red range (and radio waves) interact with particles less than those in the blue range? That is the reason why the sky is blue, is that right? ...
5
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1answer
372 views

Why can't Compton scattering happen in leading order of perturbation theory?

Why is the matrix element of Compton scattering in leading order of perturbation theory equal to zero? Why can this process only be described in second order of perturbation theory, i.e. with exchange ...
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0answers
64 views

potential barrier scattering when particle energy equals to the barrier height

What happens if we have $E=V$, where $E$ is the energy of a incoming particle and $V$ is the height of a square potential barrier? This wiki page actually gives a finite transmission probability for ...
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1answer
95 views

Finding finite square well width and depth from transmission resonance

For an electron incident a one-dimensional finite square well the transmission probability is $\approx$1 for electron energies $E_1=0.6 \textbf{ eV}$, $E_2=1.9 \textbf{ eV}$ and $E_3=3.4 \textbf{ ...
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5answers
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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?
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1answer
207 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
4
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1answer
49 views

What causes these rainbow effects using a polarizing filter on an airplane?

I know that light reflected from a surface at 45° is polarized and that for a similar reason skylight arriving from a direction orthogonal to the sun is polarized too. Photographers make use of this ...
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2answers
54 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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0answers
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plane wave state used for scattering calculation

When we do scattering calculation off a potential barrier, normally we would assume some incident plane wave and then make use of the boundary conditions. But how is this corresponding to the ...
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1answer
71 views

Altarelli-Parisi Splitting Function $P_{qq}(z)$ vanishing integral if and only if quark flavour sum rules and equivalence

Question 1: I believe both questions are in the context of Deep Inelastic Scattering. I've been given the expression for $F_{2}^{ep}(x)=(\frac{2}{3})^2[u(x)+\bar{u}(x)] +(\frac{1}{3})^2[d(x) + ...
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31 views

Model of scattering in wet things

You know that clothes and some surfaces become darker when wet (covered in an earlier question: why wet is dark?), because of the disordered reflections or of the refractive index of water or ...
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37 views

Does photon polarization take place without scattering processes?

Behind two perpendicular crossed polarisation filters (for visible light) the intensity of light will be zero. After installing a third filter between the two others non parallel to each of them some ...
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1answer
33 views

What is the reduced width amplitude of an unstable state?

Particularly used in nuclear physics when describing the lifetime (i.e. partial decay width) of a resonant state (a.k.a resonance) is the term "reduced width amplitude". I have searched online, and ...
2
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1answer
74 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
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20 views

How much of the sunshine is scattered into the space?

How much more sunshine will the earth ground receive if without the atmosphere?
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3answers
78k views

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 ...
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0answers
12 views

Solution for elastic wave on plane of ideal contact between two half spaces of elastic, homogeneous, isotropic, linear solids

Please give the solution for elastic wave of arbitrary polarization incident at arbitrary angle on plane of ideal contact (meaning no slip, homothermal, nondissipative, and no transfer of material ...
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1answer
3k views

Plane wave expansion in cylindrical coordinates

I am trying to solve scattering problem in 2D and got to expand the wave function in cylindrical system which comes out to be Hankel function. Can you tell me how to expand the plane wave $\exp(i ...
5
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3answers
118 views

How does a wave packet get scattered?

Particles can be represented as wave packet. So how do particles get scattered? Waves superimpose on one another, they don't bounce off of on one another. It can be seen from picture there is a ...
5
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1answer
32 views

How would a huge ball of air look in space from outside and from inside?

If you replaced the Earth (except the atmosphere) with air and kept the pressure linear to the center (of the now non-existing Earth) while ignoring the effects this would have on gravity and leaving ...
6
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2answers
376 views

Why must an integrating sphere be a sphere?

Why must an integrating sphere be a sphere? Why can't it be an integrating cube? What is the difference? Could I use a cube to measure total illuminance like an integrating sphere does?