Scattering Cross Section - Revision history

Vanwdani: /* Luminosity */

2016-12-18T00:44:07Z

Luminosity

2016-03-18T15:47:04Z

Luminosity

2016-03-18T15:11:17Z

Luminosity

2016-03-18T15:08:23Z

Luminosity

2016-03-18T15:07:32Z

Luminosity

2016-03-18T15:04:36Z

Luminosity

2016-03-18T15:00:12Z

Luminosity

2016-03-18T14:51:01Z

Luminosity

2016-03-18T14:50:42Z

Luminosity

2016-03-18T14:50:22Z

Scattering Cross Section

← Older revision		Revision as of 00:44, 18 December 2016
Line 23:		Line 23:


−	<center><math>\mathcal L = \Phi \rho \ell</math></center>	+	<center><math>\mathcal L = \Phi \rho \ell \approx i_{beam} \rho \ell</math></center>

	where		where

@@ Line 18: / Line 18: @@
 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>\frac{dR}{dt}=\mathcal L \times \sigma_p</math></center>
+<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.

← Older revision		Revision as of 15:11, 18 March 2016
Line 34:		Line 34:

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

	=Transforming Cross Section Between Frames=		=Transforming Cross Section Between Frames=

@@ Line 27: / Line 27: @@
 where
-<center><math>\Phi \equiv flux, or incoming particles per second</math></center>
+<center><math>\Phi \equiv </math>flux, or incoming particles per second</center>
-<center><math>\ell \equiv length of target</math></center>
+<center><math>\rho \equiv </math>target density</center>
 =Transforming Cross Section Between Frames=

← Older revision		Revision as of 15:07, 18 March 2016
Line 24:		Line 24:

	<center><math>\mathcal L = \Phi \rho \ell</math></center>		<center><math>\mathcal L = \Phi \rho \ell</math></center>
		+
		+	where
		+
		+	<center><math>\Phi \equiv flux, or incoming particles per second</math></center>
		+
		+	<center><math>\rho \equiv target density</math></center>
		+
		+	<center><math>\ell \equiv length of target</math></center>

	=Transforming Cross Section Between Frames=		=Transforming Cross Section Between Frames=

← Older revision		Revision as of 15:04, 18 March 2016
Line 23:		Line 23:


−	<center><math>\mathcal L = \Phi \rho \~~mathcal l~~</math></center>	+	<center><math>\mathcal L = \Phi \rho \ell</math></center>

	=Transforming Cross Section Between Frames=		=Transforming Cross Section Between Frames=

← Older revision		Revision as of 15:00, 18 March 2016
Line 19:		Line 19:

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

	=Transforming Cross Section Between Frames=		=Transforming Cross Section Between Frames=

← Older revision		Revision as of 14:50, 18 March 2016
Line 14:		Line 14:

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

	=Transforming Cross Section Between Frames=		=Transforming Cross Section Between Frames=