Conceptual design and Monte Carlo simulations of the AGATA array

Nuclear Instruments and Methods in Physics Research A 621 (2010) 331–343

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Conceptual design and Monte Carlo simulations of the AGATA array ¨ b, Zs. Podolya´k c, B. Quintana d, A. Gadea e, E. Farnea a,, F. Recchia a, D. Bazzacco a, Th. Kroll The AGATA Collaboration a

Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italy Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, Darmstadt, Germany c Department of Physics, University of Surrey, Guildford, UK d Departamento de Fı´sica Fundamental, Universidad de Salamanca, Salamanca, Spain e Instituto de Fı´sica Corpuscular, CSIC-Universidad de Valencia, Valencia, Spain b

a r t i c l e in fo

abstract

Article history: Received 12 February 2010 Received in revised form 7 April 2010 Accepted 12 April 2010 Available online 18 April 2010

The aim of the Advanced GAmma Tracking Array (AGATA) project is the construction of an array based on the novel concepts of pulse shape analysis and g-ray tracking with highly segmented Ge semiconductor detectors. The conceptual design of AGATA and its performance evaluation under different experimental conditions has required the development of a suitable Monte Carlo code. In this article, the description of the code as well as simulation results relevant for AGATA, are presented. & 2010 Elsevier B.V. All rights reserved.

Keywords: Monte Carlo code gray tracking array

1. Introduction Valuable information on the structure of nuclei far from stability has been obtained in the last two decades using powerful 4p arrays of Compton-suppressed high-purity germanium detectors such as GASP [1], EUROBALL [2] and GAMMASPHERE [3], or compact arrays of segmented detectors, as EXOGAM [4] or MINIBALL [5], designed to be used in the first generation of Radioactive Ion Beam (RIB) facilities. The experimental conditions at the future facilities for intense radioactive ion beams and for high-intensity stable beams are expected to be extremely challenging, requiring unprecedented levels of sensitivity and count-rate capabilities. Such performance figures are not realistically reachable with detector arrays based on the conventional Compton-suppression technique, nor with compact arrays. A different approach for the large 4p arrays, explored in the past years, implies removing the Compton-suppression shields and covering the full 4p solid angle with germanium detectors only. The large photopeak efficiency and the peak-to-total ratio of such an array are obtained through the software reconstruction of the scattering sequences of the individual g-rays. Such g-ray tracking algorithms rely on the identification of the most common interaction processes, i.e. Compton scattering, photoelectric absorption and pair production, as well as on the identification of the interaction points of the photons within the germanium crystals with a precision of a few millimetres.

 Corresponding author.

E-mail address: [email protected] (E. Farnea). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.04.043

Such a precision cannot be obtained with highly electrically segmented germanium crystals only. Rather, pulse shape analysis algorithms are used for this purpose to analyse the detailed shape of the signal and mirror pulses, which are acquired via digital electronics. Extensive Monte Carlo simulations such as those reported in the present work predict that a g-ray tracking array will have a high photopeak efficiency over a broad energy range, close to 40% for single 1 MeV photons and larger than 20% for a cascade of 30 photons of the same 1 MeV energy, to be compared with the 5–10% of conventional escape-suppressed arrays. The peak-tototal ratio of a g-ray tracking array will be approximately 55%, while the values for conventional Compton-suppressed arrays range from 45% to 50%. Moreover, the major advantage of such an array with respect to the conventional ones is the improved quality of the spectra. As a matter of fact, in cases when a sharply peaked velocity distribution for the nuclei emitting the g radiation can be assumed, the effective energy resolution reached after the Doppler correction will not depend on the finite opening angle of the individual detectors or segments in the crystal. It will rather be dominated by the position resolution obtained by pulse shape analysis, as well as by the accuracy with which the tracking algorithm identifies the first interaction point. Our group is working since the mid 1990s in the conceptual design and detector developments forming the basis of the present tracking array projects. In the framework of the pioneering efforts like the Italian MARS project [6], which became part of the European TMR network ‘‘Development of g-ray tracking detectors’’ [7], different configurations for a tracking array of Ge semiconductor detector were explored [8].

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Presently two major projects aim at the construction of an array of high-purity germanium detectors based on the concepts of pulse shape analysis and g-ray tracking: AGATA in Europe [9] and GRETA in the USA [10]. In both projects, Monte Carlo simulations play an essential role in the design as well as in the characterisation of the arrays. The complex geometry of the array requires a careful optimisation and for each possible arrangement of the detectors the performance of the array should be evaluated simulating realistic conditions. Moreover, since the overall performance of a g-ray tracking array depends critically on the tracking algorithms, a large effort has been put into their development and test. Perhaps the most important role played by Monte Carlo simulations in the AGATA project, in addition to helping the conceptual design, is the production of reference data sets which can be used to develop, train and check different tracking algorithms and to compare in a consistent way their performance. In the following sections, the Monte Carlo code developed for the AGATA project will be briefly described and a relevant selection of the results obtained will be discussed.

2. The geometry of AGATA The detector arrangements investigated for AGATA are composed of sets (clusters) of several crystals within the same cryostat. As a matter of fact, having more crystals grouped inside the same cryostat minimises the relative amount of passive materials constituted by the cryostat walls themselves with respect to the active materials constituted by the germanium crystals. With the present technology, clusters with more than four crystals are unfeasible, which is the reason why configurations built out of clusters formed by five or more crystals were not taken into consideration in the present work. Nevertheless, even clusters formed by three highly segmented germanium crystals are very complex objects. In order to ensure maximum reliability, it was decided at an early stage of the AGATA project to rely on encapsulated detectors, namely on crystals hermetically sealed in an aluminium container with thin walls, with the technology developed within the EUROBALL Collaboration for the Cluster detectors [11].

