# Performance of The Advanced GAmma Tracking Array at GANIL

J. Ljungvall  R.M. Pérez-Vidal  A. Lopez-Martens  C. Michelagnoli  E. Clément
J. Dudouet  A. Gadea  H. Hess  A. Korichi  M. Labiche  N. Lalović  H. J. Li
F. Recchia  and the AGATA collaboration  CSNSM, Université Paris-Sud,
CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France  Instituto de Física
Corpuscular, CSIC - Universidad de Valencia, E-46980 Paterna, Valencia, Spain
GANIL, CEA/DRF-CNRS/IN2P3, BP 55027, 14076 Caen cedex 5, France  Institut
Laue-Langevin, B.P. 156, F-38042 Grenoble cedex 9, France  Department of
Physics, Lund University, SE-22100 Lund, Sweden  IKP, University of Cologne,
D-50937 Cologne, Germany  INFN Sezione di Padova, I-35131 Padova, Italy
Dipartimento di Fisica e Astronomia dell’Università di Padova, I-35131 Padova,
Italy  Institut de Physique Nucléaire de Lyon, Université de Lyon, Université
Lyon 1, CNRS-IN2P3, F-69622 Villeurbanne, France  STFC Daresbury Laboratory,
Daresbury, Warrington WA4 4AD, United Kingdom

###### Abstract

The performance of the Advanced GAmma Tracking Array (AGATA) at GANIL is
discussed, on the basis of the analysis of source and in-beam data taken with
up to 30 segmented crystals. Data processing is described in detail. The
performance of individual detectors are shown. The efficiency of the
individual detectors as well as the efficiency after $\gamma$-ray tracking are
discussed. Recent developments of $\gamma$-ray tracking are also presented.
The experimentally achieved peak-to-total is compared with simulations showing
the impact of back-scattered $\gamma$ rays on the peak-to-total in a
$\gamma$-ray tracking array. An estimate of the achieved position resolution
using the Doppler broadening of in-beam data is also given.

Angular correlations from source measurements are shown together with
different methods to take into account the effects of $\gamma$-ray tracking on
the normalization of the angular correlations.

###### keywords:

AGATA spectrometer; GANIL facility; $\gamma$-ray tracking;Nuclear structure;
HPGe detectors

††journal: NIMA

##  1 Introduction

In order to perform $\gamma$-ray spectroscopy nuclear structure studies in
conditions of extreme neutron/proton asymmetry and/or extreme angular momentum
the so-called $\gamma$-ray tracking arrays are considered as indispensable
tools. Two international collaborations, Advanced-GAmma-Tracking-Array (AGATA)
[1] in Europe and Gamma-Ray Energy Tracking Array (GRETA) in the US [2] are
presently building such arrays. Position sensitive High-Purity Germanium
(HPGe) detectors will cover close to 4$\pi$ of solid angle and track the path
of the $\gamma$ rays inside the detector medium giving maximum efficiency and
an excellent energy resolution. The technique of $\gamma$-ray tracking allows
both the high efficiency needed for high-fold coincidences and the excellent
position resolution needed for Doppler Correction at in-flight fragmentation
facilities.

Gamma-ray tracking starts from the digitally recorded wave-forms of the pre-
amplified signals of the highly-segmented HPGe detectors. The wave-forms are
treated with Pulse Shape Analysis (PSA) techniques to extract the position of
the interaction points of the $\gamma$ rays in the detector, presently with a
position resolution of about 5 mm FWHM [3, 4, 5]. The interaction points
(hits) are grouped into events on the basis of their timestamp, i.e. the
absolute time of the $\gamma$-ray interaction. The sequence of interaction
points of the $\gamma$ rays in the same event is reconstructed from the hits
via tracking algorithms. A higher efficiency with a high peak-to-total is
expected as the solid angle taken by Anti-Compton shields is now occupied by
HPGe crystals and the Compton event suppression is performed by the
$\gamma$-ray tracking algorithm. The use of digital electronics allows a
higher count-rate with maintained energy resolution, and rates up to 50kHz per
crystals are routinely used during experiments. The almost continuous
measurement of $\gamma$-ray emission angles, via the PSA and tracking, allows
for the excellent Doppler correction seen in $\gamma$-ray tracking arrays and
opens up a new degree of sensitivity in the determination of nuclear structure
observables such as electromagnetic moments (e.g. lifetimes measurements based
on Doppler shift and perturbed angular correlations). This paper is meant as
both a snapshot in time of the capacities of AGATA and as a reference paper to
be used when analysing data from AGATA experiments performed at GANIL.

The first experimental campaign with the demonstrator AGATA sub-array was at
LNL (2009-2011) [6] where it was coupled to the PRISMA spectrometer for the
study of neutron-rich nuclei produced in fusion-fission and neutron-transfer
reactions. This was followed by a campaign at GSI (2012-2014). Here a larger
AGATA sub-array was coupled to the FRS separator [7] for the first campaign
with radioactive ion beams. The performance of the AGATA sub-array at GSI has
been extensively studied [8], with focus on the efficiency of the AGATA sub-
array as a function of energy and data treatment. Other performance aspects
such as the peak-to-total ratio were also investigated.

Since 2015, AGATA has been operating [9] at GANIL, Caen, France, where it has
been coupled to VAMOS (a variable mode high acceptance spectrometer) [10, 11].
Three campaigns of measurements have been performed with focus mainly on
neutron-rich nuclei populated using multi-nucleon transfer reactions or via
fusion-fission or induced fission. In 2018, a campaign with AGATA coupled to
the NEDA [12] neutron detector and the DIAMANT [13, 14] charged particle
detector was performed. AGATA is foreseen to stay at GANIL until the middle of
2021. A campaign of source measurements was performed during 2016 to, together
with in-beam data, quantify the performance of AGATA at the GANIL site as
well. Basic performance data such as efficiencies are needed to analyze the
data taken during the campaigns, but a careful follow-up of the evaluation of
the AGATA performance as the size of the array changes, detectors and
electronics age and/or are changed is also of considerable interest. It allows
one to ensure that the performance is in accordance with expectations.
Furthermore, it helps understand where efforts to improve are important - this
both at a fundamental level, e.g. Pulse-shape analyses or $\gamma$-ray
tracking, and on a more practical level learning how to best maintain the
system at a high level of performance. Extensive Monte Carlo simulations of
AGATA are performed as well in order to predict the performance in different
experimental configurations and with different number of AGATA crystals. A
thorough evaluation of the performance of such a detection system allows for
the bench-marking of the Monte Carlo simulations, further helping the analysis
of experimental data.

There is an extensive literature on the performance of $\gamma$-ray tracking
arrays (e.g. [15, 16, 17]) that address the questions of efficiency, peak-to-
total, and, Doppler correction capabilities of $\gamma$-ray tracking arrays.
As this paper aims at giving a snap shot in time of AGATA and its capabilities
during the AGATA at GANIL campaign no detailed comparisons are made with the
literature as in most cases significant differences in setups and methodology
would require extensive discussion to make sense of such comparisons.

