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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Lippmann-Schwinger equation and time dependence

Consider the Lippmann-Schwinger equation (LSE) $$ |\psi\rangle = |\phi\rangle + \hat{G}_0(\epsilon) \hat{V} |\psi\rangle \tag{1}$$ where $\hat{G}_0(\epsilon) = \frac{1}{\epsilon - \hat{H}_0 + i\eta}$...
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Atomic radii for elements as hard spheres

In neutron scattering, the atoms in a system are considered as hard spheres. Where could I find the appropriate (reliable) values of the atomic radii consistent with this physical picture? Thank you ...
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159 views

Why do shiny surfaces reflect more light than other surfaces?

I'm an A-level student and I love learning new things in physics. A new concept that I learnt says that the reflection is due to the scattering of light by electrons in the material. I've got my ...
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24 views

Why isn't every magnetic neutron scattering peak a nuclear scattering peak as well?

Neutron diffraction is a well-established technique for determining the magnetic unit cell of magnetic materials. The idea is that nuclear scattering gives you peaks that correspond to the crystal ...
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108 views

Difference between scattering and refraction?

I while back I learnt that when light is incident on a dipole the dipole will scatter the light, and when it is incident on a material of a different refractive index then the light refracts. From the ...
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174 views

Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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Why do vortices scatter at right-angles

I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him. In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ...
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31 views

Light scattering - creating an atmosphere that a laser will be visible in

I need to show the beams of red, green, yellow and violet lasers 100mW Red + 40mW Green for a demonstration in a darkened room that holds 150 people. The room has sensitive fire alarms that use ...
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126 views

Conditions to determine the Green's function for scattering phenomena

Consider the elastic scattering of particles by a potential $V$ in Quantum Mechanics. In the zone of influence of the potential the Hamiltonian may be written as $$H = H_0 + V,$$ being $H_0$ the ...
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118 views

I find there are two methods to calculate the amplitude in QFT. Is it equivalent? [duplicate]

I find there are two methods to calculate the amplitude in QFT. First method: Use LSZ reduction formula $$\langle p_1\cdots p_m;out|k_1\cdots k_n;in\rangle=\big(\frac{i}{\sqrt{Z}}\big)^{n+m}\int d^...
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151 views

Why the cross section can be obtained directly from the stationary scattering states?

I'm currently studying scattering theory in the book Quantum Mechanics, Vol. 2 by Cohen-Tannoudji. In the book the author deduces that to find the number of particles detected far from the target at a ...
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80 views

Question about Quantum Scattering and the Born Approximation in Griffiths Intro to QM

I am trying to follow Griffiths Intro to Quantum Mechanics 2nd edition, chapter 11 Section 4 on the Born approximation of scattering. My question is what exactly are the definitions of $\vec{r}$ and $...
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12 views

Light scattering and absorption in material

I would like to get your inputs on a way for measuring light characteristics (scattering + absorption) in a specific tissue. My aim is to compare characteristics at different wavelength vis and nir. I ...
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15 views

Scattering in Higher Dimensions

In 2 dimensional scattering, if the scattering situation is reflexive about the beam axis then we can relate the differential cross section to the impact parameter via $$\frac{d\sigma}{d\Omega}=\left|...
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31 views

Normalization of states of continuos spectra with complicated boundary conditions

Let's consider the following Schrödinger equation: $$\psi''(x)+k^2\psi(x)=0$$ with the following boundary condition $$\psi(0)+a\psi'(0)=0$$ $k$ is supposed to be larger that $0$. This equation is ...
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101 views

Why can I see a beam of light coming in through the window sometimes, but not all the time?

Does it have to do with moisture in the air? Does it have to do with the window itself? Could the light reflect/refract off of the air? If there were no moisture or smoke or dust, just air, would I ...
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19 views

The basic probabilistic relation of collision theory

In "Classical Mechanics", John R. Taylor gives this basic relation of collision theory $$N_{sc}=N_{inc}n_{tar}\sigma$$ for firing projectiles into targets. $N_{sc}$ is the number of projectiles ...
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33 views

What is the physical interpretation of imaginary terms in the neutron optical potential model?

