1. 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 = X0(Z+1,2)

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

3. 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 = 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

4. 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