In this paper we will describe the performance of AGATA as of mid 2016, when
it was equipped with 30 crystals. In section 2 and section 3 the experimental
set up and data acquisition are presented. The performance of individual
crystals is discussed in section 4. In section 5 the performance of AGATA as
an array is discussed, using the Orsay Forward Tracking algorithm. Estimates
of the position resolution achievable in a typical experiment are given in
section 6. As the angular coverage of AGATA increases the capabilities in
terms of measuring angular correlations increase and this is discussed in
section 7. Conclusions are given in section 8.

##  2 Experimental setup and data taking

In 2016 the AGATA array consisted of 10 triple clusters (Agata Triple Cluster,
or ATC) [18] and one double cluster (Agata Double Cluster or ADC) arranged as
schematically represented in figure 1. Two of the detectors present in the
frame where not connected to an electronics channel, giving a total of 30
active detectors. One detector showed varying performance, related to the
electronics that was used, and is excluded form the efficiency determinations.
Measurements were performed both at what is referred to as “nominal position”
i.e. the front surfaces of all AGATA crystals are positioned at 23.5 cm from
the target position, and at “compact position” with a distance of 13.5 cm
between the closest part of the imaginary sphere that touches the front of the
AGATA crystals and the target position.

Figure 1: AGATA detectors seen from the reaction chamber point of view,
labeled according to their position in the honeycomb. The two crossed over
detectors are physically present, but not connected to an electronic channel.
Positions with no labeling are empty. The red and green line are the x-, and,
y-axis, respectively, for the installation in Legnaro and GSI, showing the
rotation made of the structure at GANIL.

Different standard radioactive sources were placed at the target position, see
Tab. 1. The Aluminum materials surrounding the target position, i.e. reaction
chamber and target holder, were the same as in most of the experimental setups
of the campaign. These aluminum structures are included in the Geant4
simulations [19, 20] presented in this work.

Source | Activity [kBq] | t0
---|---|---
152Eu | 19.1 | 05/01/2016
60Co | 8.7 | 05/01/2016
Table 1: Radioactive sources used for the measurement

For each detector, the data were collected from the 36 segments as well as for
two different gains of the central contact (ranges of $\approx\,$8 and 20
MeV). The segment signals are referred to with a letter A-F and a number 1-6
where the letter gives the sector of the crystal and the number the slice,
i.e. the segmentation orthogonal to the bore hole for the central contact. The
AGATA raw data for each crystal in an event consist of, for each segment and
for the central contact, the amplitude and 100 samples (10 ns time between
samples, $\approx$ 40 pre-trigger and $\approx$ 60 post-trigger) of the rise-
time of the waveform and a time-stamp, used for the event building. For the
source data used in this paper the amplitude was extracted from a trapezoidal
filter with a shaping time of 10 $\mu$s followed by a flat top of 1$\mu$s. The
online and offline data processing is done using the same computer codes, and
are described in detail in section 3.

The preamplifier outputs were digitized and pre-processed by two different
generations of electronics. The ATCA phase 0 electronics was developed at an
early stage of the project for the AGATA Demonstrator, described in Ref. [1].
For the GANIL Phase a second generation of electronics was developed referred
to as the GGP’s [21]. The two generations of electronics use the same
algorithms for determining the energy. However, for the determination of the
time of a signal, the ATCA phase 0 electronics use a digital constant fraction
(CFD) whereas the GGPs use a low-level leading edge algorithm. These times are
used for triggering purposes only. For both generations of the electronics
discussed above digital CFDs are used for proper timing when analysing the
data. A time signal is also extracted directly from the digitizer in order to
provide a $\gamma$-ray trigger for the VME electronics of VAMOS.

##  3 Data processing

The raw data (event-by-event amplitude, timestamp and traces for segments and
central contact) are treated with the chain of Narval actors as depicted in
figure 2. Starting at the top we have data coming from the front-end
electronics into the computer farm with the first Narval actor [1], the
“Crystal Producer” that puts the data of the crystal into the Agata Data Flow.
The next step, done in the “Preprocessing Filter” is to perform energy
calibrations, time alignments, cross-talk corrections and the reconstruction
of data in crystals, which are missing a segment (in case of several missing
segments this is no longer possible), see section 4. Following the
preprocessing comes the pulse-shape analysis where the $\gamma$-ray
interaction positions are extracted using an adaptive grid search algorithm
[22] where the experimental pulses are compared to pulses calculated using the
Agata Detector Library [23]. Tests allowing to search for more than one
interaction per segment of an AGATA crystal have been performed. These tests
have shown no improvement in terms of efficiency and peak-to-total after
$\gamma$-ray tracking so presently the search is limited to one interaction
per segment. From this point on the traces are removed from the data flow. In
a typical experiment the result from the PSA are also written to disk at this
point as this allows redoing the subsequent steps in the analysis offline
without the time consuming PSA. The final step where the data from each
crystal is treated individually (Local Level Processing) is the “Post PSA”, in
which, apart from timestamp realignments, several energy correction procedures
described in section 4 are performed. After this, data from all AGATA crystals
are merged in the “Event Builder” on the basis of a coincidence condition
using the individual time stamps of each crystal. This is the start of what is
referred to as the Global Level Processing. Complementary detectors are added
into the Agata Data Flow in the “Event Merger”. This is done before
$\gamma$-ray tracking because complementary data from these detector, e.g.
data from a beam tracking detector in case of a very large beam spot, are
potentially of use for the tracking of the $\gamma$ rays. Finally $\gamma$-ray
tracking is performed. In this work the OFT $\gamma$-ray tracking algorithm
has been used [24]. Finally the data is written to disk by a “Consumer”. This
procedure is performed online for monitoring of the experiments (data
processing) but also performed as a part of the data analysis (data replay)
starting from the raw traces or from the interaction points given by the
online PSA. The possibility to also store the experimental traces to disk
depends on the experimental conditions, and is in practice only possible if
the number of validated events is lower than about 3 kHz per crystal (inducing
a dead time of about 15%). Automatic procedures have been developed, both for
energy calibration purposes and for the preparation of the configuration files
that the actors use allowing error free and fast analyses of experimental
data.

Figure 2: Chains of Narval actors used for data processing. For details see
text.

