1. Gamma calorimeter for R3B: first simulation results INDEX ● The calGamma Geant4 simulation ( a short introduction ) ● Crystal and geometry selection: – the full absorption explained – the effect of the backwards aperture on the absorption ● Outlook Héctor Alvarez Pol for the R3B collaboration GENP - Univ. Santiago de Compostela 11 January 2005

2. ● Introduction to the calGamma simulation

3. Starting the simulation: main features ● Very simple geometry: G4Sphere (inner, outer radius, initial and delta and ). ● Still no cover, encapsulation or support in the code. ● A large set of materials is included both for the crystal and the environments; for the crystals: LaBr 3, CsI, NaI, PWO, BGO...; for the environment: air, vacuum... ● Full physics (em, hadronic) packages included, please test it! ● Primaries (gammas, protons,..., coming from the origin) can be boosted according to the beam energy. Random emission (angle or energy) can be selected. ● Messenger commands for user control (next slides). ● ROOT libraries included for fully integrated analysis interface. ● Partially documented (code is documented in the C++ style, that is, readable ;-) some example macros and results directories available. More on request?

4. User interface / macros for batch ● Commands allow the control of the program from user interface or macros. ● Commands can be added easily in Messenger classes (requires code recompilation). ● OpenGL/(Dawn)/... viewers for graphical output. ● A ROOT file is created for the storage of TTree / TH1D / TH2D... ● Online histograms are available while running an interactive session.

5. An example macro – Commands for output verbosity – Commands for geometry control – Commands for primaries control –...

6. Note: about the kinematics... Lorentz transformation (P || is the component of P parallel to v): E' = E + P || = E + Pcos ( remember, for gammas, E = P ) For an isotropic angular emission the distribution in cos is flat! Then, for protons at T=700MeV ( =0.8197507, =1.74605 ) : E' = 1.74605 E + 1.43132571 E cos In the limit: cos = 1 → E'=3.1774 E cos = -1 → E'=0.3147 E and the energy distribution is also flat! See, for instance, Simply Kinematics from G.I. Kopilov, p.124-128 Gammas of 10 MeV

7. ● Crystal and geometry selection

8. Crystal selection: full absorption results ● Full sphere (4) with gamma emission from the center (no boost, 4 - iso). Inner radius is always 0. ● Results were obtained modifying the sphere outer radius and the energy of the emitted gamma. We represent the percentage of gammas with full energy deposited on the crystal, as a function of the crystal sphere radius and the gamma energy

9. Why the absorption drops at high energies? ● Number of interactions (Photo, Compton or Pair Conversion) in a 500 mm thick crystal ball (250 < r < 750) ● Conversion dominates for larger energies; conversion photons can escape from the crystal bulk.

10. Why the absorption drops at high energies? (2) Sphere params: ● inner radius: 0cm ● outer radius: 20cm ● gamma energy: 30 MeV Efficiency 65% 1.2% lost below 1% of gamma energy 4.5% lost below 511 keV peak 0.7% lost in 511 keV photons 9.9% lost below 3% of gamma energy

11. Why the absorption drops at high energies? (3) Sphere params: ● inner radius: 0cm ● outer radius: 20cm ● gamma energy: 10 MeV Efficiency 86.5% 0.6% lost below 3% of gamma energy 2.3% lost below 511 keV peak 0.5% lost in 511 keV photons 5.2% lost below 10% of gamma energy

12. Selecting the backwards opening angle ● Due to the boost, gammas are basically emitted in the forward direction. A large open zone in the backwards region reduces dramatically the crystal bulk needed. ● To check the effect on the efficiency, a set of simulations with different opening angles (“angle” in next slide) was made. ● Two different sets of gammas of 5 and 10 MeV are boosted as primary source.

13. Selecting the backwards opening angle

14. Outlook ● Simulation ready for user tests ● First conclusions on geometry for LoI ● Request for improvements and further details

15. Other topics already done... ● RPC GEANT4 simulation already working. ● 3D drawings for RPC presentation (LoI). ● 3D drawings for Gamma Calorimeter under development

16. Appendix: some calculations... Proton mass: m = 938.27203 MeV and kinetic energy T = 700 MeV Using T = E - m → T + m = m / √ (1-v 2 ) Then: v 2 = 1 – m 2 / (T + m) 2

17. Appendix: some formula Notation Rest mass: m, Energy(=mass): E = M = m Momentum: P = M = m, kinetic energy: T = E-m = m – m As usual: E 2 = P 2 + m 2 Fotones -> m = 0 -> E = P Lorentz transformation: E' = E + P || = E + Pcos P || '= P || +E