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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177 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?
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56 views

Must neutron speed and diffusion speed be comparable for neutron scattering experiments to be probe atomic diffusion?

Neutron scattering experiments are sometimes used to study atomic diffusion in solid materials. My intuition is that the typical speeds of the atoms diffusing in the material--say, the diffusion ...
4
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1answer
379 views

A question from Weinberg QFT

I'm self-studying Weinberg QFT. I'm confused by his treatment of scattering theory . I have the following question: He introduces the free particle states $\Phi_{\alpha}$ but I'm not sure what is ...
4
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1answer
291 views

Mie scattering intensity and spherical particles on

I am running an experiment where I shine infrared light on (almost) spherical particles on the micron scale (PM2.5 - PM10). I then look at the (90 deg) scattering properties to try and size the ...
7
votes
1answer
168 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 ...
3
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1answer
113 views

Tunneling and transmission

Lets say we have a tunelling problem in the picture, where $W_p$ is a finite potential step: If particle is comming from the left a general solutions to the Schrödinger equations for sepparate ...
4
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1answer
130 views

Neutron scattering for a critical magnetic-ordering system : what about critical opalescence?

Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model. We know that the liquid-gas transition is characterized by a phenomenon called critical ...
2
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1answer
407 views

Single photon's effect on conservation of momentum?

When your looking at basic Compton theory you find that if you shoot a stream of photons at a particle (usually atoms or electrons), then you have the basic laws of conservation of momentum. The ...
5
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2answers
302 views

Attenuation mass-thickness for sunset light

We are able to look directly at the sun near sunset and sunrise, which clearly demonstrates the fact that our atmosphere attenuates visible light. Let's imagine it follows the typical attenuation ...
2
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0answers
124 views

Parton Distribution Functions, average cross section of the nucleon

Say we are given the scattering cross section for neutrinos from $d$ and $\bar{u}$ quarks as $\frac{d\sigma^{d}}{dQ^2}=\frac{G_F^2}{\pi}$, $\frac{d\sigma^{\bar{u}}}{dQ^2}=\frac{G_F^2}{\pi} (1-y)^2$, ...
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0answers
38 views

How to write down the detailed balance (microreversed) amplitude

I know that time-reversal of a reaction and the detailed balance (microreversed, or reciprocal) reaction are different. Textbooks on scattering theory explain how to relate the S-matrix elements of a ...
0
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1answer
474 views

Potential step and its transmission / reflection

Lets say we have a potential step with regions 1 with zero potential $W_p\!=\!0$ (this is a free particle) and region 2 with potential $W_p$. Wave functions in this case are: \begin{align} ...
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1answer
76 views

Do particles in the solar core travel at the same speed as they would in vacuum?

I just read the Wikipedia article on the Sun. The section on Solar Core states It has a density of up to 150 g/cm3[47][48] (about 150 times the density of water) Do the particles (atomic, and ...
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0answers
176 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...
0
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2answers
122 views

Why is the energy spectrum continuous for a plane wave when it has energy less than the potential barrier?

Please explain it in the context of this task: we have a potential barrier that looks like $\prod$, with $E<U$. There are 3 regions: 1) no field 2) barrier 3) no field Solution could be ...
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0answers
152 views

Are EM waves scattered the most when the wavelength and the obstacle have a similar size?

I heard that when the wavelength and obstacle are similar in size, the scattering is the greatest. Is this true?
2
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1answer
250 views

Alternative methods to derive the static potential in the NR limit of QED

In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level ...
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0answers
184 views

Classical scattering of two particles by a Yukawa potential

A point-like particle $A$, coming from minus spatial infinity, heads at another one, $B$, with an impact parameter of $b$. Initial momenta are $p_A$ and $p_B=0$. They repel each other via a Yukawa ...
4
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1answer
494 views

Why does scattering depend on spin?

I'm reading about giant magnetoresistance (GMR), and the most important feature of this phenomenon is the spin dependance of the electron scattering inside a magnetised lattice. However, I don't quite ...
6
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268 views

Database of scattering amplitudes

I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not. I can't find any reference that has ...
0
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1answer
346 views

Expansion in solid spherical harmonics on the lattice

I'm interested in calculating scattering processes (e.g. Coulomb scattering of an electron beam by a single ion) in the context of lattice quantum field theory, and wonder if there is something like ...
8
votes
2answers
608 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 ...
2
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1answer
86 views

In the expansion of the scattered wave function, why do these two functions have the same index?