##  4 Crystal Performance

In this section the performance in terms of energy and resolution for each
crystal is discussed, named with their position in the AGATA frame at GANIL.
The performance of the individual detectors was determined using measurements
with 60Co and 152Eu sources, see table 1. A set of standard procedures are
performed to minimize the FWHM for each crystal. These procedures consist of
cross-talk corrections and neutron-damage correction. The energies for events
with more than one segment with net charge have to be corrected for cross
talk, mainly between the central contact and the segments, as the energy
calibration is performed mainly with events with segment multiplicity 1.
Correction coefficients are extracted from source data either by looking at
the shift of the full-energy peak made by the summing of segments in fold two
events or by looking at the base-line shift in fold one events. This procedure
has been described in detail by Bruyneel at al. [25, 26]. The correction for
the effects of the neutron damage on the detection of the $\gamma$ rays of
interest has been performed following the theoretical approach described by
Bruyneel and coauthors [27]. Two calibration coefficients for every detector
channel, used to correct for the electron and hole trapping, are determined.
This is done using a grid-search based minimization of the FWHM and the left
tail of the peaks in the spectra for each channel, i.e. 37 per detector. In
figure 3 the effect of the correction is shown for one detector. This
correction is more important for the segments as they are more sensitive to
hole trapping, but it is also done for the central contact, and it is thus
important also when the sum energy of hits inside a crystal for an event is
normalised to the value measured by the central contact. This correction is
particularly important for measurements of lifetimes via line-shape analysis
techniques, where the symmetry of the detector response function is extremely
important to minimize systematical errors in the lifetime determination.

###  4.1 Energy resolution

The energy resolution has been determined for each segment and central contact
for the crystals in the array at the moment of taking source data (2016).
After the exposure to fast neutrons produced in deep inelastic collisions,
fission and fusion evaporation reactions in the first campaign at GANIL in
2015, several AGATA crystals were damaged by the charge traps created by
neutron radiation damage in the Ge crystal. For the most exposed detectors the
integrated flux exceeds $10^{9}$ n/cm2. This is based on the deterioration of
the uncorrected FWHM [28]. These traps are lattice defects that lead to a
reduction of the charge collection efficiency which appears as a low energy
tailing on the energy line shape (red line in figure 3). In position sensitive
Ge detectors, like the AGATA ones, it is possible to apply an empirical
correction to the neutron damage effects [27]. These corrections were applied
to 20 of the AGATA crystals in this work (see table 3 in appendix A). As an
example of the effect of neutron damage correction the original spectra and
the ones after the corrections, for one detector, are shown in figure 3. For
the other 10 detectors good energy resolution was achieved without the
neutron-damage correction procedure.

Figure 3:  Example of the peak line shapes for the 1332 keV 60Co $\gamma$-ray
before (red) and after (black) the neutron damage correction for the 36
segments of the crystal A002 position 12A ATC3.

In figure 4 the resolutions for the central contacts and sum of segments for
the used detectors are reported. The average FWHM resolution found for the
central contacts before the neutron damage correction is 2.93 keV and is
improved to 2.57 keV after correction. In the case of the sum of segments the
average FWHM is improved from 5.22 keV to 3.08 keV, showing the difference in
sensitivity to charge trapping. The comparison with the resolutions taken from
detector data sheets or factory measurements is reported in figure 5. In
general all the measured FWHM resolutions for the crystals agree with the
original ones, except for the detector 11C (B013), which apart from being
neutron damaged had a resolution problem during the measurements, in both
central contact and segments, due to problems with the electronics.

Figure 4: FWHM at 1.332 MeV (60Co) of the central contact (blue) and the sum
of segments (red) before (dark colours) and after (light colours) the neutron
damage correction for 20 out of the 30 capsules individually named with its
position labels.  Figure 5: FWHM at 1.332 MeV (60Co) of the central contact
(blue) after the neutron damage correction compared with the original FWHM
measured by Canberra (red) for the 30 capsules individually named with its
position labels.

###  4.2 Crystal efficiency

The efficiency of each crystal has been determined first from the central
contact signal. Although this is not the normal operation mode when performing
$\gamma$-ray spectroscopy with AGATA, the crystal central contact efficiency
allows easier diagnostic of the Data Acquisition Chain and easier comparison
to Geant4 simulations. For these reasons, it is of great value. Two sets of
data for efficiency measurement at the nominal and compact position of AGATA
have been taken. All efficiency numbers quoted in this section are corrected
for dead time of the data acquisition system.

The efficiency has been determined both from $\gamma-\gamma$ coincidences,
corrected for the angular correlation effects for the given geometry, and from
singles central contact data taken with 60Co and 152Eu sources. The
coincidence data are not affected by dead-time of the processing chain. The
singles central contact measurement is. To bypass this effect, the latter have
been recorded in coincidence with the VME/VXI electronic of the GANIL
acquisition system coupled to AGATA via the AGAVA board [1, 9]. The GANIL
acquisition system is triggered by the OR of the AGATA digitizers CFDs,
triggering the AGAVA board. The individual AGATA channels are then validated
by the AGAVA request within a 300 ns coincidence time window. At the source
rate, the VME/VXI GANIL electronic has a dead-time of $40\mu s$ per read-out
event, greater than the AGATA electronic system, and it can be precisely
quantified and used for live time correction in the single central contact
efficiency measurement. For the $\gamma-\gamma$ coincidence, the 1332 keV-1173
keV from the 60Co source and 121.8 keV-1408 keV, 121.8 keV-244.7 keV and 344.3
keV-778.9 keV coincidences from the 152Eu source were used. For fitting the
$\gamma$-ray peak areas used to extract the efficiency values, the Radware
software package was used [29]. A background subtraction was made by
evaluating the correlated background on both sides of the gating energy for
the $\gamma-\gamma$ coincidences analysis.

Using the 1.3 MeV transition from the decay of 60Co the efficiency relative to
a 3 in $\times$ 3 in NaI detector (i.e., $1.2\texttimes 10^{-3}$ cps/Bq at 25
cm) for each detector at nominal position was extracted and is reported in
figure 6. In the same picture, the value at 1.3 MeV as measured at the factory
or during the customer acceptance tests is shown. The average measured value
is $79$% with a sample standard deviation of $5$%, close to the factory values
average of $81$%. Crystal 02C suffered from oscillations during the
measurement and is therefore excluded in the efficiency numbers discussed
below.