In order to maximise the solid angle coverage using a minimum number of crystal shapes, an elegant possibility is to tile the spherical surface with the projection of the same simple pattern drawn on each of the faces of an enclosed regular polyhedron, namely one of the so-called ‘‘platonic’’ polyhedra. The maximum symmetry of the spherical tiling is obtained using the icosahedron, which, having 20 equilateral triangular faces, is the platonic solid with the largest number of faces. In the attempt to cover the sphere with the best approximation of circular figures, the pattern on the faces of the icosahedron should have the shape of hexagons while the vertexes will be replaced by regular pentagons. Such tilings always end up with NP ¼ 12 pentagons and with NH ¼ 20  n hexagons, where n ¼[i2 + 3j2  4]/ 8, i+ j even, 2n, i and j integers. Some of the resulting configurations are shown in Fig. 1. Not all the possibilities are acceptable for an array such as AGATA. Since the detectors are built out of germanium crystals grown with a cylindrical shape, it is necessary to taper the front part of the crystals in order to best approximate the configurations under discussion. The configurations corresponding to small values of n result both in big losses of Ge material (due to the tapering of the crystal) and in a very small inner radius for the array. As a consequence, the performance of the tracking algorithms gets worse because of the resulting high density of g-interactions. Furthermore, the inner free space of the sphere becomes too limited to place any ancillary device. On the other hand, many of the configurations with larger n values, having a sufficient inner space, are not convenient due to the impossibility to group the detectors into alike clusters of three or four crystals. The maximum solid angle coverage for a fixed amount of germanium is obtained by tapering the cylinders in order to obtain a closer packing in the front face. It should be noticed that the space for the cryostat is obtained from the cluster boundaries, producing irregular hexagons. The shape of the detectors is obtained through the intersection of a cylinder with an irregular hexagonal pyramid resulting in the hexaconical shape shown in Fig. 2. On the other hand, the pentagon shaped crystals needed for a full coverage of the solid angle are always regular, but given the cost for their development and their limited contribution to the overall performance of the array, it was decided to minimise their volume and consider only arrangements of the hexaconically shaped crystals.

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Fig. 1. Geodesic tilings of the sphere obtained by decomposition of the regular icosahedron. For each configuration, different colours correspond to different crystal shapes. The configurations investigated for AGATA, corresponding to NH ¼ 120 and 180, have been highlighted. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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same segment and they lie within a critical radius. A smearing process is then performed, namely, a random error with a threedimensional Gaussian distribution is applied to the resulting points. Following this packing and smearing process, spectra and matrices can be produced by processing the resulting list-mode files with a tracking algorithm. In the present work the mgt tracking code was used, which can directly produce spectra or write out the tracked data in a suitable format, compatible with the GASP data analysis package [13], which can be used for further data analysis. It should be remarked that the consistent comparison of the performance of the available tracking algorithms [14] is one of the goals of the simulation. In the following sections, the relevant parts of the simulation code will be described in more detail.

Fig. 2. One of the possible crystal shapes for the detectors of AGATA.

A specific code (called marsview), performing the tiling of the spherical shell in such configurations, was developed. The code provides as an output the elementary crystal shapes (namely, the coordinates of the vertexes of the polyhedra), the geometrical transformations needed to build a cluster as well as the ones needed to place the clusters into the array. The geometrical transformations considered here are the composition of a rigid translation along the vector with Cartesian coordinates (x, y, z) and three elementary rotations, each of them around a Cartesian axis: Tðx,y,zÞ  Rz ðfÞ  Ry ðyÞ  Rz ðcÞ:

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ð1Þ

The configurations with a number of hexagons NH ¼120 and 180 have been identified as the most attractive for AGATA. A more detailed discussion on the selection of the AGATA configuration will follow in Section 4.1. In the tiling with NH ¼180 it is possible to form triple clusters out of three different crystal shapes, all of the clusters having the same composition. In the tiling with NH ¼120, approximately the same solid angle as in the case of NH ¼180 can be covered using quadruple clusters (each containing two crystals for each shape) or using two types of triple clusters, corresponding to six different crystal shapes. Solutions with only one or two encapsulated detectors in the same cryostat lead to a significant lowering in solid angle coverage.

3. The simulation code The Agata simulation code has been developed to evaluate the performance of AGATA under a wide range of experimental conditions. The present version of the code is based on the C+ + classes of Geant4 [12] Monte Carlo simulation libraries, which provide a full description of the microscopical interactions of radiation (both photons and particles) with matter as well as tools to implement the geometry of complex detector arrangements and to process and extract the relevant information. The simulation of a tracking array requires the code to have the possibility to disentangle each scattering sequence in order to verify the results of the tracking process. In the present code this is obtained by generating ‘‘simple’’ events, where only one particle or photon is emitted at a time. Events with higher multiplicity are constructed at the level of the data analysis processes, for example in the g-ray tracking code, by accumulating the required number of particles and photons. The present AGATA simulation code basically produces a formatted file in list-mode where events are stored, each one of them listing position and energy of the individual energy release locations within the active parts of the array. The results are given with the accuracy supplied by the Geant4 libraries. In order to emulate the finite precision with which the pulse shape algorithms identify the interaction points, the simulated interactions of the gray are packed together if they occur inside the

3.1. Implementation of the AGATA geometry in the simulation The detailed description of the geometry is not directly embedded in the code to ensure maximum flexibility when exploring and comparing different detector configurations. The Agata code can actually interpret the files produced by the marsview programme, described in Section 2, thus making it possible to change the geometry parameters simply by changing the input files containing the geometry description of the array. The irregular hexaconical shapes of detectors discussed in Section 2 cannot be described easily using the standard geometry tools provided by Geant4. Therefore, a specific class capable of handling irregular convex polyhedra was developed. The shape of the detectors is obtained through the intersection of an irregular polyhedron with a cylinder. The AGATA detectors are electrically segmented. The optimal number of segments was chosen on the basis of detailed electric field and signal calculations similar to those presented in Refs. [15,16], trying to maximise the performance of the pulse shape analysis algorithms using a limited number of segments. In the case of AGATA, a 36-fold segmentation was chosen for each crystal. The effective segment shape deduced through the aforementioned signal calculations and shown in Fig. 3) is quite different from the simple projection of the segment geometrical shape. In our geometrical model, the effective segment shape was approximated using four sub-segments, each of them described as a convex polyhedron as defined above. The resulting segments are shown in Fig. 3. The simulation includes also the encapsulation and cryostat passive components, relevant for the simulations. In addition, several ancillary devices (both active and passive ones) can be considered.

