Added to SVN repository

geant4/LEMuSR/include/LEMuSRMuonDecayChannel.hh

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 //             LOW ENERGY MUON SPIN RELAXATION, ROTATION, RADIATION   Geant4 SIMULATION
 //  ID    : LEMuSRMuonDecayChannel.hh , v 1.0
 //  AUTHOR: Taofiq PARAISO based on G4MuonDecayChannel $Id$
 //  DATE  : 2004-07-13 11:15
 //                   
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 //                           &
 //                         &  
 //                          MUON DECAY CHANNEL.HH
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- 
+/**
+ * The LEMuSRMuonDecayChannel class contains the implementation of the asymmetric muon decay. The process is applicable to muon (positive or negative) and muonium.
+ *
+ * It was inspired from the G4MuonDecayChannel method, which did not take into account the spin polarization of the muon.
+ * 
+ * One should notice that recent versions of Geant4 feature a G4MuonDecayChannelWithSpin class, whose role is identical to the class we are describing.
+ * 
+ * The two caracteristics of this process are 
+ * - The Michel spectrum for e+ energy distribution
+ *   \image html michel.gif Michel's Spectrum.
+ * - The cardioidal angular distribution as a function of the positron energy
+ *   \image html kardio.gif Cardioid.
+ * .
+ * The angular direction of the positron emission is in relation with the energy of 
+ * the positron. 
+ * The more energy the positron has, the smaller the angle of emission with respect 
+ * to the muon spin is. The V-A theory predicts the positron rate to be
+ * \f[ \mbox{d}\Gamma^2(w,\theta)= \frac{1}{\tau n(w)\left[1+ D(w)cos\theta \right]}\mbox{d}w \mbox{d}(\cos \theta),\f]
+ * \f$w\f$ being the ratio between the energy of the emitted positron and the 
+ * maximal energy, and \f$\theta\f$ the angle between the muon spin and the 
+ * positron momentum.
+ * 
+ * The distribution \f$n(w)\f$ along energy is given by the Michel's spectrum 
+ * \f[ n(w)= w^2(3-2w)\f] and the asymmetric factor is given by 
+ * \f[D(w) = \frac{2w-1}{3-2w}.\f] We assume, here, that the muons are fully 
+ * polarized. 
+ *
+ * The distribution along energies becomes, for \f$\Theta=0\f$, 
+ * \f[n(w)+n(w)D(w)= 2w^2\f]
+ * and for \f$\Theta = \pi\f$, 
+ * \f[n(w)-n(w)D(w)= 4(w^2-w^3)\f]
+ *
+ * The asymmetry can be derived integrating the rate \f$d\Gamma^2\f$, 
+ * and one should get
+ * \f[A(w_{min}, \Theta_0) = \frac{1+\cos\Theta_0}{6}\frac{1+2w_{min}^3-3w_{min}^4}{1-2w_{min}^3+w_{min}^4}\f]
+ * where \f$\Theta_0\f$ is the opening angle of the solid angle.
+ * This means that if one select all positron energies, \f$w_{min}\simeq 0\f$
+ * - \f$A \simeq\frac{1}{3}\f$ for small solid angles
+ * - \f$A \simeq\frac{1}{6}\f$ for large solid angles
+
+ */
 
 #ifndef LEMuSRMuonDecayChannel_h
 #define LEMuSRMuonDecayChannel_h 1
@@ -38,18 +78,12 @@ class LEMuSRMuonDecayChannel : public G4VDecayChannel
 {
 
   // Class Decription
-  // 
-  // To do list::
-  //  Find muon polarization  
-  //  Compute the positron angle distribution
-  //  Compute the positron energy as a function of angle distribution
-  //  Remove G4MuonDecayChannel in decay table and add this new one
 
 public:  
-  //Constructors 
+  //!Constructor. 
   LEMuSRMuonDecayChannel(const G4String& theParentName,
 		     G4double        theBR);
-  //  Destructor
+  //! Destructor.
   ~LEMuSRMuonDecayChannel();
   
  static LEMuSRMuonDecayChannel* pointer;
@@ -59,18 +93,24 @@ public:
 void   finalize();
 
 public:  // With Description
+  //! \mm
   virtual G4DecayProducts *DecayIt(G4double);     
   HepRandomEngine* theEngine;
   G4ThreeVector emomdir;  
 
+  //! Angles.
   G4double alpha,sinalpha, cosalpha, delta, sindelta, cosdelta;
+  //! Sines and cosines.
   G4double costheta, sintheta, phi, sinphi, cosphi, theta; 
 
   inline G4double GetTheta(){return theta;};
   inline G4double GetPhi(){return phi;};
  
 
-
+  //! Polarized decay
+  /*!
+   * Gets the muon polarization and launch the Decay it method. 
+  */
   G4DecayProducts *DecayItPolarized(G4double,G4ThreeVector polar);