void RadioNuclides()
{
// Macro that demonstrates usage of radioactive elements/materials/mixtures
// with TGeo package.
//
// A radionuclide (TGeoElementRN) derives from the class TGeoElement and
// provides additional information related to its radioactive properties and
// decay modes.
//
// The radionuclides table is loaded on demand by any call:
//    TGeoElementRN *TGeoElementTable::GetElementRN(Int_t atomic_number, 
//                                                  Int_t atomic_charge, 
//                                                  Int_t isomeric_number)
// The isomeric number is optional and the default value is 0.
//
// To create a radioactive material based on a radionuclide, one should use the
// constructor:
//    TGeoMaterial(const char *name, TGeoElement *elem, Double_t density)
// To create a radioactive mixture, one can use radionuclides as well as stable
// elements:
//    TGeoMixture(const char *name, Int_t nelements, Double_t density);
//    TGeoMixture::AddElement(TGeoElement *elem, Double_t weight_fraction);
// Once defined, one can retrieve the time evolution for the radioactive 
// materials/mixtures by using one of the 2 methods:
//
//    void TGeoMaterial::FillMaterialEvolution(TObjArray *population,
//                                             Double_t   precision=0.001)
// To use this method, one has to provide an empty TObjArray object that will
// be filled with all elements coming from the decay chain of the initial 
// radionuclides contained by the material/mixture. The precision represent the
// cumulative branching ratio for which decay products are still considered.
// The POPULATION list may contain stable elements as well as radionuclides,
// depending on the initial elements. To test if an element is a radionuclide:
//    Bool_t TGeoElement::IsRadioNuclide() const
// All radionuclides in the output population list have attached objects that
// represent the time evolution of their fraction of nuclei with respect to the
// top radionuclide in the decay chain. These objects (Bateman solutions) can be
// retrieved and drawn:
//    TGeoBatemanSol *TGeoElementRN::Ratio();
//    void TGeoBatemanSol::Draw();
//
// Another method allows to create the evolution of a given radioactive 
// material/mixture at a given moment in time:
//    TGeoMaterial::DecayMaterial(Double_t time, Double_t precision=0.001)
// The method will create the mixture that result from the decay of a initial
// material/mixture at TIME, while all resulting elements having a fractional
// weight less than PRECISION are excluded.
//Author: Mihaela Gheata

