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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Can you calculate the radius of a hypothetical singular surface inside a black hole from observing changes to its linear momentum?

Say there is a ball of unknown radius surrounded by a bubble. The ball represents a hypothetical singular surface inside a black hole and the bubble represents the event horizon. If you threw marbles ...
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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]

In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be ...
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Square of the Feynman amplitude for $a +b\to c+d$ and its reverse

In quantum field theory, if a process $a +b\to c+d$ is allowed by a certain interaction Lagrangian (hermitian), the reverse process, $c+d\to a+b$, must also be allowed (as far as I understand) by the ...
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Mandelstam variables sign

I am self-studying the book "Quantum Field Theory and the Standard Model" by Schwartz, on page 99 (paragraph "Mandelstam variables"), the context is the $2\rightarrow 2$ scattering ...
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Justifying that the gold nucleus is at rest in a Rutherford experiment

This is an example on the Rutherford Experiment from Young and Freedman's University Physics. In the last paragraph of the solution the book states that it is valid to assume that the gold nucleus ...
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Question on 1D Scattering Resonances

I'm reading Henley and Garcia's Subatomic Physics. To introduce the concept of resonances they use a 1D square well scattering example. Resonances are where the transmission coefficient goes to one. ...
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Extracting electron wave functions from experiments

In nuclear and nucleon physics it’s quite standard to extract electromagnetic form factors – which are the Fourier transforms of charge and current distributions – from elastic electron-nucleon or ...
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Asymptotic states and physical states in QFT scattering theory

Context In the scattering theory of QFT, one may impose the asymptotic conditions on the field: \begin{align} \lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
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Jet events and Deeep Inelastic Scattering (Scaling Behavior) at the same time?

I am a philosopher of physics, so I already apologize for potential ignorance. I have also graduated in physics, but I now analyze problems on another level and also forgot some of the mathematical ...
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What is the energy of a photon in an electron-muon scattering?

Currently I am reading about this process in an Introduction to Quantum Field Theory by Peskin and Schroeder (pages 153-154). It should be mentioned that they are working in a center-of-mass (CM) ...
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Can you create fusion through scattering?

Could you scatter deuteron molecules (D-D) at high energies into some heavy metal target such that at the time of impact the bond in the deuteron molecule is compressed to such a degree that fusion is ...
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Binary black hole merging condition

Assuming two black holes with the same rest mass $m$ collid coming from infinity with velocity $v$ and impact parameter $b$. Lets ignore spin at first. For which values of $v$ and $b$ would these ...
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Could the scattering of molecules lead to bond compression?

Suppose you were to send a fast moving binary molecule (such as H-H) at another large target atom A such that the molecule is aligned with the direction of its travel towards the target atom. In other ...
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Inconsistency in scattering length of spherical well potential