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Fig. 3. Left: effective shape of the segments of an AGATA detector, deduced through detailed signal calculations with the mgs code. Right: shape of the segments as implemented in the simulation code.

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3.2. Embedded event generator The Agata code has an embedded event generator suited to simulate in-beam experiments, in which the g radiation is emitted by a nucleus moving with respect to the laboratory reference ~  c. The event generation is quite frame with velocity ~ v¼b ~ schematic, b being the only available information about the b for all emitting nucleus. It is possible to consider a fixed value of ~ of the events, or change this value on an event-by-event basis, to emulate the typical dispersion in velocity of the residual nuclei produced in a reaction. Several options for the emission spectra for each particle species are available in the centre-of-mass (CM) reference frame, including discrete and continuous spectra. The momentum of the emitted particle or photon in the laboratory reference frame is computed by applying the relativistic transformations. Since more realistic events are required to simulate complex experimental conditions, the Agata code provides the possibility of using a external event generator producing an input formatted file. In this case, the Agata code is merely used to evaluate the response function of the detector setup to such pre-generated events. These more sophisticated events can contain fine details such as ion trajectories, different particle emission and the directional correlations in a cascade of grays. In this case, a specific beam/target combination is provided by the input file, and therefore it is possible to apply momentum conservation following the emission of each particle or photon. The momentum of the residual nucleus is recalculated after each particle emission and its value is used to perform the relativistic transformation from the CM to the laboratory reference frame in case energies and directions of the emitted particles are provided in the CM frame. It is also possible to give energies and directions of the emitted particles directly in the laboratory frame.

3.3. Interaction of the radiation with matter In the present version of the code, the user is provided with some options to select the processes which will be considered when simulating the interaction of the emitted particles and photons with the detector model. The options reflect mostly the possibilities available in the underlying Geant4 libraries. By default, the low-energy set of electromagnetic interactions of Geant4 is used. The processes which have been considered for the photons are photoelectric absorption, Compton scattering, pair production and Rayleigh scattering. The latter process is relevant only for low-energy photons, its cross-section rapidly decreasing with the increasing photon energy and vanishing above 700 keV. In addition, this process is less probable than photoelectric absorption or Compton scattering (for a 300 keV photon, the ratios between the cross-sections for Rayleigh scattering, photoelectric absorption and Compton scattering are, respectively, 1:2:16). In principle, Rayleigh scattering, in which a photon undergoes a scattering leaving its energy unaltered, has profound implications on the capability to perform gray tracking. As a matter of fact, this process is strongly peaked in the forward direction, leaving the photon direction essentially unaltered in most cases. The effects of the finite momentum of the Comptonscattered electrons (Compton profile), included in the latest versions of the Geant4 libraries, could be considered in earlier versions of the code by activating the G4LECS treatment of the Compton scattering [17]. The effect of linear polarisation of the photons can be considered, but only if the G4LECS option is not active.

Electrons and positrons can undergo multiple scattering, ionisation and bremsstrahlung. In addition, the annihilation process has been considered for positrons. For the charged hadrons, scattering (elastic and inelastic) and ionisation have been considered, while for neutrons are instead considered scattering (elastic and inelastic) and capture. For simplicity, the possibility of high-energy hadrons-induced reactions in the detectors and in the passive materials surrounding the detectors has not been considered. 3.4. Retrieval of the energy release information Two options are available for the retrieval of the information from the ‘‘active’’ parts of the geometrical set-up. The default option assumes that in the case of photons and neutrons the actual energy deposition is performed by the secondary charged particles created following the interaction. Energy depositions can be found at some distance from the primary point of interaction. For instance, photons with energies less than 1 MeV release secondary electrons with energies of a few hundred keV, which deposit all of their energy within 1 mm from the interaction point of the primary g ray [18]. It should be remarked that the position resolution from the PSA algorithms as extracted from in-beam experiments is of the order of a few millimetres [6,19], therefore the volume over which the secondary electrons release their energy is not expected to affect the performance of the tracking algorithms. With the second option, the above described behaviour can be overridden by assuming a simplified scheme, i.e. whenever the primary particle emitted in the event interacts within the active volume, the difference in its energy is deposited at the interaction point. This simplified option makes the scattering sequence of the grays clearer.