   TGeoManager *geom = new TGeoManager("","");
   TGeoElementTable *table = gGeoManager->GetElementTable();
   TGeoElementRN *c14 = table->GetElementRN(14,6);
   TGeoElementRN *el1 = table->GetElementRN(53,20);
   TGeoElementRN *el2 = table->GetElementRN(78,38);
   // Radioactive material
   TGeoMaterial *mat = new TGeoMaterial("C14", c14, 1.3);
   printf("___________________________________________________________\n");
   printf("Radioactive material:\n");
   mat->Print();
   Double_t time = 1.5e11; // seconds
   TGeoMaterial *decaymat = mat->DecayMaterial(time);
   printf("Radioactive material evolution after %g years:\n", time/3.1536e7);
   decaymat->Print();
   //Radioactive mixture
   TGeoMixture *mix = new TGeoMixture("mix", 2, 7.3);
   mix->AddElement(el1, 0.35);
   mix->AddElement(el2, 0.65);
   printf("___________________________________________________________\n");
   printf("Radioactive mixture:\n");
   mix->Print();
   time = 1000.;
   decaymat = mix->DecayMaterial(time);
   printf("Radioactive mixture evolution after %g seconds:\n", time);
   decaymat->Print();
   TObjArray *vect = new TObjArray();
   TCanvas *c1 = new TCanvas("c1","C14 decay", 800,600);
   c1->SetGrid();
   mat->FillMaterialEvolution(vect);
   DrawPopulation(vect, c1, 0, 1.4e12);
   TLatex *tex = new TLatex(8.35e11,0.564871,"C_{N^{14}_{7}}");
   tex->SetTextSize(0.0388601);
   tex->SetLineWidth(2);
   tex->Draw();
   tex = new TLatex(3.33e11,0.0620678,"C_{C^{14}_{6}}");
   tex->SetTextSize(0.0388601);
   tex->SetLineWidth(2);
   tex->Draw();
   tex = new TLatex(9.4e11,0.098,"C_{X}=#frac{N_{X}(t)}{N_{0}(t=0)}=\
   #sum_{j}#alpha_{j}e^{-#lambda_{j}t}");
   tex->SetTextSize(0.0388601);
   tex->SetLineWidth(2);
   tex->Draw();
   TPaveText *pt = new TPaveText(2.6903e+11,0.0042727,1.11791e+12,0.0325138,"br");
   pt->SetFillColor(5);
   pt->SetTextAlign(12);
   pt->SetTextColor(4);
   text = pt->AddText("Time evolution of a population of radionuclides.");
   text = pt->AddText("The concentration of a nuclide X represent the  ");
   text = pt->AddText("ratio between the number of X nuclei and the    ");
   text = pt->AddText("number of nuclei of the top element of the decay");
   text = pt->AddText("from which X derives from at T=0.               ");
   pt->Draw();
   c1->Modified();
   vect->Clear();
   TCanvas *c2 = new TCanvas("c2","Mixture decay", 1000,800);
   c2->SetGrid();
   mix->FillMaterialEvolution(vect);
   DrawPopulation(vect, c2, 0.01, 1000., kTRUE);
   tex = new TLatex(0.019,0.861,"C_{Ca^{53}_{20}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(1);
   tex->Draw();
   tex = new TLatex(0.0311,0.078064,"C_{Sc^{52}_{21}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(2);
   tex->Draw();
   tex = new TLatex(0.1337,0.010208,"C_{Ti^{52}_{22}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(3);
   tex->Draw();
   tex = new TLatex(1.54158,0.00229644,"C_{V^{52}_{23}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(4);
   tex->Draw();
   tex = new TLatex(25.0522,0.00135315,"C_{Cr^{52}_{24}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(5);
   tex->Draw();
   tex = new TLatex(0.1056,0.5429,"C_{Sc^{53}_{21}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(6);
   tex->Draw();
   tex = new TLatex(0.411,0.1044,"C_{Ti^{53}_{22}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(7);
   tex->Draw();
   tex = new TLatex(2.93358,0.0139452,"C_{V^{53}_{23}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(8);
   tex->Draw();
   tex = new TLatex(10.6235,0.00440327,"C_{Cr^{53}_{24}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(9);
   tex->Draw();
   tex = new TLatex(15.6288,0.782976,"C_{Sr^{78}_{38}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(1);
   tex->Draw();
   tex = new TLatex(20.2162,0.141779,"C_{Rb^{78}_{37}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(2);
   tex->Draw();
   tex = new TLatex(32.4055,0.0302101,"C_{Kr^{78}_{36}}");
   tex->SetTextSize(0.0388601);
   tex->SetTextColor(3);
   tex->Draw();
   tex = new TLatex(117.,1.52,"C_{X}=#frac{N_{X}(t)}{N_{0}(t=0)}=#sum_{j}\
   #alpha_{j}e^{-#lambda_{j}t}");
   tex->SetTextSize(0.03);
   tex->SetLineWidth(2);
   tex->Draw();
   TArrow *arrow = new TArrow(0.0235313,0.74106,0.0385371,0.115648,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(0.0543138,0.0586338,0.136594,0.0146596,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(0.31528,0.00722919,1.29852,0.00306079,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(4.13457,0.00201942,22.5047,0.00155182,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(0.0543138,0.761893,0.0928479,0.67253,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(0.238566,0.375717,0.416662,0.154727,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(0.653714,0.074215,2.41863,0.0213142,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(5.58256,0.00953882,10.6235,0.00629343,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(22.0271,0.601935,22.9926,0.218812,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
   arrow = new TArrow(27.2962,0.102084,36.8557,0.045686,0.02,">");
   arrow->SetFillColor(1);
   arrow->SetFillStyle(1001);
   arrow->SetLineWidth(2);
   arrow->SetAngle(30);
   arrow->Draw();
}

void DrawPopulation(TObjArray *vect, TCanvas *can, Double_t tmin=0., 
   Double_t tmax=0., Bool_t logx=kFALSE)
{
   Int_t n = vect->GetEntriesFast();
   TGeoElementRN *elem;
   TGeoBatemanSol *sol;
   can->SetLogy();
   
   if (logx) can->SetLogx();
   

   for (Int_t i=0; i<n; i++) {
      TGeoElement *el = (TGeoElement*)vect->At(i);
      if (!el->IsRadioNuclide()) continue;
      TGeoElementRN *elem = (TGeoElementRN *)el;
      TGeoBatemanSol *sol = elem->Ratio();
      if (sol) {
         sol->SetLineColor(1+(i%9));
         sol->SetLineWidth(2);
         if (tmax>0.) sol->SetRange(tmin,tmax);
         if (i==0) {
            sol->Draw();
            TF1 *func = (TF1*)can->FindObject(
               Form("conc%s",sol->GetElement()->GetName()));
            if (func) {
               if (!strcmp(can->GetName(),"c1")) func->SetTitle(
                  "Concentration of C14 derived elements;time[s];Ni/N0(C14)");
               else func->SetTitle(
                  "Concentration of elements derived from mixture Ca53+Sr78;\
                  time[s];Ni/N0(Ca53)");
            }   
         }   
         else      sol->Draw("SAME");
      }
   }      
}