The absolute central contact efficiency for the whole array, composed of 29
operational crystals, is reported in figure 7 for the nominal position of
AGATA and figure 8 for the compact position of AGATA. Here each crystal is
treated as a single detector like in a standard $\gamma$-ray detector array.
The values obtained in the singles measurement are compared with the
$\gamma-\gamma$ results and simulations and overlap well. For the nominal
geometry, the efficiency measured using singles is 2.95(6)% at 1332 keV
whereas for the compact geometry it is 5.5(1)% at 1332 keV. Geant4 simulations
using the AGATA simulation package [20] have been performed. These simulations
include a realistic implementation of the reaction chamber used during the
experimental campaign at GANIL [9], a steel block to emulate the effect of the
VAMOS quadrupole, as well as the two crystals that were present but not used
during the measurements. There is 12% discrepancy between the simulation and
the experimental results. This difference is larger than the 2.5% average
discrepancy for the individual crystals, as shown in figure 6, between factory
measurements and measurements made within the AGATA collaboration. However,
Geant4 simulations of the three differently shapes crystals used by AGATA give
a relative efficiency of 86%, 86%, and 87%, for type A,B, and C, respectively.
The average measured value is 79%, or 8% lower. This is in reasonable
agreement with the 12% of efficiency missing when compared with simulations,
as is illustrated in figures 7 and 8 (green line) where the efficiency of each
crystal has been scaled to its measured value. Here the question of how the
12% of effective germanium is lost has to be raised. The presence of a dead
layer or missing germanium will have an impact on the PSA as the pulse shapes
depend on the active volume and shape of the germanium diode. Simulations
assuming a thicker dear layers improve the correspondence with experimental
data. It is however difficult to pin down the contribution from different
surfaces of the detectors, i.e., one can reproduce experimental data with
different combination of dead layers around the central contact and at the
back of the detector. Moreover, the mismatch of the efficiencies at low
energies cannot be corrected reducing the active volume around the central
contact or at the back of the detector. In figures 7 and 8 simulations with a
dead layer of 2.5 mm around the central contact and 3 mm at the back are also
shown. For estimates of dead layers in HPGe detectors see, e.g., the work of
Eberth and Simpson [30] or Utsunomiya et al. [31]

Figure 6: Relative central contact efficiency at 1.3 MeV (60Co) in comparison
with the initial relative efficiency as provided by manufacturer for the 29
capsules individually named with its position label. Figure 7: Absolute
central contact efficiency for the 29 capsules AGATA sub-array in nominal
position (23.5 cm distance source to detectors) obtained with the data from
152Eu and 60Co in singles (black circles) and in coincidences (red circles) in
comparison with the simulations (magenta, blue, and green lines). The green
line corresponds to simulations where the efficiency has been scaled according
to the difference between the simulated absolute efficiency and the measured
absolute efficiency. Simulations performed with increased dead layers are also
shown (blue line). See text for details. The rate per crystal at this position
was around 200 Hz. Figure 8: Same as figure 7 for the compact configuration
and with a data rate per between 300 and 500 Hz.

##  5 Performance of the AGATA array with the Orsay Forward Tracking

#### Description of OFT

The Orsay Forward Tracking (OFT) algorithm [24] was developed with simulated
data sets produced with the Geant4 AGATA code [20]. The output of the
simulations was modified to emulate the expected experimental conditions, such
as energy resolution and threshold and position resolution allowing the
optimization of the algorithm using a realistic input. As all forward-tracking
algorithms the OFT starts with clustering interaction points. These clusters
are evaluated using a $\chi^{2}$-like test where scattered energies after
every interaction point as given by the energies in each interaction point are
compared to scattered energies as given by the Compton scattering formula
using the measured positions of the interaction points. The best permutation
for each cluster is calculated and the clusters are sorted in order of best
figure of merit. Clusters that pass a threshold called $P_{track}$ are
accepted as good $\gamma$ rays. The most influential parameter in this is
$\sigma_{\theta}$ corresponding to the error in scattered energy derived from
the error in interaction positions from the PSA. Using simulations this
parameter was optimized to $\sigma_{\theta}$=2.4 mm corresponding to the
assumed position resolution in the simulations of 5 mm FWHM at 100 keV
interaction point energy. Single interaction points that are further away than
40 mm from the closest other interaction point are treated as a photo-electric
absorption event. Here the probality for a $\gamma$ ray to have penetrated to
a given depth and been absorbed via the photo electric effect is evaluated and
compared to the $P_{sing}$ parameter. The single-interaction-point evaluation
is an important part of the tracking algorithm since the efficiency loss when
it is not included is very large for low-energy events, and non negligible at
higher energies: $\sim$20$\%$ of 1.4 MeV total-absorption events in each
individual detector are single interaction points. This last fact is due to
the way PSA identifies interaction points in the AGATA detectors. As mentioned
above, the Grid Search algorithm [22] used online only looks for 1 interaction
point per segment. This is at variance with what is currently done at GRETINA
[32] where the fits of the segment traces allow for more than one hit per
segment. For a detailed explatation on the OFT algorithms see Lopez-Martens et
al. [24].

#### OFT parameters

The definition and typical ranges of the main parameters of OFT are summarised
in table 2.

Table 2: Table summarising the meaning and standard ranges of the main adjustable parameters of OFT.  parameter | definition | typical value
---|---|---
$\sigma_{\theta}$ | average interaction-point | 0.3-3
| position resolution (cm) |
$P_{sing}$ | minimum probability to accept | 0.02-0.15
| single-interaction-point clusters |
$P_{track}$ | minimum figure of merit to accept | 0.02-0.05
| mutliple-interaction-point clusters |

Tuning the parameters can affect the spectral quality and shape. As an
example, a high value of $\sigma_{\theta}$ corresponds to nearly fully
relaxing the comparison between scattered energies obtained from interaction
positions and scattered energies obtained from energy differences. Basically,
using a very large $\sigma_{\theta}$ reduces the cluster evaluation stage to
finding the most likely sequence of interaction points in a cluster on the
basis of ranges and interaction probabilities only. Increasing
$\sigma_{\theta}$ increases the high-energy efficiency. However, it also
decreases the low-energy efficiency in the case of medium to high photon-
multiplicity events since single-interaction points are being accepted as
members of multi-interaction point clusters and are therefore lost as
potential $\gamma$ rays absorbed in a single interaction. There is an optimal
value of $\sigma_{\theta}$, which maximises the gain in efficiency at medium
and high energy while minimizing the loss of efficiency at low energy. By
analysing source and in-beam data obtained at Legnaro, GSI and GANIL, the
optimal value of $\sigma_{\theta}$ is found to be around $\sim$6 and 8 mm.
This corresponds to an average experimental position resolution a factor of 2
to 3 worse than anticipated. This is consistent with measurements of the
position resolution of an interaction point as a function of the deposited
energy [5] as well as with the observed clusterisation of interaction points
in specific areas of the detector segments.

Another example is given by the energy range of the single-interaction
spectrum, which grows when the threshold for validation of the corresponding
clusters is lowered. For $P_{sing}$=0.15, the spectrum extends to $\sim$600
keV, while for $P_{sing}$=0.02, it goes beyond 2 MeV. Extending the spectrum
increases the overall efficiency at high-energy. There is however a trade off
in the form of a larger background: for $P_{sing}$=0.02, the single-
interaction points are responsible for nearly two thirds of the background
present in the spectrum of tracked photon energies. Recent developments in the
OFT code have improved on this point by using an empirically deduced
energy-“distance in germanium” relationship instead of the single parameter
$P_{sing}$, allowing an improved peak-to-total. The new single-interaction
treatment, that is tailored not to have a negative impact on efficiency, is
further discussed in section 5.2.

The optimal value of $P_{track}$ is found to be around 0.05. Some very slight
adjustments can be made as a function of $\sigma_{\theta}$, but the general
trend is that a smaller value leads to more background and a larger value
reduces the peak intensities.