4. Results: the geometrical design of AGATA In this section, and in the following ones, when not explicitly stated otherwise, the results have been obtained by packing and smearing the raw data with an energy-dependent position resolution of 5 mm FWHM for 100 keV photons and an inverse dependence on the square root of the photon energy with the constraint of a minimum positional error of 2 mm. As mentioned earlier, the resulting interaction points were processed with the mgt forward tracking code. It should be pointed out that it was assumed that the PSA algorithms always identify correctly the number of interaction points within each crystal. The effect of incorrect identifications of the number of interaction points will be discussed in Section 6.1. In this section the simulation work performed to sustain the selection of the final geometrical design of AGATA will be presented. 4.1. Possible configurations One of the main goals of the present simulation code is the evaluation in a realistic way and the consistent comparison of the performance of various proposed configurations for tracking arrays like AGATA or GRETA. It has been also discussed before that only configurations with a sufficient number of elements can be considered. Four possible configurations have been extensively compared in the calculations which will be presented in Sections 4.3 and 4.4. As mentioned in Section 2, they can be distinguished on the basis of the number of hexagonal detectors NH composing the array and on the basis of how these hexagonal

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detectors are clustered to tile the maximum possible solid angle of the sphere. A single configuration with NH ¼180 has been considered, labelled in the following as A180, composed by one kind of triple cluster, built out of three different crystal shapes. For NH ¼120 three different configurations have been considered feasible instead:

 A120G: this configuration is composed by two kinds of triple

 

cluster, built out of two different crystal shapes. Actually, it is possible to arrange the clusters in two different ways, here only the arrangement having the highest degree of symmetry has been considered. A120F: this configuration is composed by two kinds of triple cluster, built out of six different crystal shapes. A120C4: this configuration is composed by one kind of quadruple cluster, built out of two different crystal shapes.

In all cases, the same characteristics for the single crystals as well as for the clusters were considered, namely:

 maximum size of the cylindrical Ge crystal: 90.0 mm length, 40.0 mm radius;

 coaxial hole size: 10.0 mm diameter, extension to 13.0 mm from the front face;

 0.6 mm thick passivated area around the coaxial hole to account for the lithium contact:

 1.0 mm thick passive area at the back of the detector to account for phenomena of partial charge collection;

Table 1 Geometrical characteristics of the configurations considered for the AGATA array. A120G Number of crystals Number of crystal shapes Number of cluster types Covered solid angle (%) Volume of germanium (cm3) Final mass of germanium (kg) Initial mass of germanium (kg) Fractional loss of germanium (%) Centre-to-detector face distance (cm)

A120F

A120C4

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120 120 120 180 2 6 2 3 2 2 1 1 71 78 78 82 43 590 42 225 43 160 67 978 232 225 230 362 289 289 289 434 19.7 22.1 20.4 16.5 19.7 18.0 18.5 23.5

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 encapsulation: 0.8 mm thickness with a 0.4 mm crystal-can distance;

 cryostat: 1.0 mm thickness with a 2.0 mm capsule-cryostat distance. A thicker backward part of the cryostat (10.0 mm thick) was considered to emulate the effects of the Dewar and of other passive parts.

4.2. Geometrical characteristics of the configurations The basic geometrical characteristics of the configurations are shown in Table 1. An artistic view showing the A120 and the A180 configurations is presented in Fig. 4, where the cryostats and the detector encapsulation are not sketched. The maximal solid angle coverage is obtained for the A180 configuration, reaching a value of 82% of the total solid angle. The A120G configuration has the smallest solid angle coverage, roughly 71% of 4p, while the other A120 configurations cover approximately the same value, 78% of the total solid angle.

4.3. Response function The most basic information which has been extracted from the simulated data sets is the plain response function of the array, that is the spectrum obtained firing single monochromatic photons and summing the individual energy depositions within the whole array. The simulations were performed assuming a point source at rest positioned in the geometrical centre of the array, emitting photons with an isotropical distribution. The plot of the photopeak efficiency as a function of the photon energy, presented in Fig. 5, shows that the overall photopeak efficiency is strongly correlated to the solid angle coverage. Thus, the configuration having the lowest solid angle coverage, namely A120G, has also the lowest photopeak efficiency. The curves for the A120F and A120C4 configurations are very similar, as one would expect since the crystal length and the solid angle coverage are roughly the same in these cases. Similarly, the A180 configuration reaches higher photopeak efficiency values, given its larger solid angle coverage. The plot of the P=T ratio as a function of the gray energy is also presented in Fig. 5. Also in this case the performance of the configuration based on 180 crystals are better than the values for the configurations based on 120 crystals, which show no appreciable difference between each other.

Fig. 4. (Colour online) Artistic view of the A120G and the A180 configurations proposed for AGATA. The cryostats and the detector encapsulation are not drawn. The threedetector clusters (two different kind for A120G, a single one for A180) are also sketched.

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Fig. 6. Photopeak efficiency for the proposed configurations for AGATA, simulated in the case of a point source at rest in the geometrical centre of the array emitting a rotational cascade of 30 photons in coincidence. The effect of the tracking algorithm has been considered.

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Fig. 5. Photopeak efficiency (top) and peak-to-total ratio (bottom) extracted from the response function of the proposed configurations for AGATA, simulated in the case of a point source at rest in the geometrical centre of the array. No tracking has been applied to the simulated data.

4.4. Tracking photopeak efficiency of AGATA The photopeak efficiency of AGATA has been simulated under realistic experimental conditions, taking into consideration the effects of the recoil velocity (Lorentz boost) and of the gray multiplicity, mimicking the prompt cascade de-exciting the nucleus. All these sequences of grays are seen as emitted simultaneously by the detector array and therefore our response function will depend on the possibility to disentangle the scatterings of the different grays in different detectors or detector segments. In order to calculate the photopeak efficiency of AGATA in a realistic way, the simulated data were processed with the tracking code mgt. The calculations assumed a point source at rest positioned in the geometrical centre of the array, emitting a cascade of up to 30 photons in coincidence with regularly spaced energies, Eg ¼ E0 þn  DEg , with E0 ¼ 80 keV, DEg ¼ 90 keV, n integer. As expected, the overall performance of the A180 configuration, for the 30 grays cascade, is superior compared to the configurations based on 120 crystals. In Fig. 6, an average 30% increment in photopeak efficiency is apparent. Besides having a larger solid angle coverage, in the case of the A180 configuration, which has a larger number of Ge crystals and a larger inner radius, the interaction points are on the average more widely spaced. Under these conditions, the clustering and tracking algorithms are more capable to disentangle the different grays composing the event. This explains the observed results.

