DV Calculations of 4-momentum components - Revision history

Vanwdani: Replaced content with " ===Verification=== Verification of Relativistic Components ===Conclusion=== Conclusion ---- [[DV_RunGroupC_Mol…"

2017-05-31T20:25:46Z

Replaced content with " ===Verification=== Verification of Relativistic Components ===Conclusion=== Conclusion ---- [[DV_RunGroupC_Mol…"

2017-05-31T17:50:23Z

Initial Conditions

2016-09-08T21:00:48Z

4-Momentum Invariants

2016-02-04T15:55:13Z

Verification

2016-02-04T15:40:51Z

Verification

2016-02-04T04:05:13Z

Electron Lab Frame

2016-02-03T05:05:08Z

Scattered and Moller Electron energies in CM

2016-01-30T02:55:27Z

Moller electron Center of Mass Frame

2016-01-30T02:55:08Z

Moller electron Center of Mass Frame

2016-01-30T02:52:30Z

xz Plane

← Older revision		Revision as of 17:50, 31 May 2017
Line 6:		Line 6:


−	~~===Lab Frame===~~

−	~~<center>[[File:lab.png \| 400 px]]</center>~~
−	~~<center>'''Figure 1: Definition of variables in the Lab Frame '''</center>~~
−
−
−
−	~~Begining with the assumption that the incoming electron, p<sub>1</sub>, has momentum of 11000 MeV in the positive z direction.~~
−
−
−	~~<center><math>\vec p_{1(z)}\equiv \vec p_{1}=11000 MeV \widehat {z}</math></center>~~
−
−
−	~~We can also assume the Moller electron, p<sub>2</sub>, is initially at rest~~
−
−
−	~~<center><math>\vec p_{2}\equiv 0</math></center>~~
−
−
−	~~This gives the total energy in this frame as~~
−
−
−	~~<center><math>E\equiv E_1+E_2</math></center>~~
−
−
−	~~where,~~
−	~~<center><math>E\equiv \sqrt{p^2+m^2}</math></center>~~
−
−
−
−	~~This gives,~~
−	~~<center><math>E\equiv \sqrt{(p_{1})^2+(m_{1})^2}+m_{2}</math></center>~~
−
−
−
−	~~{\| class="wikitable" align="center"~~
−	~~\| style="background: gray" \| <math>\Longrightarrow E\equiv \sqrt{(11000 MeV)^2+(.511 MeV)^2}+.511MeV\approx 11000.511 MeV</math>~~
−	\|}

	===Center of Mass Frame===		===Center of Mass Frame===

@@ Line 48: / Line 48: @@
 ====4-Momentum Invariants====
-<center>[[File:CM.png |400 px]]</center>
+<center>[[File:400px-CMcopy.png |400 px]]</center>
 <center>'''Figure 2: Definition of variables in the Center of Mass Frame'''</center>

@@ Line 737: / Line 737: @@
 [[Verification of Relativistic Components]]
+===Conclusion===
 ----

@@ Line 736: / Line 736: @@
 ===Verification===
 [[Verification of Relativistic Components]]
 [[DV_RunGroupC_Moller#Momentum distributions in the Center of Mass Frame]]
 [[DV_MollerTrackRecon#Calculations_of_4-momentum_components]]

@@ Line 647: / Line 647: @@
 |}
 [[DV_RunGroupC_Moller#Momentum distributions in the Center of Mass Frame]]
 [[DV_MollerTrackRecon#Calculations_of_4-momentum_components]]

@@ Line 246: / Line 246: @@
 <center><math>\Longrightarrow\begin{cases}
 E^*=\gamma^* (E_{1}+m)-\beta^* \gamma^* p_{1(z)} \\
-p^*_{z}=-\beta^* \gamma^*(E_{1}+m)+\gamma^* p^*_{1(z)}
+p^*_{z}=-\beta^* \gamma^*(E_{1}+m)+\gamma^* p_{1(z)}
 \end{cases}</math></center>

@@ Line 481: / Line 481: @@
 {| class="wikitable" align="center"
-| style="background: gray"  | <math>-p^*_{2(z)}=\sqrt {(p^*_2)^2-(p^*_{2(x)})^2-(p^*_{2(y)})^2}</math>
+| style="background: gray"  | <math>p^*_{2(z)}=-\sqrt {(p^*_2)^2-(p^*_{2(x)})^2-(p^*_{2(y)})^2}</math>
 |}

@@ Line 359: / Line 359: @@
 {| class="wikitable" align="center"
-| style="background: gray"      | <math>\Longrightarrow {p^'_{2(z)}=-p^'_{2}\cos(\theta '_2)}</math>
+| style="background: gray"      | <math>\Longrightarrow {p^'_{2(z)}=p^'_{2}\cos(\theta '_2)}</math>
 |}