Nuclear Decay Forest NucPhys I - Revision history

Foretony: /* negative beta decay */

2015-12-18T00:39:43Z

negative beta decay

2009-04-27T18:50:00Z

Forbidden decays

2009-04-27T18:49:02Z

electron capture Example

2009-04-27T18:48:47Z

electron capture Example

2009-04-27T18:48:12Z

electron capture Example

2009-04-27T18:47:28Z

positive beta decay

2009-04-27T18:47:08Z

negative beta decay

2009-04-27T18:46:02Z

positive beta decay Example

2009-04-27T16:21:10Z

Decay rate

2009-04-27T16:07:49Z

Decay rate

@@ Line 113: / Line 113: @@
 </math>
 ;where
-:<math>B_i</math> = ith elctron binding energy
+:<math>B_i</math> = ith electron binding energy
 then

@@ Line 301: / Line 301: @@
 :second-forbidden<math> \Rightarrow \vec{L} = \vec{2}\;\;\; \Delta I=2,3 \;\;\;\Delta \pi =0</math>
 :third-forbidden<math> \Rightarrow \vec{L} = \vec{3}\;\;\; \Delta I=3,4 \;\;\;\Delta \pi =1</math>
-:fourth-forbidden<math> \Rightarrow \vec{L} = \vec{4}\;\;\; \Delta I=4,5 \;\;\;\Delta \pi =1</math>
+:fourth-forbidden<math> \Rightarrow \vec{L} = \vec{4}\;\;\; \Delta I=4,5 \;\;\;\Delta \pi =0</math>
 Each of the above have Fermi <math>(\vec{S}=0)</math> and Gamow-Teller <math>(\vec{S}=1)</math> decays.

@@ Line 186: / Line 186: @@
 : <math>{7 \atop 4 }Be_{3} + \beta^- \rightarrow {7 \atop 3 }Li_{4}  + \nu_e</math>
-:<math>Q_{\epsilon} = \left [ m\left({7 \atop 4 }B\right)- m\left({7 \atop 3 }Li\right) \right] c^2 - 259 eV</math>
+:<math>Q_{\epsilon} = \left [ m\left({7 \atop 4 }Be\right)- m\left({7 \atop 3 }Li\right) \right] c^2 - 259 eV</math>
 : <math>= \left [ 7.0169292- 7.0160040 \right] 931.502 \frac{\mbox{MeV}}{\mbox {u}} - 0.259 keV</math>
 :<math>= 861.83 keV -0.259 keV= 861.57 keV</math>

@@ Line 188: / Line 188: @@
 :<math>Q_{\epsilon} = \left [ m\left({7 \atop 4 }B\right)- m\left({7 \atop 3 }Li\right) \right] c^2 - 259 eV</math>
 : <math>= \left [ 7.0169292- 7.0160040 \right] 931.502 \frac{\mbox{MeV}}{\mbox {u}} - 0.259 keV</math>
-:<math>= 861.83MeV -0.259 keV= 861.57</math>
+:<math>= 861.83 keV -0.259 keV= 861.57 keV</math>
 <math>Q_{\beta^+}(experiment) = 862 </math> keV

@@ Line 184: / Line 184: @@
 ==== electron capture Example====
-: <math>{7 \atop 4 }B_{3} + \beta^- \rightarrow {7 \atop 3 }B_{4}  + \nu_e</math>
+: <math>{7 \atop 4 }Be_{3} + \beta^- \rightarrow {7 \atop 3 }Li_{4}  + \nu_e</math>
 :<math>Q_{\epsilon} = \left [ m\left({7 \atop 4 }B\right)- m\left({7 \atop 3 }Li\right) \right] c^2 - 259 eV</math>

@@ Line 149: / Line 149: @@
 :<math>\;\;\;\;\;= T_{\beta^+} + T_{\bar{\nu}}</math> = energy shared by electron and neutrino
-<math>B_Z =</math> binding energy of most outer electron
+<math>B_Z =</math> binding energy of most outer electron in element "X"
 ==== positive beta decay Example====

@@ Line 120: / Line 120: @@
 :<math>\;\;\;\;\;= T_{\beta^-} + T_{\bar{\nu}}</math> = energy shared by electron and neutrino
-<math>B_Z =</math> binding energy of most outer electron
+<math>B_Z =</math> binding energy of most outer electron in element "Y"
 ==== negative beta decay Example====

@@ Line 152: / Line 152: @@
 ==== positive beta decay Example====
-: <math>{7 \atop 4 }Be_{3} \rightarrow {7 \atop 3 }Li_{4} + \beta^+ + \nu_e</math>
+: <math>{11 \atop 6 }C_{5} \rightarrow {11 \atop 5 }B_{6} + \beta^+ + \nu_e</math>
 :<math>Q_{\beta^+} = \left [ m\left({11 \atop 6 }C\right)- m\left({11 \atop 5 }B\right) \right] c^2 - 2m_ec^2+B_Z</math>

@@ Line 341: / Line 341: @@
 <math>\hat{H_{int}} =\left \{  {\hat{1} \hat{\tau} \;\;\;\; \mbox{Fermi decay} \atop \hat{\sigma} \hat{\tau} \;\;\;\; \mbox{Gamow-Teller Decay}} \right .</math>
+: <math>\hat{\tau}</math> = isospin transition matrix which turn protons to neutrons and vis-versa
 [[Forest_NucPhys_I]]

@@ Line 333: / Line 333: @@
 says that the transition rate <math>W</math> is given by a transition matrix element (or "Amplitude") <math>M_{i,f}</math> weighted by the phase space and Plank's constant <math>\hbar</math> such that
-: <math>W = \frac{2 \pi}{\hbar} |M_{i,f}|^2 \times </math>(Phase Space) <math>= \frac{0.693}{t_{1/2}}</math>
+: <math>W = \frac{2 \pi}{\hbar} |M_{i,f}|^2 \times </math>(Phase Space) <math>= \frac{\ln(2)}{t_{1/2}}</math>
 The underlying assumption is that the transition is a weak purturbation of the system. This assumption appears to be true based on the very short time scale (<math>10^{-20}</math> sec) it takes for the formation of quasi-stationary nuclear states compared with the time it takes for a <math>\beta</math> decay ( half lives ranging from seconds to days)