Establishing the optimal configuration for AGATA is a complex problem where the ingredients to be considered go beyond the overall performance figures of the array and other factors such as the reliability, simplicity, symmetry and cost of the adopted solution should be taken into account. From the results of the previous sections, the A180 configuration has larger photopeak efficiency and slightly better P/T ratio than the configurations based on 120 hexagonal detectors, however, the total cost of the detectors and of the associated electronics is 30% higher. In this respect, the A120F and A120C4 configurations appear as an attractive compromise between cost and performance. Nevertheless, it should be observed that the A120F configuration has a higher costs for detector and cryostat development. Furthermore, its higher number of crystal shapes has a sizeable impact on the procurement of spare components needed to keep the array in acceptable working conditions. The main drawback with the A120C4 configuration of AGATA is instead the reliability. In fact, the AGATA project requires the detector preamplifiers to use cold FETs for the input stage to comply with the segment energyresolution specifications [9]. The heat dissipation of a large number of cold FETs would make a quadruple segmented cluster too demanding from the cryogenic point of view, and will increase the unreliability of the system. As for the performance, it should be pointed out that the A180 configuration has better energy resolution, photopeak efficiency and P/T ratio than the configurations based on 120 detectors in a broad range of experimental conditions. The difference in performance is particularly evident at high multiplicity. The performance figures for 1 MeV photons of the final optimised A180 geometry are 82% solid angle coverage, 43% photopeak efficiency and 59% P/T ratio at photon multiplicity Mg ¼ 1, 28% photopeak efficiency and 43% P/T ratio at Mg ¼ 30. The values for the A120C4 geometry, having 78% solid angle coverage, are similar at Mg ¼ 1, being 37% photopeak efficiency and 52% P/T ratio, but they drop faster with the increasing multiplicity to 22% photopeak efficiency and 44% P/T ratio at Mg ¼ 30. In addition, the A180 configuration can be built out of 60 identical clusters of three crystals and provides a sensible inner space for ancillary detectors which are foreseen to be used in several experiments. It should be observed that the fractional amount of germanium material losses, due to the tapering process, is lower in the A180 configuration, where approximately 0.4 kg of material is wasted

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5.1. The simulations of the AGATA five triple cluster sub-array In a ‘‘conventional’’ array of germanium detectors, a collimator is placed in front of each detector in order to minimise the scattering of photons between different crystals. Therefore, only a small region around the target position is actually visible from the detectors. In case of the AGATA five cluster sub-array, no collimators are present, thus it is possible to modify the placement of the detectors relative to the target position depending on the specific measurement. In particular, given the lack of spherical symmetry and the limited solid angle coverage, it is feasible to place the detectors closer to the target position compared to the ‘‘reference’’ 23.5 cm distance of the full AGATA array in order to cover a larger solid angle. The simulated photopeak efficiency and P/T ratio as a function of the shift towards the geometrical centre are shown in Fig. 7. The

Photopeak efficiency (%)

The AGATA tracking array project definition [9] includes an array prototyping phase to build a limited subset of the whole system, named the AGATA Demonstrator Array, which has been used as a benchmark for the full spectrometer. Of particular relevance is the test of the reliability of the novel technology associated with the highly segmented hexagonal Ge crystal detectors and the large number of high-resolution electronics channels per detector cluster (and by extension for the full system). The strong dependency of the performance on the pulse shape analysis and gray tracking algorithms, deduced from simulations, makes it compulsory to develop a tracking system prototype and to confirm experimentally the expectations. In addition, a critical issue in the final development of the AGATA array is that pulse shape analysis and gray tracking should be performed in real time in order to reduce the data stream to amounts treatable with the present technology, as well as to be able to perform the on-line diagnostics of the experimental activity. The earliest implementation of the AGATA Array is an arrangement of the first five triple clusters, of the 60 which will compose the final array. The detectors will be distributed symmetrically around a pentagonal hole that will be used as beam input in several experimental conditions. The sub-array was commissioned at its first installation site, namely the Laboratori Nazionali di Legnaro (LNL), where the first experimental campaign will be carried out. Later it will be used for early physics campaigns to be performed in selected European nuclear physics accelerator facilities. The following sections will report on the simulated performance figures of the five triple clusters sub-array as well as in the sub-array with fifteen triple cluster that corresponds to the next phase of AGATA, presently under construction.

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simulations assumed 1 MeV photons emitted from a point source at rest in the laboratory reference frame. The shift towards the geometrical centre of the sphere is calculated assuming to move the sub-array as a whole towards the target position. It should be remarked that the actual scattering chamber

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for each crystal, which should be compared with the corresponding value of 0.5 kg per crystal in the configurations based on 120 detectors. As a matter of fact, the reduction in wasted germanium material choosing the A180 configuration is equivalent to seven full crystals. The final configuration for AGATA was chosen to be based on 180 hexagonal crystals. In the case of GRETA, the final geometry was chosen to be based on the A120C4 configuration and initially will use warm FETs instead, thus avoiding the reliability problems at the expense of a worse energy resolution at low energies. In the following sections we will refer to the A180 configuration as the AGATA array.

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Shift towards the geometrical centre (cm) Fig. 8. Absolute photopeak efficiency of the AGATA five Cluster sub-array placed at forward angles for 1 MeV photons at Mg ¼ 1 emitted by a point source recoiling along the z axis.

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GAMMASPHERE. While with the 1p configuration there is still a gain displacing the array towards the geometrical centre, the efficiency gain, for cascades with gray multiplicities larger than one, is smaller than in the case of the five cluster array due to the larger solid angle covered.

