The last step is to calculate the correspondence between the depth $z$ and its raw estimator $f_z$, which is

$$f_{z1} = \frac{\sum_i i s_i}{\sum_i s_i}, \qquad (5)$$

for the first ring using the net-charge signal as used in ref. [31],

$$f_{z2} = \frac{(\max S_t - \min S_t) - (\max S_b - \min S_b)}{(\max S_t - \min S_t) + (\max S_b - \min S_b)} \qquad (6)$$

for the middle four rings using the transient signals in the same column, and

$$f_{z3} = - \frac{\max S_b - \min S_b}{\sum_i s_i}, \qquad (7)$$

for the last ring using the transient signal from its bottom neighbor in ring 5 and normalized by segment energy $E = \sum_i s_i$. The estimators for the last five rings have also been modified with respect to what was used in ref. [31]. Then, the Jacobian correspondence between $z$ and its raw estimator $f_z$ is calculated separately for each segment, each $r$ interval, and each $\phi$ interval, see fig. 4.

In this way, we obtain a one-to-one mapping, coming from the equal probability condition, between $(x, y, z)$ and the measured $(f_r, f_\phi, f_z)$. In order to validate our codes, the method was first tested using an ADL basis with a grid size of $2 \times 2 \times 2$ mm$^3$. This gave a precision of $\sigma = 2.8$ mm ($\sigma_x = 1.7$, $\sigma_y = 1.7$, and $\sigma_z = 1.5$) for the difference between the known ADL positions and the reconstructed positions. This is in accordance with what was found for simulated pulses by Désesquelles et al. [31].

Figure 4 illustrates the procedure to generate the needed correlations between simulated distributions of interaction positions and experimental distributions of the raw estimators. Examples of simulated and experimental distributions for an A type detector are shown. The simulated 2D distribution of $\phi$ vs. $r$ is shown for segments A1, A3, and A6 in figs. 4(a), 4(b), and 4(c), respectively. Also shown are the divisions used for the $r$ and $\phi$ coordinates. In figs. 4(d), 4(e), and 4(f) the corresponding 2D raw estimator distributions are shown. For each square in the simulated distributions there is a square in the experimental distributions containing the same fraction of events. In figs. 4(g), 4(h), and 4(i) the $z-f_z$ correlations created for the squares that are filled with white in figures (a)-(f) are shown. These are examples of the correlations used for real-time PSA where the three raw estimators $f_r, f_\phi$ and $f_z$ are calculated and the $\gamma$-ray interaction point is given by linear interpolation in the corresponding voxel.

The results of our work can be used in two ways for the location of $\gamma$-ray interactions in the crystal.

1) When only one segment in a crystal is hit, the $x, y, z$ position of the hit can be deduced from the determination of $f_r, f_\phi, f_z$ (through the Jacobian correspondences shown e.g. in figs. 3 and 4). This procedure will be referred to as the Direct Method (DM) in the following.

2) When multiple hits induce pulse overlaps, the locations of the hits can only be obtained using a deconvolution code, in our case an Adaptative Grid Search algorithm. This code needs as input a basis of signals corresponding to identified locations covering the volume of the detector. In the next paragraph, we show how such a signal basis can be built using the $(f_r, f_\phi, f_z) \rightarrow (x, y, z)$ mapping. This basis will be referred to as the *in situ* basis.

To build the experimental basis, all signals giving raw estimators leading to the same voxel are averaged after normalization. The center $x, y$, and $z$ of the voxel is considered as the corresponding hit position. Figure 5 shows ten $^{60}$Co experimental pulses after normalization by the hit energy. They are all calculated to belong to the voxel at $x = 4.7$ mm, $y = 25.2$ mm, $z = 41.8$ mm in segment B4. One can see that both the net-charge signal from segment B4 and the transient signals from the direct neighbors B3, B5, A4 and C4 used for the calculations of the estimators have very similar shapes. The pulses are however not identical, which is not to be expected as the voxels used have a finite volume. The number of experimental samples per voxel varies from 10 to 400.

Examples from the experimental basis generated using the *in situ* method are shown in fig. 6. The basis signals for the same position ($x = 31$ mm, $y = 5.5$ mm, $z = 63$ mm) in three different detectors are shown. Two of the detectors have the same geometrical shape (type A) while the third detector is of type B. It is encouraging to see that the signals from the two type A detectors are very similar while the signal from the type B detector is different.