###  5.1 Tracking Efficiency measurements

The standard set of OFT parameters ($\sigma_{\theta}$=0.8, Ptrack =0.05 and
Psing =0.05) were used to extract the tracking efficiency of AGATA at GANIL in
a configuration with 29 capsules. The efficiencies to track the photons
emitted by a 152Eu source were obtained by comparing the detected peak areas
to the expected intensities given the source activity, the measurement time
interval and the electronics dead time. Since there are several 2-photon
cascades in the radioactive decay of 152Eu, the efficiencies at certain photon
energies can also be measured by comparing the detected peak area of a
transition when a coincidence with the transition of interest is required or
not. The advantage of this second method is that no knowledge of the source
activity or dead time of the system is required. The efficiencies obtained are
shown in figure 9.

Figure 9: Tracking efficiency of 29 AGATA detectors as a function of photon
energy obtained with the standard OFT parameter set and using either the total
singles tracked spectrum or the (121 keV-244 keV), (121 keV - 1408 keV) and
(344 keV - 778 keV) $\gamma$-$\gamma$ coincidences. The efficiency for 29
cores scaled from figure 7 is also shown. See text for details.

The efficiency to track a 1.4 MeV photon with 29 capsules is found to be
3.67(1)$\%$. This corresponds to an add back factor with respect to the
efficiency of the 29 detectors taken individually of 1.285(4).

In figure 9, the raw coincidence efficiencies at 121 and 344 keV lie below the
singles tracking efficiency curve. This is because the tracking efficiency
varies with the angle between the emitted photons; most notably it vanishes
for small angles due to the deficiencies of the AGATA PSA algorithm and/or due
to the fact that the tracking algorithm cannot disentangle the points
belonging to the 2 coincident photons when these lie too close to each other.
This is clearly seen in the plot of the $\gamma$-$\gamma$ angular correlations
for the 121.8-244.7 and 344.3-778.9 coincidences in 152Sm and 152Gd shown in
figure 10. By correcting the coincidence efficiencies by the missing fraction
of the experimental angular correlations compared to the theoretical curve,
the correct tracking efficiency values are recovered.

Figure 10: a) $\gamma$-$\gamma$ angular correlations obtained for the 121.8
keV - 244.7 keV cascade in 152Sm using the OFT parameter
$\sigma_{\theta}$=0.8. b) same as a) for the 344.3 keV -778.9 keV cascade in
152Gd and in the case of $\sigma_{\theta}$=2.0. The solid lines represent the
best adjustment of the theoretical curves to the data. The peaks at high
angles are associated with large statistical errors not shown in order to keep
the figure clear.

Using a larger value of $\sigma_{\theta}$ leads to a slightly lower tracking
efficiency below 200 keV, but yields 13$\%$ more efficiency at 1.4 MeV, making
the add back factor increase to $\sim$1.4. It also changes the raw coincidence
efficiencies for some coincidence couples. In the case of the 344.3 keV -778.9
keV cascade of figure 10, in particular, correlations are not only absent at
small angles, but also at larger angles, when OFT most probably misinterprets
all or a subset of the interaction points of the event as points belonging to
a back-scatter sequence.

###  5.2 Tracking Peak-to-Total ratio

An important performance parameter for a $\gamma$-ray spectrometer is the peak
to total ratio quantifying the fraction of events found in the full energy
peak as compared to the total number of detected $\gamma$ rays. Data was taken
with a 60Co source with an activity of $8.7$ kBq. Gamma-ray tracking was then
performed offline for 29 of the 30 AGATA detectors using the 30th as an
external trigger. In the 30th detector a central contact energy of $1332.5\pm
5$ keV was demanded. In this manner a $\gamma$-ray multiplicity of one can be
guaranteed for the remaining 29 detectors. In figure 11 the $\gamma$-ray
spectrum is shown, together with spectra made with the two different
treatments of the single-interaction validation used in this work. The peak-
to-total using the empirically fitted maximum distance in germanium for single
interactions is 36.4(4)%. It is well known that the peak-to-total in a
$\gamma$-ray tracking array is dominated by single-interaction points accepted
as events corresponding to a direct absorption of the total $\gamma$-ray
energy via the photoelectric effect. Excluding such events the peak-to-total
is increased to 52.4(6)%, with a reduction in efficiency for the full energy
peak of 17%. The variation of peak-to-total and efficiency at 1173 keV as a
function of the $P_{track}$ parameter is shown in figure 12, for the cases
when single interactions are included or excluded. Note that above
$P_{track}>0.7$ no events with multiple interaction points are left. From
figure 12 it is clear that for the OFT algorithm the peak-to-total has a weak
dependence on the $P_{track}$ parameter, again showing that it is
$\sigma_{\theta}$ that is the most important parameter for OFT.

Figure 11: Gamma-ray tracked spectra for 29 AGATA detectors for 60Co data
using a 30th AGATA detector as a external trigger by demanding the full
absorption of the 1332.5 keV gamma in it. The solid line (black) is using the
latest single-point interaction validation procedure, the dashed line (red) is
using the old single-point interaction validation procedure, and finally the
dotted line (blue) using the 95% absorption limit. Figure 12: Efficiency
relative to $P_{track}=0$ at 1173 keV and peak to total as a function of
$P_{track}$ used by the OFT algorithm to accept or not a $\gamma$-ray track.
This for when including or excluding single point interactions.

Monte Carlo simulations using the AGATA simulation package were made in order
to compare the simulated $\gamma$-ray tracking performance with experimental
data. In the simulations a 60Co was simulated with a source strength of 5 kBq.
An absolute time was used in the simulations allowing effects such as pile-up
and random coincidences to be simulated. Gamma-ray interactions in the same
segment were packed at their energy-weighted average positions. These were
then written into the same data format as used to store experimental post-PSA
data. This allowed the use of identical $\gamma$-ray tracking and data
analyses codes for the experimental and simulated data, i.e. the simulated
data was treated exactly as explained for the experimental data above. Four
different simulations were performed. The first one including only the HPGe
crystals and the aluminum end-caps. The second simulation included a large
piece of steel to mimic the large quadrupole magnet of the VAMOS. The third
simulation included both the large piece of steel mimicking VAMOS, concrete
walls and the target chamber. A fourth simulation was also performed adding to
the third simulations thicker dead layers to the HPGe crystals. The added dead
layers were 3 mm at the back side of the detector and 2.5 mm around the
central contact. The peak-to-total for the different simulations, when gating
on the 1332.5 keV transition to look at the 1173 keV transition were 49%, 48%,
43%, and 41%, respectively. This is to be compared to the experimental value
of 36%. In figure 13 the Compton scattering part of the 1332.5 keV gated 60Co
spectra is shown for experimental and simulated data. In the experimental
spectrum a pronounced back-scattering peak can be seen just above 200 keV. The
simulation labeled 1, only including AGATA itself, does not show such a back-
scattering peak and consequently the peak-to-total is much better than for the
experimental data. For simulation 2, where the VAMOS quadrupole has been
included in a very schematic way a clear back-scattering peak emerges.
However, at both lower and higher energies as compared to the back-scattering
peak the experimental data contains more counts. In simulation 3, where the
concrete walls are included together with the scattering chamber a shape of
the spectrum very close to the experimental one is produced. This suggests
that a significant fraction of the spectrum is not due to Compton scattering
inside the HPGe crystals of AGATA, but from the scattering on the structures
around AGATA into AGATA. Including thicker dead layers in the HPGe crystals in
the simulation, as done for the fourth simulation, increases slightly the
amount of background between the full-energy peak and the Compton edge, but
does not change the shape of the spectrum in a significant way. However, the
peak-to-total is decreased by about 5%. These “back scattered” $\gamma$ rays
are very difficult to properly discriminate against as they are from the point
of view of $\gamma$-ray tracking perfectly good single interaction point
events in the front of the crystals.