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Shift towards the geometrical centre (cm) Fig. 9. Simulated peak FWHM for 1 MeV photons at Mg ¼ 1 emitted by a point source recoiling along the z axis, with different velocities, and detected with the AGATA five cluster sub-array placed at forward angles.

used at LNL has an outer radius of 10 cm and the maximum feasible shift is approximately 13 cm. For this reason, the simulations were not performed for shifts larger than 15 cm. In case of simulation with experimental conditions corresponding to relativistic beam energies, the photopeak efficiency of this sub-array, when placed at forward angles, increases, as expected, with the average recoil velocity, reflecting the increased solid angle coverage produced by the Lorentz boost, as shown in Fig. 8. It is important to observe that the resolution (FWHM) of the peaks in the spectra is rather good even if quite high source velocities and close target-detector distances are assumed, as shown by the simulated peak FWHM values presented in Fig. 9, the consequence is an acceptable energy resolution even in extreme conditions. Although the AGATA five cluster sub-array will be composed of just 15 germanium crystals, thanks to its capabilities to work at close target-detector distance without large losses in sensitivity, its photopeak efficiency is predicted to be higher with respect to the existing conventional arrays composed of up to 100 germanium crystals. The photopeak efficiency, peak-to-total ratio and resolution of the spectra produced with AGATA will be the key parameters to show the potentialities of the gray tracking technique. Anticipating the results of Section 6.4, auxiliary devices tracking the incoming beam and/or the outgoing ions will be essential to achieve the desired level of performance. The possibility to couple this sub-array to a device measuring with high precision the vector velocity of the ions, needed for a high accuracy Doppler correction, is actually one of the reasons for the choice as the first installation site of the Laboratori Nazionali di Legnaro. Presently the AGATA five cluster sub-array has replaced the CLARA array [20] in coupled operation with the PRISMA spectrometer [21] and it is expected to begin full operation in the first half of 2010.

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Shift towards the geometrical centre (cm) Fig. 10. Photopeak efficiency (top) and peak-to-total ratio (bottom) of the AGATA 1p Array for 1 MeV photons emitted from a point source at rest.

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5.2. Simulations for the AGATA 1p sub-array The next interesting configuration of the array, presently under construction, is the sub-array built out of fifteen triple clusters, covering approximately 1p of the full solid angle with the detectors placed at the ‘‘nominal’’ distance from the target. As shown in Fig. 10, in this condition the photopeak efficiency of the AGATA 1p sub-array will be larger than the nominal values reached by previous large Ge detector arrays as EUROBALL and

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Shift towards the geometrical centre (cm) Fig. 11. Absolute photopeak efficiency of the AGATA 1p Array placed at forward angles for 1 MeV photons at Mg ¼ 1 emitted by a point source recoiling along the z axis.

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Fig. 12. Simulated peak FWHM for 1 MeV photons at Mg ¼ 1 emitted by a point source recoiling along the z axis, with different velocities, and detected with the AGATA 1p Array placed at forward angles.

This section will summarise the results of Monte Carlo simulations performed with the specific goal of placing constraints on the acceptable dead materials and on the performance of the ancillary devices to be coupled with AGATA.

6.1. Effect of approximations from the PSA algorithms In the present work, it was implicitly assumed that the PSA algorithm always identifies correctly the number of interaction points, as mentioned earlier. As a matter of fact, the PSA algorithm implemented in the early operation of the AGATA Demonstrator Array, namely an adaptive grid search [22], assumes at most a single interaction point per segment. The algorithm was indeed optimised with simulated signals. Considering the segments with more than one interaction point, the result of the algorithm is a single interaction point with energy equal to the sum of the individual energies, placed in the centre of gravity of the individual points. In order to evaluate the effect of such an approximation on the performance of the Demonstrator, the same simulated datasets were analysed both in the ‘‘standard’’ way, namely by processing the output of the simulation with mgt with the default parameters and by modifying the packing procedure of mgt in order to replace the interaction points within a same segment into their centre of gravity. The results for efficiency and P/T ratio shown in Fig. 13 prove that indeed this is a very good approximation for single photons, and that the performance of the array is rapidly degraded with the increasing photon multiplicity, with a 20% relative loss of efficiency and a 10% relative loss of P/T ratio for Mg ¼ 30. At the

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6. Performance figures of AGATA in realistic experimental conditions

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The AGATA 1p configuration is particularly interesting for in-flight studies performed with beams at relativistic energies, namely for sources moving with b ¼ v=c of the order of 50%. In fact, due to the Lorentz boost, the photopeak efficiency of the 1p sub-array of AGATA at b ¼ 0:5 raises to approximately 1.6 times the nominal efficiency simulated for a source at rest, as shown in Fig. 11. At the same time, the effective energy resolution is maintained to acceptable values, as shown in Fig. 12.

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Shift towards the geometrical centre (cm)

Shift towards the geometrical centre (cm)

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Shift towards the geometrical centre (cm) Fig. 13. Photopeak efficiency (top) and peak-to-total ratio (bottom) of the AGATA configuration with five triple clusters for 1 MeV photons emitted from a point source at rest. The results obtained with the standard parameters of mgt (full symbols, continuous lines) are compared with the approximated ‘‘pack’’ results considering only a single point per segment (empty symbols, dotted lines).

same time, as shown in Fig. 14, the impact on the FWHM of the reconstructed peaks is minimal. The effect of incorrect identifications of the number of interaction points, in which more points than the actual ones are found, was not evaluated in the present work.