I'm trying to understand the scattering length of the spherical well potential $$V(r)=\begin{cases}-V_0&r<r_0\\ 0&r>r_0\end{cases}$$ The $V_0>0$ (attractive) case is fairly well ...
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I need help with the following integral: $$\int_{0}^{\pi}\int_{0}^{2\pi} \frac{(sm_2^2+\ s^2)C(A+B)+s\left(m_2^2+s\right)C^2 }{AB} \sin\theta_1 \ d\phi_1d\theta_1$$ where $... 1 vote 0 answers 83 views Doubt in$e^{+}e^{-}\rightarrow W^{+}W^{-}$scattering I am trying to understand how to compute the scattering amplitude for the process$e^{+}e^{-}\rightarrow W^{+}W^{-}$, as a reference one could look at Peskin chapter 21. What I do not understand is ... • 475 0 votes 0 answers 23 views Distribution of scattered photons in cone-beam computed tomography (CBCT) I am using MCGPU to simulate photon transport in cone-beam computed tomography (CBCT). I ran an experiment, where a water cylinder containing spherical objects was irradiated. The simulation software ... • 273 0 votes 0 answers 34 views Relation bitween Mandelstam Variables in three-body final state What is the relation between Mandelstam variables in the three body final state? There are 5 independent Mandelstam variables. What is the relationship between them? • 11 0 votes 1 answer 146 views Green function in scattering theory I'm having a bit of trouble with a step in scattering theory. Context: The Schrödinger equation for a two-body scattering problem can be written as: $$(E - H_0) |\psi\rangle = V |\psi\rangle.$$ Here,... • 319 2 votes 0 answers 39 views A problem in Weinberg QFT Vol.1 Chapter 3 This is related to problem 5 of Weinberg's QFT vol.1 Chapter 3. The standing wave states$\Psi_\alpha^0$are defined by a modified version of Lippmann-Schwinger equation, \Psi_\... • 56 1 vote 0 answers 44 views What is the range of noon sun color temperature, when a light meter reports full expected sunlight (+/- epsilon)? My question came from trying to find what uncertainty bounds, if any, I can assign to a color temperature sensor, without access to an artifact with a precisely calibrated output spectrum. This leads ... 11 votes 2 answers 2k views What percentage of light gets scattered by a mirror? Sunlight strikes a mirror at a 45 degree angle. The vast majority of light will be reflected about the normal. Some light will be absorbed by the mirror. Some light will be transmitted through the ... • 912 0 votes 1 answer 63 views How to Express the Cross Section of a Three-Body Final State Scattering in Terms of Invariant Masses$s_{ij}$? I'm working on calculating the cross section for a scattering process that results in three bodies in the final state. My goal is to express the cross section in terms of the invariant masses$s_{ij}$​... • 11 0 votes 1 answer 47 views Elastic scattering and conservation of spin I am trying to understand conservation of spin in QED elastic scattering in these nice notes (VJ Martin, Particle Physics, Spring 2012, University of Edinburgh): https://www2.ph.ed.ac.uk/~vjm/Lectures/... • 184 4 votes 1 answer 60 views Inconsistency in transition rate derivation in "Introduction to the Quantum Theory of Scattering" by Rodberg and Thaler I've been working through the derivation of the transition rate in the book "Introduction to the Quantum Theory of Scattering" by Leonard S. Rodberg and R. M. Thaler (Chapter 8, Section 4 &... • 466 1 vote 0 answers 35 views What happens when a linear polarized EM wave encounters a perpendicular mesh of wires (which are electrically connected)? Assume a radio wave with wavelength 1 m is traveling in the negative z direction when it encounters a grid of closely spaced wires (say, 10 cm separation) laying in the xy plane, with each wire ... 7 votes 1 answer 323 views What is the difference between Born approximation and tree-level processes? The answer to this question says that Born approximation is essentially equivalent to the tree-level. This can be seen from the Feynman-diagrammatic version of Born series discussed in many NRQM ... • 785 0 votes 0 answers 60 views Looking for a reference in quantum mechanics treating Coulomb potential as Inverse of coordinate operator Most textbooks in quantum mechanics handle the Coulomb problem by solving the Schrödinger equation directly in the coordinate representation. Is there any book or reference that adopts a more formal ... 5 votes 8 answers 2k views Why does classical physics not predict particles in the double-slit experiment to land in just two different locations? I stopped being able to understand the double-slit experiment way before any of the interference and associated "quantum weirdness" came into play. I get that one needs to approach this ... 