I'm doing a computational project on neutron scattering and I've found that if you simulate (n,n) collisions on Uranium 238, the program predicts resonances not found in experimental data. The ...
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59 views

Why is the reflection coefficient in quantum mechanical scattering defined this way?

In Griffiths' "Introduction to Quantum Mechanics, second edition" section 2.5.2, p. 73, he states: For the delta-function potential, when considering the scattered states (with $E > 0$), we have ...
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mechanism responsible for red sunset

Let's say a plane EM wave passes through an air molecule. To explain scattering classically, you can consider an electron held to the rest of the molecule by a spring that makes a forced oscillation ...
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72 views

Continuity of Logarithmic derivative in Scattering theory

I am having problem in understanding why do we consider the continuity of the Logarithmic derivative of the wave function at the boundary of the Scattering Potential ? I understand that physical ...
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61 views

Derivation of exponential charge distribution and form factor from the normalized yukawa charge distribution and form factor

For a problem solving class I need to derive the normalized exponential charge distribution $\rho_e \propto e^{-\mu r}$ and corresponding form factor $F_e$, from the normalized Yukawa distribution $\...
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154 views

Rayleigh equation as explanation for sky being blue

I've been reading up on the internet as to why the sky is blue. The answer usually cites Rayleigh scattering that I've checked on wikipedia: https://en.wikipedia.org/wiki/Rayleigh_scattering: $$ I=...
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28 views

How to tell when exponentials are real valued? (Barrier Potential)

Where $k_1=\frac{\sqrt{2mE}}{\hbar}$ and $\alpha=\frac{\sqrt{2m(V_0-E)}}{\hbar}$ I'm quite confused as to why the exponentials in regions I and III are complex functions while in region II the ...
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51 views

Understanding FCC and BCC Bravais Lattices

A book I am reading states that one possible definition of a Bravais Lattice is that the surroundings will look the same from whichever lattice point you observe from. Consider for example the simple ...
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226 views

In quantum field theory, how can Compton scattering change the frequency of light?

Classically, when light scatters off matter, the frequency of the light must stay the same. This follows directly from a continuity argument: if you put in $f$ field oscillations per second, you'd ...
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Equivalence between two different ways of calculating phase shifts in quantum scattering

Quantum scattering problem from a potential of the form $ V={{a} \over {r^2}}, $ regarding the calculation of phase shifts. One standard way to solve the problem is to equate in the limit where r ...
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Formula for scattering and energy change of photons on (naked) nuclei

What is the formula for scattering and energy change of photons on (naked) nuclei? (On wikipedia Compton scattering does only explain scattering of photons by electrons, and I'm not even aware if the ...
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29 views

In Rayleigh scattering, does a light wave cause the electrons (themselves), in a particle, to move at the same frequency as the incoming light?

The excerpt below, about Rayleigh scattering, is taken from the following page: https://en.m.wikipedia.org/wiki/Rayleigh_scattering Rayleigh scattering results from the electric polarizability of ...
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62 views

Phase shift calculation in quantum scattering for potential $V=a/r^2 $. Neumann function missing

I'm tasked of finding the phase shifts for scattering from a potential of the form $V=a/r^2$. My thinking is as follows. For this specific potential I can bring the differential equation to the form: ...
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102 views

Why does compton scattering provide evidence for the particle nature of light?

I understand that compton scattering is modeled as a collision between a photon and an electron, but why does this conclusively prove that light can act as a particle? Why couldn't the same ...
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31 views

Phase shift of long-range (non-local) potential

I was reproducing some phase shift values of a specific long-range potential.But becouse I have never dealt with long-range potential before,I don't know where to start.In the textbooks,only short-...
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248 views

Resonant Scattering and the Breit-Wigner Formula

Most of what I ask relates to the derivation found here: https://farside.ph.utexas.edu/teaching/qm/lectures/node91.html The basic idea is that we first consider zero energy s wave scattering from a ...
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46 views

How does wavelength affect scattering of light rays?

