Spectrometry of high energy gamma ray Photons with energies of tenths MeV, GeV and higher Creation of electromagnetic shower – it is necessary to determine total energy, direction and time of initial photon arrival Inorganic scintillation detectors are favorable: BGO, BaF2, PbWO4 Combination of convertor (lead, tungsten ..) and track detectors of electrons and positrons (spark chambers, silicon …) Electromagnetic shower Eγ >> 1 MeV photo effect is negligible → gamma detection by means of electromagnetic shower, pair production, bremsstrahlung radiation ... Important quantity is radiation length X0 – high energy electron E → E/e Eγ ~ 100 MeV → detectors with 15 X0 are needed Width of electromagnetic shower Molier radius R0 ~ cm (about 90% of shower energy is inside, it is approximately valid: R0 = 0.0265X0(Z+1,2)

Deepness expressed with radiation lengths X0: t = x/X0 Particle multiplication – increasing number of electrons, positrons and photons Deepness expressed with radiation lengths X0: t = x/X0 Critical energy EC – energy higher it radiation losses start to dominated over ionization t 4 1 2 3 N(t) 1/2 1/4 1/8 ε(t)/E For critical energy EC and radiation length X0 is valid: Energy in EC units: Є = E/EC Number of cascade particles increases geometrically: N(t) = 2t Mean energy of particles ε is: Multiplication continues up to critical energy EC Maximal number of particles NMAX at deepness tMAX tMAX ~ ln Є 3,2 GeV v Pb maximum tMAX = 6, NMAX = 400

Segmented detectors with long crystals (diameter is two times Molier radius Sum of energies from main and surrounding modules: y z Loss of small contributions from modules, where Ei is bellow detection threshold Position of centre is determined: Other types of weights can be used Example from spectrometer TAPS (BaF2) l = 250 mm, d = 54-59 mm: X0 = 20,5 mm R0 = 33,9 mm, EC= 12,7 MeV For Eγ ~ 160 MeV: ΔE/E ~ 16% – only detector with the highest deposited energy ΔE/E ~ 6% - all detectors hit by electromagnetic shower High energies ΔE/E → 3% Position resolution of TAPS spectrometer

Detection of particles using their decay to photons: Determination of particle invariant mass: Uncertainty of invariant mass determination: Inclusion of different number Of neighboring modules Typical TOF spectrum (target distance was 4.3 m), Bi + Pb collisions 1 GeV/n Comparision of mean number of affected modules for photons and neutrons