# Tagged Questions

A cross-section is the name given to a hypothetical unit of area (often in units of Barns) for measuring the probability of scattering events in particles collisions. DO NOT USE THIS TAG for a physical non-probabilistic cross-section of a macroscopic object.

19 views

### 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 ...
44 views

### How to integrate over a circle in sperical coordinates

I have an angular distribution $\frac{s \sigma}{d\Omega} = \frac{d\sigma}{d \left(\cos\theta\right) d\phi}$. How can I calculate it over a circle which lies on the plane $X = dist$, has radius $r$ and ...
46 views

### How to calculate scattering amplitude from lagrangian? (quantum field theory)

I'm doing a question in Mark Srednicki's Quantum Field Theory. (Question 10.5) Which says that, when one changes a free field $\phi$ to $\phi + \lambda\phi^2$, the Lagrangian density would include an ...
21 views

### How to intergate the cross section over the surface of a detector?

My beam moves along the $X$ axis. I know the cross section $\frac{d \sigma}{d \Omega}$. My rectangular detector is perpendicular to the $XY$ plane and its surface is perpendicular to the line ...
42 views

### Why does cross-section decrease with density?

I read on the wikipedia page for cross-section, that cross-section is related to the reciprocal of a material's density. This seems entirely counter-intuitive. Is there an intuitive reason for this? ...
18 views

### FESR: Relation Between Total Cross Section and Spectral Function

In the papers I am reading the total cross section of electrons, positron scattering into hadrons can always be written in terms of an integral of a weight function w(s) and the spectral function ...
34 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 ...
17 views

### Evaluation of width function; thermal neutron scattering cross section

I am attempting to perform some molecular dynamics simulation, based off of this paper, and do not have the slightest clue how they evaluate the width function (Eq. 4). My attempt at figuring it ...
42 views

### Spin sums in cross sections. Summing amplitudes or probabilities?

The context: I'm calculating the cross section for a scalar particle to decay into a fermion-antifermion pair in Yukawa theory, at tree level. In doing this, when calculating the amplitude from ...
135 views

### 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 ...
35 views

### Intuitive explanation of differential scattering cross-section

I'm looking for a conceptual, intuitive understanding of the differential cross section (classical scattering). Its origin, its use, the general process for derivation (conceptually, rather than the ...
223 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 ...
141 views

### Why does an interaction see the proton instead the quark mass?

When an interaction goes deep in the nucleus, should we have some way to interpolate between the proton mass and the quark mass which is going to be the ultimate destination of the interaction? For ...
42 views

58 views

### Differential cross section $d\sigma/dp^{\gamma}_{T}$?

Why we care about $d\sigma/dp^{\gamma}_{T}$? What the physical meaning of it? Why not plot $\sigma$ follow $p^{\gamma}_{T}$?. As in this picture.
48 views

### Total cross section of particle decay

Suppose a particle A travelling along the $z$-axis and decays into particles B and C. The cross section is given by $$\frac{d\sigma}{d\cos\theta^*} = k(1+\cos\theta^*)^2$$ where $k$ is a constant ...
160 views

### Scattering amplitude, link between quantum mechanics and QFT

In quantum mechanics, we can define the scattering amplitude $f_k(\theta)$ for two particles as the magnitude of an outgoing spherical wave. More precisely, the asymptotic behaviour (when ...
37 views

### colliding point particles

when I draw e.g. the diagram of compton scattering I assume that the electron of given momentum gets 'hit' by a photon and interacts with it. How close does the photon have to get to the electron that ...
34 views

### Gamma matrices in Decay Calculations [closed]

I am trying to calculate the transition amplitude, $\lvert M^2\rvert$, for the process where a top quark (momentum p) decays to a bottom quark (momentum q) and a $W^+$ boson (momentum k). I am ...
40 views

### Why IR divergences cancel by cross sections of next-to-leading diagrams?

I was reading QFT & Standard Model by Schwartz, Chapter 20 which is about IR divergences. He says that IR divergences only cancel cross sections for processes involving different initial or ...
69 views

### Database of experimental cross sections for atomic collisions

Does the atomic-physics community keep a comprehensive database of experimental data (cross sections) for atomic collisions? I am looking for data about Bremsstrahlung, ionization, elastic and ...
62 views

### Differential Cross Section

I would like to know what exactly the term differential cross section means. It comes from electron scattering experiments which are used to deduce the charge distribution of a nucleus and the cross ...
37 views

### Interaction rates from cross sections in a thermalized gas

Consider a target particle embedded in a gas with a thermal distribution of velocities. If we know the cross section $\sigma$ for interactions between the target particle and a gas particle, how do we ...
119 views

### One dimensional scattering cross section

My quantum mechanics book (http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf, pages 94-95 of the pdf, or 86-87 of the book) considers the one dimensional step potential ...
25 views

### Why average incoming spins and sum over outgoing spins? [duplicate]

The book by Griffith on elementary particles reads: A typical experiment starts out with beam of particles whose spin orientations are random, and simple counts the number of particles in a given ...