I am asking how wavelengths affect scattering(not diffraction). We know lesser the wavelength, greater is the scattering. For example, violet ray(wavelength 0.4 micron) is scattered most and red ray(...
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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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13 views

How is the energy spectrum of a gamma ray in a material?

I'm trying to solve the following problem for a course in radiation physics. A thin ray of intensity $I_0$ and energy $E_0$ impacts in a material. What is the intensity and the energy of the ...
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32 views

Neutron scattering off molecules

From neutron scattering off molecules it is possible to get information about molecules' geometry. Given the size of a particular molecule, what are the criteria for choosing the wavelengh of the ...
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Scattering in Black Holes

Let's take your favorite Black Hole and consider the scattering problem for a scalar field around it. Suppose that the Klein-Gordon equation can be separated in the radial and the angular part. Which ...
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45 views

density of states with changing potential floor

I wish to calculate the density of states for a 1D finite potential well, for the scattering states, meaning $E>0$. I have a potential of the form: $$ V(x)=\begin{cases} -V_0 & |x|<a\\ 0 &...
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52 views

Rutherford scattering: question about impact parameter

http://wonka.physics.ncsu.edu/~blondin/py203/HW5solns.pdf I have a question about the solution to a problem I found online. I don't understand why the author plugs in $\theta=90$ when the question is ...
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51 views

Scattering amplitude Green's function integral

On page 208 of Weinberg's QM book, he calculates the following integral \begin{align} G_k (\vec{x}-\vec{y}) =& \int \frac{d^3 q}{(2\pi \hbar)^3} \frac{e^{i\vec{q} \cdot (\vec{x}-\vec{y})}} {E(k)-...
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377 views

Difference in Raman, Rayleigh, and Compton scattering

I'm studying modern physics and have some questions about these three different scattering. In the book and wiki all tells me Raman and Rayleigh scattering are inelastic and elastic collision ...
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theoretical echo from a point scatterer

How can I compute an echo coming back from a point scatterer? Let's say I know the excitation signal (plane wave), scatterer position, medium properties, what else do I need to see, how the echo will ...
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14 views

NMHV Helicity Amplitudes.

Looking for NMHV amplitudes with 2 gluons and two fermion pairs. This paper presents compact formulas for these amplitudes that look like that: $ \frac{<13>^3\ [46]^3\ [5|3+2|1>}{t_1^{[3]}\ ...
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36 views

Implication of rotational symmetry on scattering matrix/ scattering cross-section [closed]

How does the rotational invariance helps simplifying Non-relativistic quantum scattering problems? Is there any any additional information that can be extracted about the scattering amplitude? It ...
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103 views

Green's Function in the Lippmann Schwinger Equation

When deriving the scattering cross section using the Lippmann-Schwinger equation we need to calculate the Green's function defined by $$G(\mathbf{r},\mathbf{r'},E)=\langle\mathbf{r}|\frac{1}{E-H+i\...
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89 views

Scattering Theory

In non-relativistic quantum mechanical scattering theory you can derive an expression for the differential scattering cross section under the first order Born approximation as $$\frac{d\sigma}{d\Omega}...
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32 views

Maximum energy transfer in Compton process

Consider a gamma ray incident on an electron at rest with wavelength $\lambda$, in a Compton scattering process . What is the maximumc kinetic energy the electron can gain from this? Can the gamma ray ...
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91 views

What is basic difference between photoelectric effect and Compton effect?

What is basic difference between photoelectric effect and Compton effect? In both case a photon hits a loosely bound electron So whats the difference? We get current in photoelectric effect but not in ...
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271 views

Derivation of the Rutherford scattering formula

I have been trying to look for a derivation of the Rutherford scattering formula from Hyperphysics, but cannot find one. It doesn't show up in the original paper How is this equation derived? $$N(\...