See Griffiths Quantum Mechanics, eq. 11.21. Evidently, $$\psi(r,\theta,\phi)=Ae^{ikz}+A\sum\limits_{l,m}^{\infty}C_{l,m}h_{l}(kr)Y_{l}^{m}(\theta,\phi).$$ But I don't see why the $l$th Hankel function ...
5
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648 views

Particle coming across a step potential barrier

My quantum mechanics textbook says that when a particle (in the classical case) comes across a potential-step barrier of finite height, if it has sufficient energy to surmount the barrier, it will ...
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2answers
173 views

Is there an upper limit to wavelength and particle size in the Mie Scattering solution?

I figure that Mie scattering is best for finding the scattering when the wavelengths are between 1/10th to 10x the particle diameter. However, is there an upper limit to this? If I send 2.8cm ...
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0answers
31 views

Phase functions non-existent in original (J. Strutt) Lord Rayleigh's work?

This is related to my previous Phys.SE question on the derivation of the phase function - upon sifting and scanning through 600 pages of John Strutt's collected work, there is absolutely no mention of ...
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583 views

How did Lord Rayleigh derive/determine the phase function for his scattering model?

I've been researching the question for quite some time, as I understand it the phase function is actually an approximation due to the particle-wave duality inherent in participating media such as the ...
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1answer
290 views

Why can I add the Atomic form factors in the calculation of the Diamond Structure factor

When trying to calculate the structur factor for diamond I came across the calculation on the wikipedia. In the calculation they just add up the atomic form factors of alle the atoms in the unit cell ...
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vote
1answer
278 views

Specific electron energy gap values $E_{i+1}-E_i$ vs. photons with arbitrary energy $\hbar \omega$

The energy levels of electrons in an atom are quantized $E_i$. A photon of a specific momentum $\vec p$ and energy $$\omega=(E_{i+1}-E_i)/\hbar$$ hits an atom and gets absorbed. Okay now say the ...
10
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3answers
881 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 ...
1
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1answer
151 views

Scattering from a box potential of width $L$ doesn't reproduce a step potential in the limit $L \rightarrow \infty$

Consider the scattering of a quantum particle in one dimension, caused by a step in the potential (this appears in many undergrad level QM books): $$ V(x) = \begin{cases} V_1 & x<0 \\ V_2 ...
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1answer
41 views

What is pulsed neutron diffraction?

I have tried a google search and checked my condensed matter books but I can't find out what pulsed neutron diffraction is and how it differs from inelastic neutron scattering.
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373 views

Can scattering amplitudes be simplified with 1PI diagrams?

I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
2
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1answer
295 views

Integral in Peskin and Schroeder

I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
4
votes
1answer
586 views

Scattering Processes in Scalar Yukawa Theory

I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through ...
3
votes
1answer
163 views

Inclusion of information about external particles to calculate scattering amplitudes

In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states $$ A = \int\limits_{\rm{life time}} d\tau ...
2
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2answers
457 views

How does scattering work?

Why is the sky blue? I was always taught in high school that light with wavelength $\lambda$ acts like a little particle that wiggles up and down through space (in proportion to its magnitude). I was ...
2
votes
1answer
684 views

Feynman Rules for massive vector boson interactions

I am stuck at the beginning of a problem where I am given an interaction term that modifies the regular QED Lagrangian. It involves the interaction between a photon field and a massive vector boson: ...
0
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1answer
168 views

Scattering Amplitudes in Centre of Mass Frame

I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be ...
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3answers
2k views

Why is the colour of sunlight yellow?

I was going through the preliminary papers of other schools and found a question that I did not know. It was "Why sunlight appears yellow?". Can anyone answer it?
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23 views

Hamiltonian of the charged current in SM (related to the lorentz invariance)

recently when I was studying the scatterings which involves a vector boson (like W boson) as an intermediate particle, I saw that the propagator is not Lorentz invariant, I read that there is another ...
6
votes
2answers
393 views

Blue-shifting as opposed to violet-shifting

A recent XKCD comic implies that the sky is blue as opposed to violet due to human physiology, and that animals more sensitive to shorter wavelengths will perceive the Earth's sky as the shortest ...
3
votes
1answer
125 views

What are anomalous threshold singularities

In the papers of the 1950s and 1960s, I see reference to anomalous threshold singularities. What are these? Is there a good reference that discusses this subject?
4
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1answer
247 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 ...
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30 views

Impurity scattering [duplicate]

Possible Duplicate: Impurity scattering temperature dependence Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that ...
2
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3answers
642 views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
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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 ...
4
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1answer
344 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' ...
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1answer
2k 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 ...
16
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2answers
765 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 ...