3 votes 1 answer 112 views Regge Theory interpretation I have a question on the physical interpretation of the Regge limit, $$s\gg4m^2\gg|t|$$ where we are in the s-channel physical region and s and t the Mandelstam invariants. Usually, the$s$is taken ... • 71 0 votes 0 answers 23 views Blue color scattering [duplicate] I'm trying to understand, in terms of cross sections, why is the sky blue? Intuitively, blue has a smaller wavelength than the rest of the colors so it can "see" the internal structure of ... • 369 0 votes 1 answer 45 views Elastic vs inelastic scattering in particle physics Does elastic scattering occur via the Z boson and inelastic scattering via the W boson? If so, why? Does it have something to do with the fact that interactions via the Z boson don't change quark ... • 105 0 votes 1 answer 46 views Rutherford scattering closest approach distance Consider a particle 1 moving towards a particle 2 at rest. In class, my teacher said that in order to derive the minimum approach distance when the impact parameter ( b ) is 0, we had to use ... • 319 2 votes 1 answer 38 views Complex BCFW-shift of Parke-Taylor amplitude (This question stems from problem 3.3 of Elvang's and Huang's "Scattering Amplitudes in Gauge Theory and Gravity" book). Consider the Parke-Taylor amplitude given as A_n[1^- ... • 704 2 votes 0 answers 57 views Unique numerical solution to Lippmann-Schwinger (Fredholm) equation I am working in non-relativistic scattering theory and solving the Lippmann-Schwinger equations for the$T$matrix in momentum space: $$T_{fi}(k_f,k_i) = V_{fi}(k_f,k_i) + \sum_n\int_0^\infty \frac{V_{... 0 votes 1 answer 41 views Reflection of quantum particle colliding with a potential barrier Let a quantum particle be subject to a one dimensional step potential barrier V such that:$$V(x)=\begin{cases}0, \ x<0 \\ V_0, \ x>0\end{cases}$$where the particle's energy is E>V_0>0... • 1,616 0 votes 0 answers 70 views Highly relativistic electron scattering in thin plasma I am curious about how extremely relativistic electrons (10s of GeVs to single TeVs) scatter when going through the interplanetary and interstellar medium, which is a thin plasma. I have read about ... • 113 1 vote 2 answers 44 views Are reflection and transmission coefficients in 1D problem are independent of the direction in which we choose as incident? I was watching a lecture series of Quantum mechanics of Professor V. Balakrishnan, There was a problem session, “For an arbitrary potential barrier (any potential function of position and it need not ... 2 votes 0 answers 91 views Is Sakurai's derivation of the Lippmann-Schwinger equation correct? I am using Sakurai's Modern Quantum Mechanics 3rd ed. The following is from the beginning of chapter 6. The defining equation for the T-matrix is$$\langle \vec{k}' \lvert U_I(t, t_0) \lvert \vec{k} ... • 2,676 2 votes 0 answers 56 views Does Sakurai's definition of$S$-matrix assume a particular type of scattering? I am using Sakurai's Modern Quantum Mechanics 3ed. In chapter 6, Sakurai defines the$T$-matrix via the equation $$\langle \vec{k}' \lvert U_I(t, t_0) \lvert \vec{k} \rangle = \delta_{k'k} - \frac{i}{\... • 2,676 1 vote 0 answers 42 views Cubic coupling beyond Yukawa Consider a massless Dirac or Majorana fermion \psi and a massless scalar \phi. They interact through a Lagrangian \mathcal{L}_I(\phi,\psi). I would like to understand what are the cubic ... • 165 0 votes 0 answers 24 views Scattering by point potentials Suppose we consider the quantum scattering of two particles. The interaction Hamiltonian is given by:$$H = -\Delta_{\vec{x}}-\Delta_{\vec{y}} +V(x-y)$$where V is the interaction potential between ... 1 vote 1 answer 112 views Power-series expansion in coupling/Planck constant By using Feynman rules of the interacting theory, one obtains the scattering amplitude$$\mathcal{M} = \mathcal{M}_0 + \mathcal{M}_1 + \cdots = \sum^{\infty}_{i = 0}\mathcal{M}_i\tag{1}$$Where \... 0 votes 0 answers 30 views Seeking specific Scientific American form mid 1980s on semiclassical interpretation of Compton Scattering I seem to recall seeing an article in Scientific American which discussed the possibility of interpreting Compton scattering in terms of classical electromagnetic wave theory. If anybody is familiar ... 0 votes 0 answers 23 views Extending Quantum Treatment of Attentuation Coefficient I was reading this document to understand the links between the attenuation coefficient and quantum scattering. Consider a beam of number density \rho and velocity v in the z direction. I = \rho ... • 199 0 votes 1 answer 54 views Compton scattering angle formula and drawings The Compton formula for scattering angles \varphi and \theta for electron and photon, respectively, can be shown as:$$ \cot\varphi = (1+\frac{\lambda_c}{\lambda_i})\tan\frac{\theta}{2} \tag{1}\... • 191 0 votes 0 answers 29 views Understand Laue condition intuitively I understand that it is the necessary condition in elastic scattering for scattering to happen, and for the wave to stay coherent, thus it stays able to interfere with other diffracted rays. But I ... • 319 7 votes 1 answer 363 views Determining Bound States from Møller Operator Hello I came across an interesting property of the Møller operator, which I summarize below: The Møller operator$\Omega^{(+)}\$ maps in-states that belong to the continuum spectrum of the free ...
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I am following Sakurai's Modern Quantum Mechanics, 3ed. Define the scattering, or S-matrix elements as $$S_{ni} \equiv \delta_{ni} - 2\pi i\delta(E_n - E_i)T_{ni}.$$ We can then derive the ...