Figure 13: Comparisons between experimental spectrum (in black) and spectra
from four different simulations. The spectra are normalized to the same number
of counts in the region 0-1165 keV. Simulation 1 includes only AGATA,
simulation 2 also includes a schematic implementation of the VAMOS dipole
magnet, simulation 3 further adds concrete walls around the experimental
setup. Finally, simulation 4 has thicker dead layers added to the HPGe
crystals. For further details on the simulations, see the text.

###  5.3 In-beam efficiency of AGATA coupled to VAMOS

The in-beam efficiency of AGATA is different from that of source measurements,
as the efficiency is also a function of count rate in the individual detectors
due to pile-up (rejected and non rejected) and rate limitations in the
electronics. In-beam efficiency varies from experiment to experiment therefor
exact numbers are both difficult to reliably produce and not of general
interest. The aim of the section is to give a useful rule of thumb to allow
consistency checks when analysing data. The in-beam efficiency for events with
a higher $\gamma$-ray fold than one also depends on the angular distribution
of and correlation of the $\gamma$-ray transitions used to measure it. This
both via pure geometrical effects and via the lowered $\gamma$-ray tracking
efficiency for $\gamma$ rays with a preference for being emitted in parallel.
The in-beam efficiency has been estimated for AGATA coupled to VAMOS for an
experiment where a 92Mo beam impinged on a 92Mo target, and the beam-like
reaction products were unambiguously identified in VAMOS, also providing the
velocity vector for Doppler correction. During this experiment 23 AGATA
crystals were operational in the array, each counting at around 45 kHz with a
shaping time of 2.5 $\mu$s. As the target and the beam both were 92Mo, de-
excitation of target-like and beam-like particles could be studied. The beam-
like and target-like nuclei travel with a relative angle of about
$90^{\circ}$, allowing an estimate of the effect of the angular distribution
on the measured efficiency.

The coincidence method was used to determine the efficiency at 1510 keV,i.e ,
the number of detected $2^{+}_{1}\rightarrow 0^{+}_{1}$ $\gamma$ rays per
detected $\gamma$ ray from the $4^{+}_{1}\rightarrow 2^{+}_{1}$ transition was
determined. Peak intensities were extracted from singles spectra and from
$\gamma\gamma$ coincidence matrices. The projected gate in the $\gamma\gamma$
coincidence matrix is shown in figure 14.

Figure 14: Gamma-ray spectra showing the 1510 keV $2^{+}_{1}\rightarrow
0^{+}_{1}$ transition in 92Mo used to estimate the in beam efficiency.

The efficiency at 1510 keV extracted using this method is after $\gamma$-ray
tracking 1.5(1)%, to be compared with the expected efficiency of about 2.5%
for 23 AGATA crystals at an energy of 1.5 MeV. This loss of efficiency, some
40% lower, has several origins. In this section we will try to identify the
sources of this reduction. At count rates of about 45 kHz and a shaping time
of 2.5 $\mu$s there is a loss of the order of 20% due to the pile-up
protection built in the AGATA pre-processing firmware [33]. There is also the
loss in tracking efficiency for higher fold events. A lower limit for this can
be estimated using the smallest used cluster angle in the OFT of $8^{\circ}$
(as can be seen in figure 10 the efficiency to track two $\gamma$ rays inside
this cone is close to zero) which corresponds to approximately 6% of the solid
angle of 23 AGATA detectors. These contributions add up to about 25% of losses
(i.e. more than half of the lost efficiency) that are rate dependant, via the
pile up, and related to the detector physics (i.e. the rise time of the HPGe
crystals and average cluster size for typical $\gamma$ rays) and therefore
always will be present. There is an open question from where the remaining
about 15% of efficiency loss is coming. Measurements suggests that 5% to 10%
could come from overload beyond specification of the trigger distribution
system related to the high total rate (more than 1MHz).

##  6 Position resolution of the PSA

Figure 15: Estimated position resolution for two detectors in the AGATA array.
The lines are fits to the FWHM of simulated data sets for the two different
detectors where the assumed position resolution has been varied. Large symbols
show the measured FWHM for each detector (y-axis) and corresponding deduced
position resolution (x-axis). For details on simulation and experiment, see
text. Note that the lower x-axis is a scaling factor of the position
resolution given in Söderström et. al. [5] for the FWHM in one dimension. The
upper x-axis shows the average resolution for the interaction points used for
Doppler Correction.

The VAMOS allows for a very precise determination of the recoil vector of the
identified ion. The direction can in this context be considered as exact
whereas the velocity has an error in the order of a few per mill. Given that
the recoil velocity has a very small error the position resolution can be
estimated by the Doppler Broadening of the $\gamma$-ray peaks via the Doppler
Shift given by (for details see, e.g., Söderström et al. [5])

$E_{\gamma}=E_{\gamma 0}\frac{\sqrt{(1-\beta^{2})}}{(1-\beta cos\theta)}$ (1)

where $E_{\gamma}$ is the energy detected in the detector, $E_{\gamma 0}$ is
the energy of the $\gamma$ ray in the rest frame of the nucleus, $\beta$ is
the velocity of the nucleus emitting the $\gamma$ ray and $\theta$ is the
angle between the velocity of the emitting nucleus and the $\gamma$ ray in the
laboratory frame. From this we have a $\gamma$-ray peak width $\Delta
E_{\gamma 0}$ of

$(\Delta E_{\gamma 0})^{2}=\left(\frac{\partial E_{\gamma 0}}{\partial
E_{\gamma}}\Delta E_{\gamma}\right)^{2}\ +\left(\frac{\partial E_{\gamma
0}}{\partial\beta}\Delta\beta\right)^{2}+\left(\frac{\partial E_{\gamma
0}}{\partial\theta}\Delta\theta\right)^{2}.$ (2)

This can be used to evaluate the performance of the PSA via the relation

$\cos\theta=\frac{\vec{v}\cdot\vec{r}}{|\vec{v}||\vec{r}|}$ (3)

where $\vec{v}$ is the recoil velocity as detected by VAMOS and $\vec{r}$ is
the position vector of the first $\gamma$-ray interaction as given by
$\gamma$-ray tracking. The method employed to determine the position
resolution for six different AGATA crystals is to perform Geant4 simulations
that in a realistic way take into account all experimental contributions to
the FWHM of the $\gamma$-ray peaks while varying the assumed position
resolution of the PSA. The experimental FWHM of the $\gamma$-ray peak can then
be used to interpolate the actual position resolution of the PSA as done by,
e.g., Recchia et al. [4].

