Limit of Scattering Angle Theta in Lab Frame - Revision history

Vanwdani at 17:52, 29 December 2018

2018-12-29T17:52:04Z

Vanwdani at 17:42, 29 December 2018

2018-12-29T17:42:21Z

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-16T17:21:26Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-16T17:19:18Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-16T17:12:08Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-15T20:09:17Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-15T19:43:40Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-15T19:39:52Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-15T19:35:20Z

Maximum Moller Scattering Angle Theta in Lab Frame

Vanwdani: /* Maximum Moller Scattering Angle Theta in Lab Frame */

2018-03-15T19:33:41Z

Maximum Moller Scattering Angle Theta in Lab Frame

@@ Line 8: / Line 8: @@
 </center>
-The quantity is known as the
+The quantity u does not have a simple physical relationship, but is related to the t channel with the roles of the outgoing particles switched.
 <center><math>u \equiv \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^{*}}- {\mathbf P_1^{'*}}\right)^2</math></center>

← Older revision		Revision as of 17:42, 29 December 2018
Line 1:		Line 1:
		+
		+	<center><math> \underline{\textbf{Navigation} }</math>
		+
		+	[[Uniform_distribution_in_Energy_and_Theta_LUND_files\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Moller_Scattering\|<math>\triangle </math>]]
		+	[[Relativistic_Units\|<math>\vartriangleright </math>]]
		+
		+	</center>
		+
	The quantity is known as the		The quantity is known as the

Line 154:		Line 163:

	<center><math>u=-2p_1^* p_2^{'*}=m^2-E_1E_2^{'}+\left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>		<center><math>u=-2p_1^* p_2^{'*}=m^2-E_1E_2^{'}+\left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>
		+
		+
		+	----
		+
		+
		+	<center><math> \underline{\textbf{Navigation} }</math>
		+
		+	[[Uniform_distribution_in_Energy_and_Theta_LUND_files\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Moller_Scattering\|<math>\triangle </math>]]
		+	[[Relativistic_Units\|<math>\vartriangleright </math>]]
		+
		+	</center>

← Older revision		Revision as of 17:21, 16 March 2018
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	<center><math>u=-4p_1^* p_2^{'*}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>		<center><math>u=-4p_1^* p_2^{'*}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>
		+
		+
		+	<center><math>u=-2p_1^* p_2^{'*}=m^2-E_1E_2^{'}+\left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>

← Older revision		Revision as of 17:19, 16 March 2018
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	<center><math>u=-2p_1^* p_2^{'}+2 \left \| p_1^ \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>		<center><math>u=-2p_1^* p_2^{'}+2 \left \| p_1^ \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>
		+
		+
		+	At 180
		+
		+	<center><math>u=-4p_1^* p_2^{'*}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>

← Older revision		Revision as of 17:12, 16 March 2018
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	<center><math>u=2m^2-2E_1^E_2^{'}+2 \left \| p_1^* \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>		<center><math>u=2m^2-2E_1^E_2^{'}+2 \left \| p_1^* \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>

−	~~<math>E_1^=53\ MeV=p_1^</math>~~


−	~~<math>E_1=11000\ MeV=p_1</math>~~	+	<center><math>u=-2p_1^* p_2^{'}+2 \left \| p_1^ \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}=2m^2-2E_1E_2^{'}+2 \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>
−
−
−	<center><math>-~~E_1~~^~~E_2^{'}+ \left \| p_1^* \right \| \left \|~~ p_2^{'*~~} \right \| \cos \theta_{1\ 2^{'}}\approx -E_1E_2^{'~~}+ ~~\left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\~~ 2~~^{'}}</math></center>~~
−
−
−	~~<center><math>E_1^E_2^{'}-~~ \left \| p_1^* \right \| \left \| p_2^{'*} \right \| \cos \theta_{1\ 2^{'}}~~\approx E_1E_2~~^~~{'}- \left \| p_1 \right \| \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}}</math></center>~~
−
−
−
−	<center><math>E_1^{*2~~}(1~~- ~~\cos \theta_{1\ 2~~^{'}~~})\approx E_1(E_2^{'}- \left \| p_2^{'} \right \| \cos \theta_{1\~~ 2~~^{'}})</math></center>~~
−
−
−	~~<center><math>(53\ MeV)^{*2}(1- \cos \theta_{1\ 2^{'}})\approx (11000\ MeV)(E_2^{'}-~~ \left \| ~~p_2^{'} \right \| \cos \theta_{1\ 2^{'}})</math></center>~~
−
−
−	~~<center><math>(2553636.36364\ MeV)(1- \cos \theta_{1\ 2^{'}})\approx (E_2^{'}- \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}})</math></center>~~
−
−
−	~~At <math>\theta \approx 180^{\circ}</math>~~
−
−	~~<center><math>2(2553636.36364\ MeV)\approx (E_2^{'}- \left \| p_2^{'}~~ \right \| ~~\cos \theta_{1\ 2^{'}})</math></center>~~
−
−
−	~~<center><math>5107272.7272728\ MeV\approx (E_2^{'}-~~ \left \| p_2^{'} \right \| ~~\cos \theta_{1\ 2^{'}})</math></center>~~
−
−
−	~~For <math>p \approx 13.6\ eV</math>~~
−
−	~~<math>E=\sqrt {(13.6 eV)^2+(.511MeV)^2}=\sqrt {184.96+261121000000}\ eV=\sqrt{261121000185}\ eV=511000.000181\ eV</math>~~
−
−
−	~~This gives~~
−
−	~~<center><math>51072727.272728\ MeV\approx (.511000181\ MeV)- (13.6\ eV)~~ \cos \theta_{1\ 2^{'}}</math></center>

