Questions tagged [scattering]

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, Rayleigh, Mie, geometric).

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Weird scattering problem my professor had us do that he couldn't solve [closed]

My teacher(and I use the word loosely) gave the class, which is only two people, including myself, this weird analytical mechanics problem. From working on it on my own, I found that y=x^2 should be x=...
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Problem with calculation atmosphere extinction coefficient

I found the formula calculating the atmospheric extinction coefficient, which is here: https://articles.adsabs.harvard.edu//full/1999BASI...27..601M/0000602.000.html| for Rayleigh scattering and ...
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Rate of scattering [closed]

I am reading this paper "Thermalization in Weakly Coupled Nonabelian Plasmas" from Kurkela and Moore. They say that the rate of elastic scattering is $$\frac{d\Gamma}{d^2q}\sim \int dq_z \...
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1 answer
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Repulsive force between electrons at relativistic speeds

What happens to the repulsive force between two electrons, once one of the electrons travel at relativistic speeds? Let's consider two electrons in an atom with magnetic dipole moment, one of which is ...
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1 answer
53 views

Complex Refractive Indices, Absorption, and Transparency

A complex refractive index is defined as $n = n_0 + \kappa$ where $n_0$ is the "standard" refractive index, and $\kappa$ is the optical extinction coefficient. The optical extinction ...
-1 votes
1 answer
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Calculation of illumination from the Sun and sky - explanation needed

I found a nice text about the illumination of the sky with respect of the position of the Sun https://www.brikbase.org/sites/default/files/ies_030.pdf where I could find the following formula: What I ...
5 votes
1 answer
197 views

Details in the derivation of the Lippmann-Schwinger equation

So the argument goes that for a slightly perturbed Hamiltonian $$ H = H_0 + V, $$ there will be some exactly known states, $\left|\phi\right>$, solving $$ H_0\left|\phi\right> = E\left|\phi\...
-3 votes
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Is there a one-to-one correspondence between gauge symmetry breaking and scattering? [closed]

Can electron scattering be directly associated with the breaking of Gauge Symmetry (GS)? E.g.: Problem of electron impinging on a potential step: Scalar-electric potential, $V(z)$, GS breaking and ...
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Scattering by Inverse square Potential

I stumbled upon the following question in a textbook. The direct translation would be, for a potential: $$ V(r)=\frac{\alpha}{r^2} $$ perform partial wave analysis. What I assume this means is, use ...
3 votes
1 answer
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Clarifications on the assumptions made for QFT interactions

I am reading about scattering and S-matrix in the context of quantum field theory and although I understand the math and the physical interpretation of the final results, I am confused about some ...
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2 answers
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Justification of discarding the backward wave in step potential scattering

I'm following Shankar's treatment of 1D scattering in Principles of Quantum Mechanics (Page 167 to Page 172). In general, the eigenstates of the single-step potential $$V(x)=\begin{cases} 0 & \...
37 votes
4 answers
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Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
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An S-matrix description of the photoelectric effect?

As is well known, the photoelectric effect is an experimental phenomenon that had enormous historical importance for the emergence of the concept of photons and quantum mechanics itself. As is well ...
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Definition of (Differential) Scattering Cross Section in QED

In QED we like to define the (differential) cross section for a scattering process as follows: $$d\sigma \ \dot= \ \frac{w_{fi}dN_f}{|j_{inc}|}\tag{1}$$ where $w_fi$ is the probability of transition ...
7 votes
3 answers
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What happens at the QM level with a photon hitting a mirror?

I have read these questions: Reflection of light at a microscopic level About photons and mirrors Photons and perfect mirror Do photons bounce at mirrors? How do mirrors work? What happens when a ...
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Why does Jost function have analytic continuation on the $p$-plane? [migrated]

I have question in the analyticity of Jost function on the $p$-plane. The chapter 12 of the book Scattering Theory by John R. Taylor states (p.218): The Jost function is defined as $$ f_{l}(p)=1+\frac{...
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Interpreting Feynman diagram of Coulomb scattering of positron

I am trying to understand Coulomb positron scattering. This course explains that: Here the incoming state is in the future and is to be interpreted as a negative-energy electron of four-momentum $-...
18 votes
1 answer
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What are the exact relations between bound states, discrete spectra, and negative energies in quantum mechanics?