In this case the experiment was a fusion-fission experiment populating, among
other nuclei, 98Zr. A beam of 238U impinged on a 10 $\mu$m think 9Be foil. The
VAMOS was positioned at 28∘ relative to the beam axis. Six AGATA detectors
close to $112^{\circ}$ relative to the recoil direction were used to sample
the position resolution of the detectors in the array, as they had the largest
Doppler Broadening, increasing the sensitivity to the position resolution. As
all data were analyzed after $\gamma$-ray tracking it was the interaction used
for Doppler Correction that determined which detector was studied. The FWHM of
the $\gamma$-ray peaks were determined using Gaussian fits. An error
$\Delta\beta/\beta=0.0045$ as deduced from the mass resolution of VAMOS gives
a constant contribution to the FWHM of the $\gamma$-ray peak of 0.13%.

The simulations took into account the energy loss in the target and straggling
as the reaction products leave the target as well as the acceptance of VAMOS.
For these simulations the AGATA geant4 simulations package was used [20]. In
the simulations a perfect knowledge of the recoil velocity was assumed
($\Delta\vec{v}=0$). An intrinsic resolution of the AGATA detectors of 2.6 keV
at 1332 keV was assumed for all detectors. Peak widths as a function of
position resolution were determined for seven different position resolutions.
As a baseline the experimentally determined energy dependent position
resolution from Söderström et al. [5]

$\Delta r_{i}=1.9+4.4*\sqrt{100keV/E_{i}}\text{~{}mm FWHM}$ (4)

where $E_{i}$ is the energy of the interaction point i. The resolution was
scaled with a value ranging 0.36 to 1.41 for the different simulations. This
procedure allows to correctly capture the variation in position resolution
with the energy of the interaction point used for Doppler correction. From the
simulations it was determined that the average position resolution for the
interaction point used for the Doppler Correction when using the non-scaled
function of Söderström et al. [5] is 4.3 mm FWHM. For each assumed position
resolution the FWHM of the simulated $\gamma$-ray peak for each detector was
determined by a Gaussian fit. The extra width coming from the error in recoil
velocity was added quadratically. In figure 15 these values are shown with
small symbols for detector 39 and 41 (which has the best and worst
experimental position resolution, respectively). To each set of FWHM coming
from the variation of position resolution a second degree polynomial function
was fitted. Using the inverse of these functions the position resolution of
the individual detectors can be determined (see large symbols in figure 15).
Note that in figure 15 the x-axis is a scaling factor with the previously
determined position resolution as base, i.e. 1 means the detector has the same
PSA performance that was previously measured. The six detectors used to sample
the position resolution are located in the span 0.79-1.4 (as compared to
Söderström et al. [5]), with five detectors larger than 1.08 and a weighted
average of 1.15. This corresponds to an average position resolutions used for
Doppler Correction of 3.7 mm-6.1 mm FWHM, with a weighted average of 5.1 mm
FWHM. The average error on the estimated position resolution is 1 mm. There is
no obvious difference in how the detectors perform for other parameters than
the PSA, nor in how they have been treated. It should be noted that the
probability of having a maximum difference of 2.4 between six values randomly
taken from a Gaussian distribution with a $\sigma=1$ is in the order of
50$\%$, i.e. our results is rather probable even if all the detectors are
performing identically. It is however of interest in a future work to
investigate the variance of detector performance with respect to PSA in AGATA.

##  7 Angular Correlations in AGATA

The use of AGATA for angular correlation measurements to determine the
multipolarity of $\gamma$ decays has been investigated using source data. Two
pairs of $\gamma$-$\gamma$ cascades from the decay of 152Eu were used: The
first pair was the 1408 keV-121.8 keV coincidence in 152Sm de-exciting the
2${}^{\text{-}}_{\text{1}}$ level at 1530 keV to to the ground state via the
2${}^{\text{+}}_{\text{1}}$ level at 121.8 keV. The second pair is the 244.7
keV-121.8 keV de-exciting the 4${}^{\text{+}}_{\text{1}}$ level at 366.5 keV
and the 2${}^{\text{+}}_{\text{1}}$ level, also in 152Sm.

The tracking algorithm identifies the first interaction point of each $\gamma$
ray and as the position of the source is known the angle between the $\gamma$
rays in the 1408 keV-121.8 keV pair and the 244.7 keV-121.8 keV pair could be
determined and histogramed, see lower panel in figure 16. The main features of
the two pairs of $\gamma$ rays are similar. The cut at about 8 degrees is a
result of the tracking algorithm, whereas for larger angles the geometry of
AGATA as used for the source measurement dominates the shape of the spectra.
The slower rise in intensity for the 244.7-121.8 keV cascade at low angles
comes from the intrinsic difficulty to track two low-energy $\gamma$ rays
emitted into a small solid angle, since they often will be reconstructed as
one $\gamma$ ray with sum energy. The angular correlation is then extracted by
normalizing for geometrical effects and the already mentioned decrease in
efficiency for two low-energy $\gamma$ rays absorbed close to each other. The
normalisation was created by tracking events consisting of the interaction
points of two events each with a total energy corresponding to one of the
$\gamma$ rays in the cascade of interest concatenated into one event, thus
generating pairs of $\gamma$ rays with the correct energies, but with no
angular correlation. From the tracked events the angle between the $\gamma$
rays was then again extracted. The resulting histograms for the two pairs of
$\gamma$ rays are shown in the upper panel of figure 16.

Figure 16:  Histograms used for angular correlation measurements using AGATA.
The lower panel shows the angle between the two correlated $\gamma$ rays
detected in AGATA. The upper panel shows the angle between $\gamma$ rays from
uncorrelated events concatenated before tracking.

