DV XSECT - Revision history

Vanwdani: /* Scattering Cross Section */

2018-04-17T18:38:28Z

Scattering Cross Section

Vanwdani: /* Scattering Cross Section */

2018-04-17T18:28:10Z

Scattering Cross Section

Vanwdani: /* Scattering Cross Section */

2018-04-17T18:06:06Z

Scattering Cross Section

Vanwdani: /* Scattering Cross Section */

2018-04-17T18:01:00Z

Scattering Cross Section

Vanwdani: Created page with "=Scattering Cross Section= 400 px $\frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}…"$

2016-04-20T14:22:49Z

Created page with "=Scattering Cross Section= <center> 400 px</center> <center><math>\frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}…"

New page

=Scattering Cross Section=

<center>[[File:Scattering.png | 400 px]]</center>

<center><math>\frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}{d\Omega}\right)}{\left(\frac{number\ of\ incoming\ particles/second}{cm^2}\right)}=\frac{dN}{\mathcal L\, d\Omega} =differential\ scattering\ cross\ section</math></center>

<center><math>where\ d\Omega=\sin{\theta}\,d\theta\,d\phi</math></center>

<center><math>\Rightarrow \sigma=\int\limits_{\theta=0}^{\pi} \int\limits_{\phi=0}^{2\pi} \left(\frac{d\sigma}{d\Omega}\right)\ \sin{\theta}\,d\theta\,d\phi =\frac{N}{\mathcal L}\equiv total\ scattering\ cross\ section</math></center>

Since this is just a ratio of detected particles to total particles, this gives the cross section as a relative probablity of a scattering, or reaction, to occur.
==Luminosity==

Luminosity is the quantity that measures the ability of a particle accelerator to produce the required number of interactions and is the proportional to the number of events per second dR/dt and the total cross section σp:

<center><math>dN=\frac{dR}{dt}=\mathcal L \times \sigma_p</math></center>

In order to compute a luminosity for fixed target experiment, it is necessary to take into account the properties of the incoming beam and the stationary target.

<center><math>\mathcal L = \Phi \rho \ell</math></center>

where

<center><math>\Phi \equiv </math>flux, or incoming particles per second</center>

<center><math>\rho \equiv </math>target density</center>

<center><math>\ell \equiv </math>length of target</center>

For the differential cross-section:

<center><math>\frac{d\sigma}{d\Omega} =\frac{dN}{\mathcal L d\Omega}=\frac{dN}{\Phi \rho \ell d\Omega}</math></center>

← Older revision		Revision as of 18:38, 17 April 2018
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−	<center>[[File:~~Scattering2~~.png ~~\| 400 px~~]]</center>	+	<center>[[File:DCScattering.png]]</center>

← Older revision		Revision as of 18:28, 17 April 2018
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−	<center>[[File:~~Scattering3~~.png \| 400 px]]</center>	+	<center>[[File:Scattering2.png \| 400 px]]</center>

← Older revision		Revision as of 18:06, 17 April 2018
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	=Scattering Cross Section=		=Scattering Cross Section=

−	<center>[[File:~~Scattering2~~.png \| 400 px]]</center>	+	<center>[[File:Scattering3.png \| 400 px]]</center>

← Older revision		Revision as of 18:01, 17 April 2018
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	=Scattering Cross Section=		=Scattering Cross Section=

−	<center>[[File:~~Scattering~~.png \| 400 px]]</center>	+	<center>[[File:Scattering2.png \| 400 px]]</center>

DV XSECT - Revision history

Vanwdani: /* Scattering Cross Section */

Vanwdani: /* Scattering Cross Section */

Vanwdani: /* Scattering Cross Section */

Vanwdani: /* Scattering Cross Section */

Vanwdani: Created page with "=Scattering Cross Section= 400 px \frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}…"

Vanwdani: Created page with "=Scattering Cross Section= 400 px $\frac{d\sigma}{d\Omega} = \frac{\left(\frac{number\ of\ particles\ scattered/second}…"$