6.2. Effect of the passive materials In principle, any passive material placed inside the array will cause the absorption or scattering of a fraction of the emitted photons. Regarding efficiency, and with the exception of the Rayleigh scattering, any interaction happening before the photons arrive to the active part of the detector will eliminate the possibility of having a full energy absorption in AGATA and therefore the photopeak efficiency will be reduced. The effect of passive material inside the array in the peak-to-total ratio is less straightforward, since differently from conventional Comptonsuppressed arrays the reduction of non-fully absorbed components of the spectra relies on the tracking algorithms. Actually, the detector encapsulation and the cryostats are passive materials themselves and have an impact on the performance of the tracking algorithm. However, the fact that the tracking algorithm produces sensible results with the encapsulation and the cryostats considered in the simulation, as shown in the previous section, suggests that the present

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90 80

P/T Ratio (%)

70 60 50 40 30 20 10 0

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Energy (keV) Fig. 15. Impact of ancillary devices placed inside the AGATA array on the photopeak efficiency (top) and on the P/T ratio (bottom). A point source at rest in the geometrical centre of the array was considered, emitting a rotational cascade of 30 photons in coincidence. The effect of the tracking algorithm has been considered. See text for more details.

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Photopeak efficiency (%)

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Fig. 14. Simulated peak FWHM for 1 MeV photons at Mg ¼ 1 emitted by a point source recoiling along the z axis, with different velocities, and detected with the AGATA configuration with five triple clusters placed at forward angles. The results obtained with the standard parameters of mgt (full symbols, continuous lines) are compared with the approximated ‘‘pack’’ results considering only a single point per segment (empty symbols, dotted lines).

algorithm is quite ‘‘robust’’, resulting in a limited impact of passive material on the overall performance. Extensive simulations were performed to evaluate the impact of passive materials (other than the detector encapsulation and cryostats) inserted inside the array, such as a scattering chamber or light charged particle detectors. As shown in Fig. 15, when a reaction chamber made with aluminum (2 mm thick) is inserted inside the AGATA array, there is a slight reduction in the total photopeak efficiency and in the P/T ratio. It should be noted that the effect is similar to what would be observed with a conventional array of Comptonsuppressed detectors. The impact of ancillary devices similar to those used in the past with EUROBALL such as a Si-ball or an array of CsI detectors for light charged particle detection was estimated in a schematic way considering in the calculations a shell of silicon 1 mm thick and a shell of CsI 5 mm thick, respectively. These values are quite similar to the detector thicknesses used in existing devices such as EUCLIDES [23] and DIAMANT [24]. Also in this case the effect is comparable to what would be observed with a conventional array, in particular the drastic reduction of the photopeak efficiency below 400 keV in the case of the shell of CsI and a general reduction of the P/T ratio in both cases. It should be remarked that calculations performed considering the detailed geometrical simulation of the ancillary devices, for instance EUCLIDES, confirm the trend observed with these schematic ones.

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10

In Sections 5.1 and 5.2 the efficiencies and resolution (FWHM), as a function of the velocity of the emitting source, of the five and fifteen AGATA triple cluster configuration were presented. This section summarises the calculations performed in order to evaluate the effect of the source velocity on the overall performance figures of the full AGATA array, considering a point source positioned in the geometrical centre of the array, moving along the z axis with constant velocity. The plot of Fig. 16 shows the photopeak efficiency of the AGATA array when the same rotational cascade of 30 photons defined in Section 4.4 is emitted at various source velocities and gray tracking is performed. It should be observed that the photopeak efficiency is slightly affected by the source velocity up to quite large values, namely up

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Energy (keV) Fig. 16. Photopeak efficiency for the AGATA array, calculated in the case of a point source positioned in the geometrical centre of the array, emitting a rotational cascade of 30 photons in coincidence at various recoil velocities. The effect of the tracking algorithm has been considered.

to v=c ¼ b ¼ 20%. Only at b ¼ 50% there is a sizeable reduction of the efficiency. This effect can be explained by noticing that at such a high source speed the photon emission is strongly forward focused, because of the Lorentz boost, resulting in densely packed

E. Farnea et al. / Nuclear Instruments and Methods in Physics Research A 621 (2010) 331–343

interaction points, more difficult to be resolved by the tracking algorithm. 6.4. Effect of beam tracking devices The assumption made in the previous section of perfectly known forward source velocity is quite simplistic and it is not completely suited to describe most of the real experimental conditions. When a beam of heavy ions interacts with a target, the velocity of the residual nuclei emitting the photons changes on an event-by-event basis, depending on the reaction used to reach or excite the nucleus, on the point in which the reaction occurs and on the detailed interactions of the residual nuclei with the target itself. The emission point of the radiation depends not only on the trajectory and target thickness, but also on the beam spot size, which might be non-negligible in the case of unstable beams produced by fragmentation of a primary beam, and on the halflife of the depopulated level. In the case of a tracking array such as AGATA, the quality of the resulting spectra will depend critically on the knowledge, on an

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event-by-event basis, of the position and velocity of the emitting nuclei, since the capability of Doppler correction depends on these quantities. For instance, the spectra shown in Fig. 17 refer to the AGATA array, considering a point source positioned in the geometrical centre of the array and emitting a rotational cascade of 30 photons. In both cases, the source has constant speed, respectively, b ¼ 5% and 20% for the top and the bottom spectrum, and velocity direction uniformly dispersed, on an event-by-event basis, in a cone centred on the z axis and having a half-opening of 101. Assuming that the source direction is perfectly known on an event-by-event basis, one obtains the spectra sketched with a thick line. The FWHM of the peak at 2330 keV is, respectively, 3.5 and 5.8 keV at b ¼ 5% and 20%. The spectra sketched with a light line are instead obtained assuming an average source direction along the z axis. At b ¼ 5%, the same 2330 keV peak has a FWHM of 21.0 keV, while at b ¼ 20% it is not possible to identify a peak at this energy. Considering point sources of fixed velocity direction and variable speed, or diffused sources having fixed velocity, the situation is similar to that shown in Fig. 17.

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Energy (keV) Fig. 17. Simulated response of AGATA to a cascade of 30 photons in coincidence emitted from a point source positioned in the geometrical centre of the array at a 5% (top) and a 20% (bottom) recoil velocities. In both cases a recoil cone opening of 101 was considered and the tracking reconstruction was performed considering an average direction along the z axis (light line) or the true event-by-event direction (thick line).