Consider the nonrelativistic quantum mechanics of one particle in one dimension ("NRQMOPOD") with the time-independent Schrodinger equation $$ \left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(...
3 votes
1 answer
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Are QED Feynman diagrams readable in any order?

I have somewhat of a basic question regarding QED Feynman diagrams. To expose my doubts let's take the Feynman diagram of the Compton scattering (at the second order) as an example: With the solid ...
1 vote
2 answers
217 views

What makes electron scattering more useful than alpha particle scattering for resolving the structure of the nucleus?

I hear of a lot of people say that electron scattering is more useful than scattering with heavier particles like the $\alpha$ particle, but I'm not sure why this is the case. This is the first Born ...
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Small-Angle X-Ray Scattering of Bulk Polymers

Does anyone have any recommendations on how to get useful information from SAXS of polymers when the system is not dilute? This is the type of data we're working with: My understanding is that since ...
2 votes
2 answers
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Why do small particles deferentially scatter colors (i.e scatter more blue light than red in Rayleigh scattering) while larger particles don't?

In both small and large particles, light as an EM wave will accelerate charged particles such as electrons and induce a dipole forcing the electrons to oscillate at the same frequency of incident ...
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Sunset and blue light scattering

During Sunset we see the lower part of the sky changing into red colour wich is of course due atmospheric thickness increased... The higher parts of the sky are still blue suggesting that as blue ...
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1 answer
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Free particle encountering an infinite potential barrier

I understand that a wave function cannot penetrate through a barrier that has infinite potential. However when the wave function reflects off from the barrier what does this look like? If we're in a ...
15 votes
2 answers
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Is there an analogue of the LSZ reduction formula in quantum mechanics?

In quantum field theory the LSZ reduction formula gives us a method of calculating S-matrix elements. In order to understand better scattering in QFT, I will study scattering in non-relativistic ...
1 vote
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Discontinuity of the scattering amplitude and optical theorem

The generalized optical theorem is given by: \begin{equation}\label{eq:optical_theorem} M(i\to f) - M^*(f\to i) = i \sum_X \int d\Pi_X (2\pi)^4 \delta^4(p_i-p_X)M(i\to X)M^*(f\to X).\tag{Box 24.1} ...
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Can the probability of finding a particle in a certain finite region be zero?

Don't worry this time isn't about doubleslit but I'll still use it for my question. Imagine an electron is emitted from the source and I shall allow a certain amount of time to lapsed so as to provide ...
4 votes
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In JJ Thompson's experiment, why are electrons not making U turns?

In JJ Thompson's experiment, Why are some electrons able to pass through the slit of the anode, rather than hitting the anode plate itself? Even though electrons manage to get past the anode, will ...
11 votes
2 answers
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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 ...
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Can Raman spectrometers detect Rayleigh scattering?

Can Raman spectrometets detect Rayleigh scattering? The sample I have got turned blue after annealing. And I am wondering if this happened because of Rayleigh scattering. I saw some articles about ...
3 votes
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Derivation of the Lippmann-Schwinger equation

I was trying to understand the derivation of the Lippmann-Schwinger equation in Sakurai's Modern Quantum Mechanics, Section 6.1. Our teacher presented a much simpler derivation, similar to that on ...
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What is the Critical impact parameter for photons of a black hole?

What is the "Critical impact parameter" for photons of a Black hole with a Radius $r$? Here I'm defing the Critical impact parameter $C$ as the value such that. A photon with an impact ...
1 vote
2 answers
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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 ...
3 votes
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Deriving a contradiction from the LSZ condition

I'm reading the LSZ reduction formula in the wikipedia: https://en.wikipedia.org/wiki/LSZ_reduction_formula To make the argument simple, let $$\mathcal{L}=\frac{1}{2}(\partial \varphi)^2 - \frac{1}{2}...
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Scattering angle center of mass

It may be a silly question but I don't see why all the drawings in the books represent the scattering Will I have made a mistake if I represented the scattering in this way ? It should be the same ...
13 votes
1 answer
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How does one describe individual particles in QFT in practice?

