TF SPIM HadronicInteractions - Revision history

Foretony: /* Lethargy */

2013-11-22T00:22:33Z

Lethargy

2013-11-22T00:22:16Z

Lethargy

2013-11-22T00:21:42Z

Lethargy

2013-11-22T00:21:01Z

Lethargy

2013-11-22T00:20:19Z

Lethargy

2013-11-22T00:19:50Z

Lethargy

2013-11-22T00:19:27Z

Lethargy

2013-11-22T00:19:12Z

Lethargy

2013-11-22T00:17:47Z

Lethargy

2013-11-22T00:16:46Z

Lethargy

@@ Line 155: / Line 155: @@
 ====Lethargy====
-Lethargy<math> \equiv u(\that)  \equiv  \ln \frac{E_0}{E}</math> = logarithmic energy change
+Lethargy<math> \equiv u(\theta)  \equiv  \ln \frac{E_0}{E}</math> = logarithmic energy change
 :=<math>\ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2A \cos{\theta}_{CM}} \right )</math>

@@ Line 155: / Line 155: @@
 ====Lethargy====
-Lethargy<math> \equiv</math> u<math> \equiv  \ln \frac{E_0}{E}</math> = logarithmic energy change
+Lethargy<math> \equiv u(\that)  \equiv  \ln \frac{E_0}{E}</math> = logarithmic energy change
 :=<math>\ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2A \cos{\theta}_{CM}} \right )</math>

@@ Line 157: / Line 157: @@
 Lethargy<math> \equiv</math> u<math> \equiv  \ln \frac{E_0}{E}</math> = logarithmic energy change
-:=<math>\ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2Acos{\theta}_{CM}} \right )</math>
+:=<math>\ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2A \cos{\theta}_{CM}} \right )</math>
 The average lethargy
 <math><u(\theta)> = \int u(\theta) \frac{d \Omega}{4 \pi}</math>
-:=<math>\frac{1}{2} \int \ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2Acos{\theta}_{CM}} \right ) d[cos(\theta)]</math>
+:=<math>\frac{1}{2} \int \ln \left ( \frac{(1+A)^2} {A^2 + 1 + 2A \cos{\theta}_{CM}} \right ) d[ \cos(\theta)]</math>

@@ Line 166: / Line 166: @@
 N = # of collisions = <math>\frac{\mbox{Desired Energy Change}}{\mbox{Average Energy change per collision}}</math>
-:<math>= \frac{\ln \left (\frac{E_0}{E} \right )}{1 + \frac{\left (A-1 \right )^2}{2A}}</math>
+:<math>= \frac{\ln \left (\frac{E_0}{E} \right )}{1 + \frac{\left (A-1 \right )^2}{2A}\ln \left ( \frac{A-1}{A+1} \right )}</math>
 ==== Inelastic Scattering====

@@ Line 166: / Line 166: @@
 N = # of collisions = <math>\frac{\mbox{Desired Energy Change}}{\mbox{Average Energy change per collision}}</math>
-:<math>= \frac{\ln \left (\frac{E_0}{E} \right )}{1}</math>
+:<math>= \frac{\ln \left (\frac{E_0}{E} \right )}{1 + \frac{\left (A-1 \right )^2}{2A}}</math>
 ==== Inelastic Scattering====

@@ Line 165: / Line 165: @@
-N = # of collisions = \frac{\mbox{Desired Energy Change}}{\mbox{Average Energy change per collision}}
+N = # of collisions = <math>\frac{\mbox{Desired Energy Change}}{\mbox{Average Energy change per collision}}</math>
-:= \frac{\ln{\frac{E_0}{E}}}{1}
+:<math>= \frac{\ln{\frac{E_0}{E}}}{1}</math>
 ==== Inelastic Scattering====

@@ Line 161: / Line 161: @@
 The average lethargy
-<math><u(\theta)> = \int (u(\theta) \frac{d \Omeg}{4 \pi}</math>
+<math><u(\theta)> = \int (u(\theta) \frac{d \Omega}{4 \pi}</math>
 ==== Inelastic Scattering====