## 3 Application to in-beam $\gamma$-ray spectroscopy from fusion-fission reactions

The width of a $\gamma$-ray peak in a spectrum after Doppler correction can be deduced from the Doppler shift formula

$$E_{\gamma} = E_{\gamma 0} \frac{\sqrt{1 - \beta^2}}{1 - \beta \cos \theta}, \qquad (8)$$

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 formula one gets a $\gamma$-ray peak width $\Delta E_{\gamma 0}$ of

$$(\Delta E_{\gamma 0})^2 = \left(\frac{\partial E_{\gamma 0}}{\partial E_{\gamma}} \Delta E_{\gamma}\right)^2 + \left(\frac{\partial E_{\gamma 0}}{\partial \beta} \Delta \beta\right)^2 + \left(\frac{\partial E_{\gamma 0}}{\partial \theta} \Delta \theta\right)^2. \qquad (9)$$

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

$$\cos \theta = \frac{\mathbf{v} \cdot \mathbf{r}}{|\mathbf{v}| |\mathbf{r}|}, \qquad (10)$$

where $\mathbf{v}$ is the velocity of the nucleus and $\mathbf{r}$ is the first interaction position of the $\gamma$ ray as determined from PSA.
<figure><img src="image_101.png" /><figcaption>**Fig. 5.** (Color online) Ten experimental signals that are found to belong to the same voxel by present method. The average of the pulses is used as the experimental basis pulse for the grid position corresponding to the center of the voxel. The inset (a) is an enlargement on the transient signals.</figcaption></figure>

This was used to assess the performance of PSA using the experimental *in situ* data bases and to investigate the precision that could be achieved using the correlations to extract the γ-ray interaction position in the case a crystal had only one segment hit. Data from an in-beam experiment was analyzed in three different ways producing three different sets of data corresponding to:

- Adaptive Grid Search using the ADL bases (1).

- Adaptive Grid Search using the ADL bases + the Direct method for one net-charge segment events (2).

- Adaptive Grid Search using the *in situ* bases (3).

The analysis was performed using the AGATA data analysis chain as described in ref. [1] with a modification to the PSA code to give the possibility to treat one-hit-segment events with the Direct Method. This means that all γ-ray energies are tracked γ-ray energies and that all calibrations, pre- and post-processing of data are identical for all three cases. Experimental bases for six different detectors were constructed.

The data used is from an experiment performed for the spectroscopy of neutron-rich nuclei in the mass 80–100 region. An $^{238}$U beam with an energy of 6.2 MeV/u impinged on a 10 µm-thick $^{9}$Be target. Excited nuclei were produced by either fusion-fission or induced fission of the beam, and they were fully identified in the VAMOS spectrometer [36–38]. The γ rays were detected by AGATA configured in its compact mode [5], i.e. moved 88 mm closer to the target. Details of the experiment can be found in ref. [39]. Clusters 12 and 13 at circa 112° to the recoil direction were used for the PSA test as they allowed maxi-

mum Doppler broadening for this experimental setup. The recoil velocity *v*/*c* of about 10% was also sufficiently high for the Doppler broadening of the γ-ray peaks to be sensitive to the PSA. This experiment was performed within 2 months of collecting the $^{60}$Co data used to construct the experimental data bases.

The strongly populated channel $^{98}$Zr [40] was used for the investigations, as its 1223 keV γ ray de-exciting the $2_1^+$ state provides good sensitivity to the position resolution via the angle used for Doppler correction, and hence the PSA. Lower energy γ rays are also emitted in the reaction, but as the impact of the position resolution in terms of Doppler correction is proportional to the γ-ray energy they were not analyzed. Furthermore, a recent lifetime measurement [41] gives an upper limit for the lifetime of the $2_1^+$ of $\tau < 11$ ps. This is in a range that will not give any line shape effects comparable to those from pulse-shape analysis. Estimates of the different components of the peak width for a γ ray at 1.2 MeV have been made using eq. (9). A recoil with a velocity β of around 10%, and a $\Delta\beta = 0.4\%$ [42] produces a Doppler broadening $\Delta E_{\gamma 0}/E_{\gamma 0}$ of 0.11% at 112° (term 2 in eq. (9)). An uncertainty of $\Delta\theta = 1°$ (6°) for the determined angle between the recoil and emitted γ ray will give a 0.16% (0.97%) Doppler broadening in the energy spectra (term 3 in eq. (9)). For our case, $\Delta\theta = 1°$ corresponds to a PSA resolution of about 2.3 mm FWHM. Given that a reasonable estimate for the intrinsic energy resolution of the detectors in the conditions of the experiment is $\Delta E_{\gamma} = 0.2\%$, a perfect position determination would give a $\Delta E_{\gamma 0}/E_{\gamma 0} = \sqrt{0.11^2 + 0.2^2} = 0.23\%$ whereas the use
<figure><img src="image_102.png" /><figcaption>**Fig. 6.** (Color online) Pulse shapes coming from two same shaped detectors of type A and one type B detector for the same position (x = 31 mm, y = 5.5 mm, z = 63 mm) in the detectors. The core signal is shown in more detail in inset (a), the net-charge signal in inset (b), and the transient signals from the nearest neighbours are shown in detail in insets (c)–(e).</figcaption></figure>