By dividing the histograms in the lower panel in figure 16 by the upper panel
the histograms shown in figure 17 are created. The upper panel is for the
4${}^{\text{+}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
cascade, the lower panel for the
2${}^{\text{-}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
cascade. For each angular correlation the expression

$W(\theta)=1+a_{22}P_{2}(cos(\theta))+a_{44}P_{4}(cos(\theta))$ (5)

where $a_{22,44}$ are the directional correlations coefficients and $P_{2/4}$
are the Legendre polynomials of order 2 and 4 respectively, have been fitted,
and the $a_{22}$ and $a_{44}$ coefficients extracted. For the stretched
4${}^{\text{+}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
cascade the fitted values are $a_{22}=0.13\pm 0.02$ and $a_{44}=-0.02\pm 0.03$
to be compared with theoretical values of $a_{22}=0.102$ and $a_{44}=0.0091$.
For the non-mixed the
2${}^{\text{-}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
cascade our fit gives $a_{22}=0.25\pm 0.02$ and $a_{44}=-0.01\pm 0.03$, for
which the theoretical values are $a_{22}=0.25$ and $a_{44}=0$. With three out
of four values within $1\sigma$ this is in agreement with what is expected if
AGATA is correctly reproducing the angular correlations.

Figure 17:  Gamma-gamma angular correlations measured with AGATA. The upper
panel shows the angular correlation for the
4${}^{\text{+}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
pair of transitions in 152Sm. The lower panel is for the
2${}^{\text{-}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
transitions

A particularity of a $\gamma$-tracking array as compared to a classical multi-
detector $\gamma$-ray spectrometer is the continuous variation in efficiency
with the angle between the detected $\gamma$ rays. For angular correlations
this means the normalisation of the angular correlations need not only to
consider geometrical coverage. This can be seen by looking at the difference
between using uncorrelated hits that are concatenated and tracked or tracked
uncorrelated $\gamma$ rays concatenated into events when constructing the
normalisation used to extract the angular correlations from the experimental
correlations. In the top panel of figure 18 the histogram drawn with a black
solid line shows the distribution of $\theta$ angles between uncorrelated
$\gamma$ rays concatenated after tracking. The histogram drawn with red dashed
line shows the $\theta$ angle distribution if one instead concatenates
uncorrelated events using the individual hits and then preforms the tracking.

Figure 18:  Normalisation histograms and angular correlations for
4${}^{\text{+}}_{\text{1}}\rightarrow$2${}^{\text{+}}_{\text{1}}\rightarrow$0${}^{\text{+}}_{\text{1}}$
using the "concatenate before tracking" and "concatenate after tracking"
methods.

The bottom panel shows the resulting angular correlations using the two
different methods of generating the normalisation. It is clear that the
effects of $\gamma$-ray tracking, included when events are concatenated before
tracking, are needed for a correct normalisation over the entire angle range.
This procedure works well for source data where the peak-to-background ratio
is high and $\gamma$ rays from different decays have no correlations. The
application of this method to in-beam data is however more problematic due too
the lower peak-to-background ratio and cross-event angular correlations coming
from aligned nuclei.

##  8 Conclusions and perspective

The performance of AGATA installed at GANIL, coupled to the VAMOS has been
characterized. The efficiency of AGATA, as a whole as well as for individual
crystals, has been determined using both singles measurements and coincidence
methods. It has been done both using AGATA as a standard array and as a
$\gamma$-ray tracking array. A total efficiency for AGATA of 3.8(1)% at 1332
keV for the nominal geometry when using $\gamma$-ray tracking was determined.
This is to be compared to 2.9% at 1332 keV if AGATA is used as normal multi-
detector array. It is also shown how the efficiency extracted from coincidence
has to be corrected for angular correlation effects, as the increased
probability to emit parallel $\gamma$ rays combined with the clustering stage
of $\gamma$-ray tracking generates a loss of efficiency that depends on the
angle between the two $\gamma$ rays. This correction has to be made on top of
the typical correction made for angular correlations effects.

As the AGATA detectors have been used in different campaigns the segments of
some of the detectors are showing clear signs of neutron damages. Annealing
procedures are complicated for these detectors and ingenious neutron damage
correction procedures have been developed allowing an almost full recovery of
the intrinsic energy resolution. The average central contact energy resolution
for AGATA (beginning of 2016) is 2.57 keV at 1332 keV and for the segments
3.08 keV at 1332 keV. Corresponding values before applying neutron damage
correction are 3.08 keV and 5.22 keV for central contacts and segments,
respectively. The neutron damage correction procedure is effective, but at
some point the detectors will need to be annealed. Maintenance, such as
annealing, are as important for the future of AGATA as the more appealing
technical developments that can be made.

The position resolution given by the PSA for AGATA at GANIL has been estimated
for 6 AGATA crystals using data from an experiment performed in the first half
of the campaign. This was done by comparing experimental data with Monte Carlo
simulations in which the position resolution was varied. It turns out that the
average position resolution found was a factor of 1.16(5) larger than what was
measured in a dedicated experiment [5].

As the number of crystals in AGATA increases the interest in using AGATA for
angular correlations and distributions increases. Using a 152Eu source angular
correlations have been produced and methods to properly normalize for the
combined effect of geometry and $\gamma$-ray tracking have been devised.

Finally, the AGATA detector system is performing very well, as proven by the
physics results that have been produced. However, improvements in the PSA and
further tuning of $\gamma$-ray tracking algorithms would be beneficial. A
better understanding of the details of the signal generation in the segmented
detectors is needed to improve the PSA. This would also allow for better
handling of multiple interactions in one segment and removing the nonphysical
clustering of interaction points. Such improvements would allow for an
increased peak-to-total.

##  9 Acknowledgments

The authors would like to thank the AGATA collaboration and the GANIL
technical staff. Gilbert Duchêne is thanked for providing the in-beam data set
used to extract the position resolution of the pulse-shape analysis. The
excellent performance of the AGATA detectors is assured by the AGATA Detector
Working group. This work was partially supported by the Ministry of Science,
Spain, under the Grants BES-2012-061407, SEV-2014-0398, FPA2017-84756-C4 and
by the EU FEDER funds. The research and development on AGATA was supported by
the German BMBF under Grants 06K-167, 06KY205I, 05P12PKFNE, 05P15PKFN9, and
05P18PKFN9. The AGATA project is supported in France by the CNRS and the CEA.
The UK Science and Technology Facility Council (STFC) supports the AGATA
project.

##  Appendix A Detector and crystal positions and ids

Table 3: Crystal lookup table for the 32 crystals present in the set-up, although only 30 were used in the measurement. The capsules in position 11A and 14A were not operational and shown in italic. Neutron damage correction was performed on detectors marked in bold. Cluster | Crystal A | Crystal B | Crystal C | Position Array
---|---|---|---|---
ATC6 | A001 | B004 | C010 | 00
ATC8 | A009 | B005 | C008 | 02
ATC5 | A005 | B002 | C009 | 03
ATC9 | A004 | B008 | C013 | 04
ATC10 | A010 | B012 | C012 | 05
ADC9 | - | B011 | C011 | 09
ATC2 | A003 | B003 | C005 | 10
ATC7 | A006 | B013 | C006 | 11
ATC3 | A002 | B010 | C001 | 12
ATC4 | A007 | B007 | C007 | 13
ATC1 | A008 | B001 | C003 | 14

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