← Older revision		Revision as of 20:09, 15 March 2018
Line 180:		Line 180:
	This gives		This gives

−	<center><math>51072727.272728\ MeV\approx (.511000181\ MeV- 13.6\ eV) ~~\cos \theta_{1\ 2^{'}}</math></center>~~	+	<center><math>51072727.272728\ MeV\approx (.511000181\ MeV)- (13.6\ eV) \cos \theta_{1\ 2^{'}}</math></center>
−
−
−
−	~~<center><math>51072727.272728\ MeV\approx (.510986400181\ MeV~~ \cos \theta_{1\ 2^{'}}</math></center>

@@ Line 162: / Line 162: @@
-<center><math>(255363636364\ MeV)(1-  \cos \theta_{1\ 2^{'}})\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
+<center><math>(2553636.36364\ MeV)(1-  \cos \theta_{1\ 2^{'}})\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
 At <math>\theta \approx 180^{\circ}</math>
-<center><math>2(255363636364\ MeV)\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
+<center><math>2(2553636.36364\ MeV)\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
-<center><math>51072727272728\ MeV\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
+<center><math>5107272.7272728\ MeV\approx (E_2^{'}- \left |  p_2^{'} \right | \cos \theta_{1\ 2^{'}})</math></center>
@@ Line 180: / Line 180: @@
 This gives
-<center><math>51072727272728\ MeV\approx (.511000181\ MeV- 13.6\ eV) \cos \theta_{1\ 2^{'}}</math></center>
+<center><math>51072727.272728\ MeV\approx (.511000181\ MeV- 13.6\ eV) \cos \theta_{1\ 2^{'}}</math></center>
-<center><math>51072727272728\ MeV\approx (.510986400181\ MeV \cos \theta_{1\ 2^{'}}</math></center>
+<center><math>51072727.272728\ MeV\approx (.510986400181\ MeV \cos \theta_{1\ 2^{'}}</math></center>

← Older revision		Revision as of 19:35, 15 March 2018
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	<math>E=\sqrt {(13.6 eV)^2+(.511MeV)^2}=\sqrt {184.96+261121000000}\ eV=\sqrt{261121000185}\ eV=511000.000181\ eV</math>		<math>E=\sqrt {(13.6 eV)^2+(.511MeV)^2}=\sqrt {184.96+261121000000}\ eV=\sqrt{261121000185}\ eV=511000.000181\ eV</math>

−	<center><math>51072727272728\ MeV\approx (.511000181\ MeV- 13.6\ eV \cos \theta_{1\ 2^{'}})</math></center>	+
		+	This gives
		+
		+	<center><math>51072727272728\ MeV\approx (.511000181\ MeV- 13.6\ eV) \cos \theta_{1\ 2^{'}})</math></center>
		+
		+
		+
		+	<center><math>51072727272728\ MeV\approx (.510986.400181\ eV \cos \theta_{1\ 2^{'}})</math></center>

← Older revision		Revision as of 19:33, 15 March 2018
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−	<center><math>51072727272728\ MeV)\approx (E_2^{'}- \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}})</math></center>	+	<center><math>51072727272728\ MeV\approx (E_2^{'}- \left \| p_2^{'} \right \| \cos \theta_{1\ 2^{'}})</math></center>
		+
		+
		+	For <math>p \approx 13.6\ eV</math>
		+
		+	<math>E=\sqrt {(13.6 eV)^2+(.511MeV)^2}=\sqrt {184.96+261121000000}\ eV=\sqrt{261121000185}\ eV=511000.000181\ eV</math>
		+
		+	<center><math>51072727272728\ MeV\approx (.511000181\ MeV- 13.6\ eV \cos \theta_{1\ 2^{'}})</math></center>