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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Relationships between optical depth, $\tau$, and probability of being scattered

The optical depth is given by many as: $$ \tau=n_e\sigma_{cs}L $$ Where $n_e$ is the number density of the medium, $\sigma_{cs}$ is the scattering cross section and L is the linear extent of the ...
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4answers
3k views

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 ...
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0answers
48 views

What is the formula for light emission from a point source in scattering media?

I'm trying to model the light output emitting from a point source somewhere in R3, and impinging on a fiber optic at distance r, that may be angled relative to the point source at some angle $\theta$. ...
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26 views

IBP Identities to solve differential equation

I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand ...
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0answers
38 views

The $i\epsilon$ in non-relativistic scattering theory

When doing quantum mechanical scattering theory, we obtain the Lippman-Schwinger equation $$|\psi\rangle=|\psi_0\rangle+(E-H_0)^{-1}V|\psi\rangle$$ Here $\psi_0$ is the unperturbed wavefunction, ...
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1answer
89 views

Photon-Photon-scattering (Feynman diagram)

The feynman diagram for the Delbrück-scattering (photon-photon-scattering) in the lowest order looks like as in the picture: But why is the following diagram equal to one of the upper three? There ...
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1answer
47 views

Quantum entanglement and Compton Effect

Suppose we generate 2 entangled photons (via a beam-splitter or similar apparatus). They have an arbitrary indeterminate initial frequency $\nu_i$. One of these photons is allowed to propagate through ...
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1answer
50 views

Scattering off of a bi-local potential

I am trying to figure out the scattering wave function for the following potential: $$V(x,x')=-A \phi(x)\phi^*(x')$$ Such that the SE can be written as $$[\frac{\hbar^2\partial^2_x}{2m}-E]\psi = ...
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150 views

Rutherford scattering: Alpha particle scattering angle probability

An alpha particle (charge $q$) of energy $E$ is normally-incident upon a flat surface made of material with atomic number Z, number density n, and thickness d. What is the probability that it will ...
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1answer
96 views

Particle in a double delta potential, scatter states

I was studying the scatter states of a particle in a double delta potential given in this link: Double delta function well – scattering states But I dont understand how equations (20) and (21) were ...
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3answers
93 views

Finite square wall with $E > V_0$

I'm working through a problem for homework and feel as if there is a typo or I am confused. The problem is with a one sided finite square wall such as this: So the energy is more than $V_0$. I'm ...
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0answers
65 views

Proof of reflected and refracted waves being in the same plane as that of the incident wave and its projection on a planar interface

Please give a proof of reflected and refracted waves being in the same plane as that of the incident wave and its projection on an ideal planar interface between two linear, homogeneous, isotropic, ...
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125 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 ...
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0answers
74 views

The second order scalar quartic field theory Feynman diagrams

I'm trying to find the second order Feynman diagrams for the scattering of a scalar phion, described by the Lagrangian $$ L = L_0 + L_I \\ L_0 = \frac{1}{2}[\partial_{\mu} \phi(x)]^2 - \frac{1}{2}m^2 ...
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1answer
64 views

Evidence for standard model description of neutrons

as I don't know too much about experiments I have the following question concerning the evidence about the quark constituents in neutrons. After a quick google investigation I found some sentences ...
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0answers
22 views

What's the electromagnetic boundary condition on axis for a 2D axisymmetric problem?

I have a basic but also kinda confusing question here. We know for electromagnetic scattering from a body of rotation symmetry it's possible to reduce the 3D problem to 2D axisymmetric ones, which ...
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0answers
14 views

Canonical treatment of thermalization of two gases at different temperatures

I'd like to understand the thermalization process when two gases of different species and different temperatures are allowed to mix in an insulated container, interacting only through an elastic ...
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1answer
49 views

minimum hyperbolic distance for Rutherford Scattering

I saw in a textbook that gave the minimum distance for a hyperbolic trajectory in Rutherford scattering is given by $$r_{min}= ...
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1answer
159 views

Normalization of potential barrier solution

I don't understand a point in the solution attached to this barrier potential problem. Below equation 4.209, they say Assume first that the wave function on the right side of the barrier in the ...
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1answer
133 views

S-matrix in Weinberg QFT

I'm a bit confused by Weinberg's discussion of scattering. He defined the in and out states $|\Psi^{\pm}_\alpha\rangle$ with particle content $\alpha$ as states that transform under the Poincare group ...
4
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0answers
119 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 ...
6
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4answers
767 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 ...
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0answers
41 views

Derivation of the dynamical master equation for collisional decoherence of a massive particle

I'm working on the problem of collisional decoherence of a massive particle interacting with an environment of light particles. The problem. I have some confusion regarding the derivation of the ...
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1answer
101 views

Rutherford scattering in Quantum Mechanics terms?

Rutherford scattering stands as the first evidence of atoms having the positive charge concentrated in a small nucleus. While the classical description of the phenomenon is satisfactory, it puzzles ...
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1answer
244 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 ...
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2answers
174 views

Rectangular potential barrier

Take the usual rectangular potential barrier, that is: $$V(x)=0 \: \text{if} \: x<0 \: \text{or}\: \: x>a$$ $$V(x)=V_0 \: \text{if} \: 0\leq x \leq a.$$ I've looked at several notes and books ...
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1answer
84 views

Compton's formula for change in wavelength [closed]

I want to measure the shift in wavelength predicted by Compton's formula. I find that I cant measure a shift of less than 5% and that I also cannot measure at angles greater than 150 degrees. What is ...
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1answer
55 views

Bragg Scattering of Thermal Neutrons [closed]

I'm currently reviewing Bragg scattering. The particular problem below has me slightly confused on whether I'm thinking about it correctly. Questions Is the problem below referring to the kinetic ...
0
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1answer
89 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
518 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
votes
1answer
77 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
177 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
59 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 ...
2
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1answer
84 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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0answers
22 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 ...
0
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1answer
65 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
66 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 ...
0
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1answer
28 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 ...
1
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2answers
58 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 ...
2
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2answers
95 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 ...
0
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0answers
41 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 ...
0
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1answer
232 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 ...
2
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1answer
103 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 ...
3
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0answers
192 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
votes
2answers
914 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
votes
3answers
270 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
79 views

Difference between Rayleigh scattering and fluorescence spectroscopy [closed]

How can we differentiate Rayleigh scattering from fluorescence spectrum?
3
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1answer
333 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
201 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
202 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 ...