A similar question was posted on this site at least ten times, but not quite in this formulation, and with no satisfactory answers, so I give it another try. Quantum field theory textbooks almost ...
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1 answer
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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 take ...
1 vote
2 answers
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Finding the Lagrangian term from a scattering amplitude

I am reading the book Scattering Amplitudes in Gauge Theory and Gravity from Elvang and Huang. In section 2.6 they seem to suggest that the mass-dimension of the kinematic part of the amplitude is in ...
3 votes
1 answer
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Asymptotic behavior of wave function in scattering of spin 1/2 particles against spin 0 target

I need a little hand here. My professor left me as homework to study the chapter VII of the Ref. [1]. Everything was going well until the section "Particle with spin". In Eq.(7.1), is given the ...
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High energy collision of two proton

Suppose there are two protons ( as we have in LHC). One proton is coming from +ve z axis and other from -ve z axis toward the collision point(origin). Both proton collide with equal velocity. Now as ...
5 votes
1 answer
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$T$ Matrix elements in Scattering Theory (Sakurai 2nd edition)

I am currently unable to see how the $T$ Matrix elements discussed in 6.1 of Sakurai's Modern Quantum mechanics 2$^\mathtt{nd}$ edition can be expressed as they are in equation (6.1.26) (see below). ...
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1 answer
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Difference in light falling into a room depending on the positioning of the sun

How does the lighting falling into a room differ in color temperature, shadow productions, directionality and other aspects, in relation to the positioning of the sun and the room? For example, if the ...
2 votes
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For Rayleigh scattering, what is the phase difference between the incident field and the scattered (or reradiated) field?

I am asking within the context of electromagnetic theory. Much of the discourse I could find in the literature was more focused on the phase differences between the scattered fields of various ...
1 vote
1 answer
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Why is deep open ocean blue?

If we assume the ocean is sufficiently deep so that the blue light transmitted inside the water gets absorbed completely before it reaches the ocean floor and be scattered back towards the surface, ...
3 votes
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LSZ reduction formula and connected Feynman diagrams in Peskin & Schroeder [duplicate]

I don't understand why in the LSZ reduction formula I need to consider only connected Feynman diagrams when I compute scattering amplitudes. From what I read in Peskin & Schroeder it seems that ...
5 votes
1 answer
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Why does the LSZ reduction formula only give the connected part of the $S$ matrix?

As an example, using the LSZ reduction formula, the $S$ matrix element for $2\rightarrow 2$ scattering is found in Peskin and Schroeder to be $$\langle \boldsymbol{p}_1 \boldsymbol{p}_2\rvert S \lvert ...
1 vote
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Seeking an expression for phase shifts for scattering by a complex potential

Scattering from a complex potential, $V(r)=V_R(r)+iV_I(r)$, can take into account the absorption of a beam of particles. In this case, the phase shifts, $\delta_\ell(k)$, are complex. It is expected ...
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1 answer
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Boundary condition of hard wall potential

I have a potential that is like $$ V(x)= \left\{\begin{matrix} 0 & x >0 \\ \infty & x \leq 0 \\ \end{matrix}\right. $$ Using the boundary condition at $\psi(x=0)=0$ I have found that the ...
8 votes
2 answers
504 views

Is there a sharp definition of an unstable nuclide?

This may be a somewhat philosophical question, but here goes. Wikipedia claims that several nuclides (e.g. hydrogen-5) have half-lives shorter than $10^{-22}$ seconds. This is on the same order of ...
1 vote
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When will an electron fired at a proton be captured instead of scattered?

Suppose electrons of energy $E>0$ are fired toward a proton. Since energy is always conserved in a central motion, and because an electron bound to a hydrogen atom must have negative energy $(E<...

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