Simulation of the energy response of  rays in CsI crystal arrays Thomas ZERGUERRAS EXL-R3B Collaboration Meeting, Orsay (France), 02/02/ /03/2006

Purposes Study of photon interaction with energies from 100keV to 25MeV in CsI crystals using a simple geometry (energy response, multiplicity, efficiency...). Study of the response with a 5*5 array of 22*22*200mm 3 crystals. Tests of some position reconstruction algorithms and their pertinence by using simulated data. Comparison of 5*5 arrays of different crystal sizes: 11*11*200mm 3, 22*22*200mm 3, 32*32*200mm 3 Comparison of 5*5, 7*7 and 9*9 arrays made with 22*22*200mm 3 crystals. Only pure physics interactions are considered here(neither threshold nor noise nor light collection effects are included).

Part 1: Study with a 5*5 array of 22*22*200mm 3 CsI crystals

Geometry Parallepipedic crystals: 22*22*200mm 3 Material: CsI 5*5 array Distance between 2 consecutive crystals: 100µ Space between two crystals filled with Kapton.

Physics list ‘’Low Energy ’’ Electromagnetic list was used. Physics Processes involved are: For  : Photoelectric effect Compton scattering Rayleigh scattering Conversion For e - and e + : Bremsstrahlung Multiple scattering Energy loss by ionisation (dE/dX) Annihilation (for e + ) This list takes atomic relaxation processes (Auger effect, X ray) into account.

Primary event Incident photon on the center of the central crystal. Momentum vector perpendicular to the crystal face. Energies: 100keV, 500keV, 1MeV, 2MeV, 5MeV, 10MeV, 20MeV, 25MeV in the laboratory frame events generated at each energy  20MeV

Total energy deposited Escape peaks of Xray transitions of iodine and cesium Compton background 0.511MeV  escape peak 1.022MeV  escape peak

Multiplicity

Energy detection efficiency 95% Cut: Events rate with 95% of incident energy measured in the array. 75% Cut: Events rate with 75% of incident energy measured in the array. Difference due to Compton background shape.

Position reconstruction Simple approach choosing first hit crystal as this measuring maximal energy could induce large energies between 0.5 and 5MeV where Compton scattering is dominant. Position reconstruction using energy weighted crystals is investigated

2D view of energy weighted position reconstruction 100keV500keV1MeV 2MeV5MeV10MeV 20MeV25MeV

Reconstructed radius r = (x rec 2 +y rec 2 ) 1/2 100keV500keV1MeV 2MeV5MeV10MeV 20MeV25MeV

Position reconstruction efficiency Good event: If the reconstructed (x,y) coordinates are inside the first hit crystal

Conclusions of part 1 At energies higher than 5MeV, energy measurement error is between 5 and 25% for more than 30% of events. What happens by changing crystal dimensions ? Is this problem solved by increasing the size of the array ? Using simple geometry and primary event, 2 position reconstruction methods were tested: search of the crystal measuring maximal energy and Energy weighted position reconstruction. Both look promising. Position reconstruction seems to be better at very low (less than 500keV) and higher energy (higher than 10MeV). At intermediate energies, the Compton scattering affects the precision of the position reconstruction. Can it be improved ?

Part 2: Comparison of 5*5 arrays with following crystal sizes: 11*11*200mm 3, 22*22*200mm 3 and 32*32*200mm 3

Energy deposit for the different crystal sizes

Multiplicity for the different crystal sizes

Energy detection efficiency 5*5 array

2D reconstruction view 11*11*200mm 3 32*32*200mm 3

Reconstructed radius Results shown here are obtained by using the energy weighted method 100keV500keV1MeV 2MeV5MeV10MeV 20MeV25MeV

