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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92 views

Lippmann-Schwinger equation and $T$ expansion

Lippmann-Schwinger equation, in operator form, is: $$ T=V+V\frac{1} {E-H_0+i \hbar \varepsilon} T=:V+V\Theta_0T, $$ where $H_{tot}=H_0+{V}$ is the hamiltonian ($H_0$ is the free particle hamiltonian ...
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1answer
708 views

What would the sky look like if the sun was a different type of star?

Barring, of course, all other issues that wold naturally arise from the following question - if we made the sun a cooler, red star or a hotter, blue star, what impact would that have on the colour of ...
-1
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1answer
84 views

Photon energies and attenuation [closed]

I hope you can help. I am trying to understand which attenuation effect (photoelectric, compton scatter and pair production) is dominant at which level of photon energy and why. The levels are 10keV, ...
4
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1answer
189 views

Strange use of complex analysis in Weinberg QFT 1?

In the beginning of chapter 3 on scattering theory in Weinberg's QFT book there is a use of the Cauchy residual theorem that I just cannot get. First some notation, we are looking at states that are ...
3
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1answer
61 views

What type of matrices do we mean by $I_{D2}$ and what is Chandrasekhar decomposition?

Suppose that $A_{2\times 2}$ is a hermitian matrix, so it has real eigenvalues $\lambda_1$ and $\lambda_2$ and corresponding orthonormal eigenvectors $\underline u_1$ and $\underline u_2$ and we know ...
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1answer
91 views

Difference between scattering amplitude and scattering lenght

I'm studying neutron scattering theory and I noticed that one usually writes the scattered wave as a spherical wave: $$\psi \sim \frac{-b} {r}e^{ikr}$$ where $b$ is known as scattering lenght. From ...
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23 views

How is the frequency unchanged in elastic wave scattering with a crystal?

it makes sense that with an inelastic scattering process, a wave approaches a crystal, and then some energy is imparted to the phonons, so that the outgoing wave has a different frequency from the ...
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1answer
66 views

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 ...
3
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1answer
68 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 ...
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1answer
30 views

Non-square transfer matrix from square scattering matrix

I'm trying to construct the transfer matrix for an arbitrary system with 1 input and 2 outputs, like a splitter (shown below) or 1x2 multi-mode interferometer. (Image borrowed from http://www....
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3answers
66 views

Why conductors don't scatter light?

Air molecules can be oscillated by E field and re-radiate EM waves in different directions. However, if light is shined to a conductor the E field oscillate the free charges but the effect is to ...
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2answers
106 views

Will neutral particles be affected by EM waves?

Air molecules scatter sunlight and makes the sky blue. Many books say that the air molecules are oscillated by E field and so they become sources of EM waves. Is it because the air molecules have ...
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43 views

Relaxation time approximation in anisotropic potential scattering event

In relaxation time approximation (RTA) of Boltzmann transport theory, the relaxation time is calculated by $\frac{1}{\tau(\mathbf{k})}=\frac{2 \pi}{\hbar V}\sum_{\mathbf{k^{'}}} \delta (\epsilon(\...
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1answer
263 views

Direct vs. Compound reactions

I know there are different types of direct reactions like inelastic scattering and such. But is the main difference between direct and compound reactions that one excites (Or at least can) the whole ...
4
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1answer
118 views

Dirac delta function definition in scattering theory

I'm studying scattering theory from Sakurai's book. In the first pages he gets to the following expression: $$\langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle n|V|i\rangle\int_{t_0}^...
3
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0answers
204 views

One-particle scattering: LSZ vs Feynman [duplicate]

This question is about Klein-Gordon theory (the field is hermitian). If I calculate the amplitude for the process $\phi\to\phi$, I get two different results depending on whether I use Feynman rules ...
5
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2answers
1k views

Why is space black? [duplicate]

We on earth see the space black only at night. But on moon it observed that the space is black in both day and night even though the source is same for both ( the sun).Why? And also there are many ...
7
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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 ...
2
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1answer
90 views

Difference between Rayleigh scattering and fluorescence spectroscopy [closed]

How can we differentiate Rayleigh scattering from fluorescence spectrum?
3
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1answer
358 views

How is Lippmann-Schwinger equation derived?