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40

v/c = 50% v/c = 20% v/c = 5%

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Fig. 18. FWHM of a peak of 1 MeV obtained for the AGATA array considering a diffused source distributed in the xy plane with a Gaussian distribution centred on the origin and having sx ¼ sy ¼ 5 cm, with a fixed velocity along the z axis. For each point, gray tracking was performed assuming to measure with a limited precision the source position on an event-by-event basis. See text for more details.

v/c = 50% v/c = 20% v/c = 5%

50

In complex spectra such as those shown in Fig. 17, the parameter identifying most easily their quality is the energy resolution, namely the FWHM of the peaks. Simulations were performed in order to estimate the precision on the event-byevent measurement of the source position and velocity, needed to maintain an adequate quality of the spectra for the AGATA array, assuming a source of single monochromatic photons of 1 MeV energy. In each calculation, an inaccuracy was introduced only in one out of the three relevant parameters (source position, source velocity direction, source speed), in order to get a clear indication of the impact of each parameter on the effective energy resolution. The results are summarised in the plots shown in Figs. 18 and 19. In Fig. 18, the case of a huge beam spot was emulated by assuming a bidimensional source diffused in the xy plane with a Gaussian distribution centred on the origin and having sx ¼ sy ¼ 5 cm. The finite precision on the event-by-event measured source position was emulated during the data analysis by adding to the true position ðx,yÞ an uncertainty generated with a bidimensional Gaussian distribution with the width being equal in the x and y directions. In Fig. 19 (top) the case of speed inaccuracy is considered. In the calculations, a point source positioned in the geometrical centre of the array is assumed. The velocity direction is kept fixed along the z axis, while, in order to mimic realistic experimental conditions, the source speed is sorted on an event-by-event basis following a Gaussian distribution centred on an average value bav and with a standard deviation s ¼ 0:1  bav . The simulated data were analysed by adding to the true value known from the simulation an additional uncertainty generated on an event-byevent basis with a monodimensional Gaussian distribution. The resulting peak FWHM is plotted as a function of the standard deviation used to generate this additional uncertainty, presented in the plot as relative to bav . The case of varying velocity direction is shown in Fig. 19 (bottom). In the calculations, a point source with fixed speed positioned in the geometrical centre of the array is assumed. The source velocity direction is uniformly dispersed in a cone centred along the z axis, having a half-opening of 101. In this case, the true W and j values were smeared during the data analysis with uncertainties generated with two Gaussian distributions, having both the same width.

FWHM (keV)

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Uncertainty on the recoil direction (deg) Fig. 19. Top panel: FWHM of a peak of 1 MeV obtained for the AGATA array as a function of the uncertainty on the measurement of the source velocity. The simulation has been performed by considering a point source moving along the z axis. In order to mimic the real experimental conditions, the source speed is varied on an event-by-event basis following a Gaussian distribution centred on bav , indicated in the graph box, and with standard deviation s ¼ 0:1  bav , but still the velocity is unequivocally determined. For each point in the graph, gray tracking was performed assuming to measure the source speed with the limited precision indicated in the abscissa axis as a fraction of bav . See text for more details. Bottom panel: FWHM of a peak of 1 MeV obtained for the AGATA array considering a point source having fixed speed and velocity direction uniformly dispersed in a cone centred along the z axis with a half-opening of 101. For each point, gray tracking was performed assuming to measure with a limited precision the source direction on an event-by-event basis. See text for more details.

In the three cases, the plots show quite a similar behaviour, each curve tending to a limiting value when the uncertainty on the varying quantity becomes smaller than a threshold and the resolution values getting worse with the increasing average speed of the source. The limiting resolution value depends essentially on the intrinsic resolution of the detectors and on the position resolution of the individual interaction point within the crystals. The degree of precision on the measurement of the source position, speed and velocity direction needed to keep the quality of the spectra to good values can be extracted by the plots shown in Figs. 18 and 19, for instance by assuming the values for which the peak FWHM is 10% larger than the limiting values. These values are presented in Table 2. As one would expect, the requirements become more stringent with the increasing average source speed, however, they are reachable with the present technology even at relativistic velocities. For instance, in the case of the PRISMA magnetic spectrometer [21], the velocities of the

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Table 2 Precision required for the measurement of the source position and velocity in order to obtain energy resolution values 10% larger than the limiting value. See text for details.

b (%)

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0.3 0.3 0.3

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Acknowledgements A.G. and E.F. acknowledge the support of MICINN, Spain, and INFN, Italy through the FPA2008-03774-E/INFN bilateral action. Th.K. acknowledges support from HIC for FAIR and BMBF (06DA9040I). B. Quintana acknowledges support also from MICINN through projects FPA2008-06419-C02-02 and Consolider-Ingenio CSD2007-00042 and from Junta de Castilla y Leon through project GR12. References

recoiling nuclei will be in the range b ¼ 5210%. In this case, the source position is defined by the beam spot size, which is typically of the order of 2  1 mm2. The direction of the recoiling nuclei, measured with the start detector of PRISMA, is defined with a precision of approximately 11, while the speed, deduced via trajectory reconstruction and time-of-flight measurements, is measured with a 0.5% relative precision.

7. Conclusion A Monte Carlo code based on the C++ classes of Geant4 has been developed to evaluate the performance of a tracking array such as AGATA. From the results obtained with this code and a tracking algorithm, the decision was taken to base the geometry of AGATA on a 180 hexagonal crystals configuration. The impact of passive materials on the performance of the array was estimated to be comparable to the case of conventional arrays of high-purity escape-suppressed germanium detectors. Finally, it was shown that precise measurements of the position and velocity vector of the emitting nuclei will be essential for a tracking array, and that the precision required for such measurements is reachable with the present technology even at relativistic velocities.

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