Position reconstruction efficiency (1) Photon hit the center of central crystal. We use 3 tolerances : Reconstructed X and Y must be in the range of initial hit crystal (Energy Weighted methods). The crystal measuring the maximal energy must be the initial hit crystal (maximal method). Then by including the closest neighbours (cross configuration) Then by considering the 3*3 array of crystals centered on the hit crystal Tolerance ITolerance II Tolerance III

Position reconstruction efficiency (2) Hit crystal Cross configuration 3*3 array Size effect

Conclusions of part 2 The choice of the crystal dimension is a compromise between the angular resolution required and the necessity to have accurate energy and position reconstructions. When Compton scattering is dominant, the energy spread in more crystals. If the crystal size is too small, this could affect the accuracy of position reconstruction. But to choose the crystal sizes, other important points like the light collection efficiency must be considered.

Part 3: Comparison with different 22*22*200mm 3 crystals arrays : 5*5, 7*7 and 9*9

Energy detection efficiency of each array

Position reconstruction efficiency of each array Using Energy weighted method, efficiency decreases by increasing number of crystals Consequence of energy spread Hit crystal Cross configuration 3*3 array

View of energy spread (1) E 1 / E tot E hit / E tot E 2 / E tot E tot =  81 crystals E i E 1 =  8 crystals E i E 2 =  16 crystals E i Study of ratios

View of energy spread (2) E hit / E tot E 1 / E tot Multiplicity>1

View of energy spread (3) E hit / E tot E 2 / E Intermediate energies (from 500keV to 10MeV), events on a slope 1 straight line Jump of a crystal line !!! Multiplicity>1 x y e(MeV)

Photon hitting in a crystal corner (1) 9*9 array of 22*22*200mm 3 crystal. Photon 1mm in X and Y from the corner of the central crystal.

Photon hitting in a crystal corner (2) Tolerance:

Photon hitting in a crystal corner (3) Energy detection efficiency 22*22*200mm 3

Conclusions of part 3 Even with an 9*9 array of 22*22*200mm 3 crystals, there are 30% of the events where error on energy measurement is between 5 to 25% for photon energy higher than 5MeV). The energy spread in the detector and for about 10% of the non contiguous crystals configurations occur. Reconstruction position with maximum energy method or energy weighted crystals method is accurate: when hitting on the center of a crystal, in a range of a 3*3 array centered on this crystal in a range of a 2*2 crystal array when hitting the corner of a crystal This limitation is due to Compton scattering, which dominates between 300keV and 7MeV in CsI.

Sum up and conclusions We checked energy and multiplicity response of a 5*5 array of 22*22*200 crystals using the Low Energy Electromagnetic Interaction model provided by GEANT4. We tested position reconstruction methods: the maximum energy and energy weighted methods look promising, in both cases when a photon hit the center or the corner of a crystal. We studied 5*5 arrays made with different crystal sizes (11*11*200mm 3, 22*22*200mm 3, 32*32*200mm 3 ). Energy spread and angular resolution are elements to consider before fixing the crystal sizes. We compared 5*5, 7*7 and 9*9 arrays of 22*22*200mm 3 crystals. At energies where Compton scattering dominates, events (about with non continuous crystals clusters occur, thus limiting the position reconstruction accuracy. At energies above 5MeV, even with a 9*9 array, more than 95% of incident energy is measured for only 70% of the events. For the remaining events, error on energy measurement is between 5 and 25%. But position reconstruction seems sufficiently accurate at these energies.

Perspectives Only physics interactions were studied here. Some other important points must be considered: Light collection in crystals: simulations performed with LITRANI (see talk of B. Genolini) and validation with experimental measurements. Noise and threshold effects (electronics, APDs...) can be included in GEANT4 simulations. Implementation of a more complicated geometry (using trapezoid crystals). Check the consequences of energy and position reconstruction errors by going back in the center of mass frame. Find out other methods to reconstruct position (algorithms using crystals energy correlation ? Cluster finding algorithms ?...) Improve the primary generator event, following physics requirements (see talk of F. Skaza)