I'd like to know the derivation of Lippmann-Schwinger equation (LSE) in operator formalism and on what assumptions it is based. I consulted the Ballentine book as advised in this Phys.SE post, but I ...
0
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1answer
228 views

X-ray diffraction on thin film

As far as I am concerned, when we perform an X-ray diffraction experiment using a Bragg-Brentano diffractometer using the "powder method" we have that the scattering pattern depends on only one angle ...
3
votes
1answer
227 views

Plane wave expansion of cylindrical functions:Summation of the Hankel functions

I understand that; in cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hankel function of integer order times a complex exponential term ($E=H_{n}(kr)e^{in\alpha}...
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0answers
30 views

Optimal wavelength for low IR attenuation under normal atmospheric conditions?

I can't find any good data about the transmit attenuation of infrared light in the atmosphere transmitted horizontally (there is a bunch of stuff detailing penetration of radiation from space, but ...
4
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2answers
505 views

Why can't gravitons be created in traditional particle accelerators?

I've heard that it is incredibly difficult to detect a graviton, but I don't quite understand why. With all of the knowledge I have at the present time it seems like it should be possible to create a ...
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1answer
50 views

Coulomb collision

I was reading an article by N. Bohr and came upon the following problem (the following wording is actually taken from a book by Thompson - Conduction of Electricity Through Gases): Let $M_1, M_2$ ...
3
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106 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 ...
4
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1answer
147 views

Interactions and scattering length in Feshbach resonances

In the context of cold atoms, one can make use of the Feshbach resonance mechanism to alter the sign and value of the two-particle scattering length by applying and varying an external magnetic field. ...
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151 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 ...
1
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1answer
136 views

Deformation parameters of a nucleus

How are the deformation parameters (quadrupole, hexadecapole etc) of a nucleus mathematically related to the reduced transition probabilities $B(El)$ values obtained experimentally?
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1answer
45 views

Multiparticle Mandlestam Variables Extension

So in 4D we have three Mandlestam variables for a 4-particle scattering process. This corresponds to $p_i^\mu$ giving us 16 degrees of freedom. Momentum conservation reduces this by 4, and we have 4 ...
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121 views

Fermion - Antifermion (annihilation) scattering amplitude

I'm trying to get the scattering of the diagrams described here in the "annihilation, part ii" (fermion/antifermion - scalar/scalar) http://www.physics.umd.edu/courses/Phys624/agashe/F10/solutions/HW7....
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0answers
46 views

Scalar spherical wave in terms of Cylindrical coordinates

I am looking at a problem where a scalar spherical wave is scattered by an uncharged cylinder. I want to work in cylindrical coordinates in order to simplify it. Can anyone tell me how to expand the ...
3
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1answer
196 views

Why do we use Mie scattering to describe light scattering off large objects?

I'm an undergraduate student who has recently come across Rayleigh and Mie scattering and I'm trying to understand them a little better. As I understand it Rayligh scattering is used only when the ...
3
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1answer
98 views

How to compute scattering amplitude $\gamma\pi^+\to\pi^+\pi^0$

I wish to find the amplitude for process $\gamma\pi^+\to\pi^+\pi^0$ at low energies. I am familiar with the basic concepts and techniques of QFT but have never dealt with the scattering processes ...
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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\...
3
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0answers
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 ...
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2answers
76 views

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: $$\...
3
votes
1answer
250 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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0answers
64 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 $...
2
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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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1answer
108 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 p_1',p_2'|:...
2
votes
1answer
440 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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0answers
76 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?
4
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1answer
293 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 inelastic....
2
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3answers
175 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 ...
0
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1answer
32 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 ...
1
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1answer
129 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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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 $H$. ...
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43 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
votes
1answer
440 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 ...