Is it possible to improve the conventional γ-ray collimator by integrating cones? In this small study the above question is answered on the basis of Monte-Carlo simulations performed with the Geant4 toolkit. It is a Lundium sub-project with the intention to evaluate what collimator that should be used in the construction of a HPGe crystal scanning system in Lund.
A big part of the Lundium project is comprised of the development and study of a novel high purity germanium (HPGe) detector set-up. In nuclear spectroscopy experiments in the superheavy element region the detection of x-rays is particularly interesting since they enable a pin point of the Z number of the decaying nucleus. To increase the detection efficiency of the x-rays it is important to have a compact composition of HPGe crystals. The compact and x-rays together bring Compex and this is the name of the new type of HPGe crystal detectors which are to play an important role in the Lundium set-up. In its’ beauty the HPGe set-up will consist of five so called CLOVERS, i.e. five groups of four Compex crystals brought together within a capsule.
In order to claim new nuclear structure physics it is of utmost importance to know the characteristics of the detectors, especially if it is a new type of detector. In this regard it is hence essential to characterise the Compex set-up in detail.
The characterisation of HPGe crystals is achieved with a scanning system. There exist some different scanning systems [1, 2, 3]. All systems utilise a collimator in some way. The purpose of a collimator is to create a collimated γ-ray beam, a pencil beam or a focused beam with the use of an isotropical γ-ray source.
In the traditional scanning system, cf. Figure 1, a γ-beam is directed to one end of the crystal in a right angle. Surrounded on the sides of the crystal other γ-detectors, such as scintillators, are placed. With the help of slits, only 90° Compton scattered γ-rays, are detected in the scintillators. Coincidence measurements in the Compex crystal and a scintillator determines a γ-ray interaction at a certain (x, y, z) coordinate in the HPGe crystal. With a positioning system the collimator is moved and the (x, y) coordinate is varied. With multiple slits the z coordinate is varied. This way a HPGe crystal is scanned and the response signals are studied.
A scanning system, as described above, is intended to be built in Lund. A main ingredient in the scanning system is the γ-ray collimator. Important properties of the collimator are:
- Divergence of the transmitted γ-rays
- Scattering efficiency (full energy efficiency)
- Transmittance or required source activity to obtain a desired count rate in the detector
The divergence of the beam governs the position precision that is possible to obtain with the collimator. The scattering efficiency determines the amount of γ-rays that exit the collimator which have full energy. It is an important quantity since scattered particles increase the general divergence of the beam and do not fill a purpose if the γ-ray energy is utilised in the analysis (as is the case for the system to be built in Lund). The transmittance governs the count rate in the detector and in the continuation the required duration of the measurements. A known transmittance enables a well chosen source activity to obtain a desired detector count rate.
The simplest collimator is a volume with a cylinder hole where the volume can absorb γ-rays which are emitted with a too large divergence. The scattering efficiency is not trivial to know for any collimator. A rumour said that a collimator with integrated cones actually can increase the scattering efficiency and this triggered this work. In this small project, the rumour is set to a test and the performance of different collimators are studied with Geant4 simulations in order to choose a suitable collimator to be used in the scanning system in Lund.
The constructed geometry in Geant4 (see Figure 1) consisted of a lead cylinder of length 10 cm, with an outer radius of 10 cm and a varied inner diameter (1, 1.5 mm or 0 in the configuration of integrated cylinders). These dimensions were chosen on the basis to work as well as possible in the future Lund scanning system. Two additional alternative volumes of air were also created:
- Integrated cones
- N integrated cones were placed within the mother volume cylinder, with a set inner diameter to match that of the mother and an outer diameter which varied for optimised performance.
- The cones were placed in such a way that the complete cylinder in +z was filled and the direction of the cones was set as indicated in Figure 2.
- Integrated cylinders
- N integrated cylinders were placed within the mother volume cylinder, now with an inner diameter set to zero. Cylinders, first one with a diameter of 1 mm and then N-1 with a varied increasing diameter for best performance, were placed such that the cylinder with the smallest diameter was at the exit of the collimator.
γ-rays with an energy of 661.7 keV (to resemble a source of 137Cs) was shot from the centre of the entrance to the collimator (cf. Figure 2). The direction of the photons were sampled from a circular distribution around the z-axis, large enough to cover radii of the largest integrated cone outer radii. For every collimator configuration 2 million γ-rays were simulated.
5 cm away from the exit of the collimator the divergence of the γ-rays and their energy were probed on a 5 x 5 cm surface (resembling the size of a Compex crystal). A measure of the divergence was chosen as 3σ of the γ-ray spread and hence this is rather not a measure of the spread of the beam but more a measure of leakage γ-rays making it through the lead block. The scattering efficiency was defined as the ratio of the 661.7 keV bin count and the total detected γ-rays. The required source activity to achieve a 1 kHz count rate was calculated with the simulation angle coverage, the probe solid angle coverage and the total number of detected γ-rays.
The main result is presented in Figure 3. The configurations included in the results have been chosen from optimisations of the dimensions of the above-mentioned configurations. The used configurations are described in the following list:
Simple, 1 mm diameter A cylindrical collimator with inner diameter 1 mm.
Simple, 1.5 mm diameter A cylindrical collimator with inner diameter 1.5 mm.
Integrated cones (i) 5 cones (20 mm length) with an inner diameter of 1 mm
and an outer of 1.4 mm.
Integrated cones (ii) 5 cones (20 mm length) with an inner diameter of 1.5
mm and an outer of 1.9 mm.
Integrated cylinders 5 cylinders (20 mm length) where the last one had a
diameter of 1 mm and the rest an increasing diameter of 0.05 mm.
The required activity to achieve a count rate of 1 kHz for the first configuration was about 130 MBq and for the third configuration 78 MBq.
It seems true that a collimator with integrated cones actually is able to increase the scattering efficiency, but it largely depends on the dimensions of the cones. However, many factors speak against such a configuration:
- The scattering efficiency is only increased marginally.
- The scattering efficiency is already close to maximum with the conventional collimator type.
- The beam divergence increases.
- It is unclear of whether it is possible to manufacture such a structure.
An implication of the larger divergence is a lower required source activity to achieve a 1 kHz count rate but this cannot be seen as a direct advantage since it is merely an effect of the larger divergence. The more possible integrated cylinder configuration (from a manufacturing perspective) did not improve on the scattering efficiency. Several further configurations were investigated to see if they possibly could better optimise a collimator. None were found. As a final remark it is important to note that this study has been limited to collimator dimensions relevant for the future Lund scanning system.
 M. Dimmock. Characterisation of AGATA Symmetric Prototype Detectors. PhD thesis, University of Liverpool, 2008.
 F. Crespi et al. A novel technique for the characterization of a HPGe detector response based on pulse shape comparison. Nuclear Instruments and Methods in Physics Research Section A, 2008.
 C. Domingo-Pardo. A novel γ-ray imaging method for the pulse-shape characterization of position sensitive semiconductor radiation detectors. Nuclear Instruments and Methods in Physics Research, Section A, 2010.