RadioNuclides.C File Reference

Detailed Description

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.

 
void DrawPopulation(TObjArray *vect, TCanvas *can, Double_t tmin = 0., Double_t tmax = 0., Bool_t logx = kFALSE);
 
void RadioNuclides()
{
   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);
   pt->AddText("Time evolution of a population of radionuclides.");
   pt->AddText("The concentration of a nuclide X represent the  ");
   pt->AddText("ratio between the number of X nuclei and the    ");
   pt->AddText("number of nuclei of the top element of the decay");
   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, Double_t tmax, Bool_t logx)
{
   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");
      }
   }
}

Author

Mihaela Gheata

Definition in file RadioNuclides.C.