Forest AngMomRecoupling - Revision history

Oborn at 21:03, 11 January 2010

2010-01-11T21:03:23Z

2010-01-11T21:02:26Z

2010-01-09T22:34:14Z

2010-01-09T20:58:48Z

2010-01-09T20:54:34Z

2010-01-09T20:53:14Z

2010-01-09T20:50:05Z

2010-01-08T22:44:04Z

2010-01-08T22:43:17Z

2010-01-08T22:42:10Z

← Older revision		Revision as of 21:03, 11 January 2010
Line 17:		Line 17:


−	<math>\Gamma_1 = \~~int_x~~^{x_o} g_1(x,Q^2) dx</math>	+	<math>\Gamma_1 = \int_0^{x_o} g_1(x,Q^2) dx</math>

	<math>g_1 = \frac{F_1}{1+\gamma^2} (A_1+\gamma A_2)</math>		<math>g_1 = \frac{F_1}{1+\gamma^2} (A_1+\gamma A_2)</math>

← Older revision		Revision as of 21:02, 11 January 2010
Line 17:		Line 17:


		+	<math>\Gamma_1 = \int_x^{x_o} g_1(x,Q^2) dx</math>
		+
		+	<math>g_1 = \frac{F_1}{1+\gamma^2} (A_1+\gamma A_2)</math>

	<math>\sigma \propto \|M_{if}\|^2</math>		<math>\sigma \propto \|M_{if}\|^2</math>

← Older revision		Revision as of 22:34, 9 January 2010
Line 23:		Line 23:

	<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}} = \frac{\frac{1}{3} - 1}{\frac{1}{3} + 1} = -1/2</math>		<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}} = \frac{\frac{1}{3} - 1}{\frac{1}{3} + 1} = -1/2</math>
		+
		+
		+	[http://wiki.iac.isu.edu/index.php/Forest_Classes] [[ Forest_Classes]]

← Older revision		Revision as of 20:58, 9 January 2010
Line 1:		Line 1:
	The recoupling of two subsystems <math>\psi</math> with angular momenta <math>j_1</math> and <math>j_2</math> to a new system<math> \Psi</math> with total angular momentum <math>J</math> is written as		The recoupling of two subsystems <math>\psi</math> with angular momenta <math>j_1</math> and <math>j_2</math> to a new system<math> \Psi</math> with total angular momentum <math>J</math> is written as

−	<math>\Psi^{J}_{M} = \sum_{m_1,m_2} C^{j_1,j_2,J}_{m_1,m_2,M} \psi^{j_1}_{m_1} \psi^{j_2}_{m_2}</math>	+	<math>\Psi^{J}_{M} = \sum_{m_1,m_2} C^{j_1,j_2,J}_{m_1,m_2,M} \psi^{j_1}_{m_1} \psi^{j_2}_{m_2}</math> = expansion of the systems total angular momentum in terms of the uncoupled original basis states of each individual constituent

← Older revision		Revision as of 20:54, 9 January 2010
Line 9:		Line 9:

	<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>		<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>
		+
		+	<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{0,\frac{1}{2},\frac{1}{2}}= \frac{2}{\sqrt{3}}</math>

	<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{2}{\sqrt{3}}</math>		<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{2}{\sqrt{3}}</math>

← Older revision		Revision as of 20:53, 9 January 2010
Line 10:		Line 10:
	<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>		<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>

−	<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= 1</math>	+	<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{2}{\sqrt{3}}</math>
		+
		+	<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{0,\frac{1}{2},\frac{1}{2}}= -\frac{1}{\sqrt{3}}</math>
		+

← Older revision		Revision as of 20:50, 9 January 2010
Line 9:		Line 9:

	<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>		<math>C^{1,\;\;\frac{1}{2},\frac{3}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= \frac{1}{\sqrt{3}}</math>
		+
		+	<math>C^{1,\;\;\frac{1}{2},\frac{1}{2}}_{1,-\frac{1}{2},\frac{1}{2}}= 1</math>

← Older revision		Revision as of 22:44, 8 January 2010
Line 15:		Line 15:
	<math>M_{fi} = <\Psi_f \| H_{int} \| \Psi_i></math>		<math>M_{fi} = <\Psi_f \| H_{int} \| \Psi_i></math>

−	<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}}</math>	+	<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}} = \frac{\frac{1}{3} - 1}{\frac{1}{3} + 1} = -1/2</math>

@@ Line 11: / Line 11: @@
-<math>\sigma \equiv |M_{if}|^2</math>
+<math>\sigma \propto |M_{if}|^2</math>
 <math>M_{fi} = <\Psi_f | H_{int} | \Psi_i></math>
-<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}</math>
+<math>A = \frac{\sigma_{\frac{1}{2}} - \sigma_{\frac{3}{2}}}{\sigma_{\frac{1}{2}} + \sigma_{\frac{3}{2}}}</math>