<figure><img src="image_103.png" /><figcaption>**Fig. 7.** Approximate width of the 1223 keV γ ray de-exciting the $2_1^+$ state as a function of angular and position resolution. On the upper scale are indicated the approximate linear resolutions for 1° angular resolution, the stated design goal of AGATA, the size corresponding to a segment, and finally the linear resolution corresponding to 9° angular resolution.</figcaption></figure>

of the segment center for Doppler correction would give $\Delta E_{\gamma 0}/E_{\gamma 0} = \sqrt{0.11^2 + 0.2^2 + 0.97^2} = 0.996\%$. Therefore, PSA can improve the energy resolution by at most a factor of 4 as compared to Doppler correction only using the segment centers for γ-ray hit locations in this particular experiment. In fig. 7, an estimate of the FWHM as a function of position resolution is shown for the 1223 keV γ ray given the experimental setup used for this work. The size of a segment is also indicated.

The hit distributions in the *xy*-plane and *z* direction for events with only one net-charge segment are shown in figs. 8 and 9, respectively. In the columns of fig. 8 the *xy*-plane hit distributions for the six rings for detector 13A are shown for PSA performed using the Adaptive Grid Search (AGS) and the ADL basis, PSA performed using the Direct Method, and finally PSA performed using AGS and the *in situ* basis. The distributions are clearly different but none is very homogeneous, which could indicate a better PSA. For the Direct Method, one can see a ring-like cluster near the core in ring 1 and six clusters in ring 2 and ring 3 in the corners of the hexagonal part of the crystal. This is because for small or large *r*, $\varphi$ is divided into only one interval, causing the small clusters. For the *z* distributions shown in fig. 9, the present method tends to assign the *z* coordinate at the center of the segment as compared to AGS, which clusters points closer to the segment boundaries.

To, tentatively, compare the position resolution for the three different cases, two different sets of γ-ray spectra were produced with Doppler corrected γ-ray energies emitted from $^{98}$Zr. The first set, referred to as set I, is made with all tracked γ rays, and the resulting spectra are shown in fig. 10. The strong transitions populated from $^{98}$Zr are marked in fig. 10(a) with the information taken from ref. [40]. Here, the solid line is the result from the simulated ADL bases using AGS, dashed is from combining the direct method with AGS and an ADL bases, dotted is for AGS using *in situ* bases, and dash-dotted when corrected with the segment center (i.e., without PSA). As PSA performance and basis fidelity vary from crys-
<figure><img src="image_104.png" /><figcaption>**Fig. 8.** (Color online) Comparisons of hit distributions in xy-plane between PSA performed with AGS and ADL basis (left), PSA performed with the Direct Method (center), and PSA performed with AGS using the *in situ* basis (right) for the six rings in detector 13A. Events with only one net charge segment were used. The color scale goes from black (0 counts), via blue (10 counts), green (100 counts), red (250 counts), and finally white (500 counts).</figcaption></figure>

tal to crystal the performance was evaluated individually for each crystal, this by demanding that the interaction whose position was used for Doppler correction was in the investigated crystal. An example of such spectra for one out of six studied crystals is shown in fig. 10(b). In this way the six different sets of bases could be compared. A second set of γ-ray spectra produced to highlight the performance of the Direct Method, referred to as set II,

<figure><img src="image_105.png" /><figcaption>**Fig. 9.** (Color online) Comparisons of z hit distributions between AGS using the ADL basis, AGS using the *in situ* basis, and the Direct Method. Events from detector 13A with only one segment hit have been used.</figcaption></figure>

<figure><img src="image_106.png" /><figcaption>**Fig. 10.** (Color online) (a) Doppler corrected γ-ray spectra of $^{98}$Zr for all events. Solid line is the result using the AGS with the ADL bases, dashed is from combining the Direct Method with the AGS using the ADL bases, dotted is for the AGS using the *in situ* bases, and dash-dotted when corrected with the segment center (i.e., without PSA). (b) Same as (a) with the energy zoomed in on the $2_1^+ \rightarrow 0_1^+$ transition of $^{98}$Zr and only when the interaction position used for Doppler correction was in crystal 13A (see text for details).</figcaption></figure>

were created by demanding that the interaction position used for Doppler correction was in a crystal with only one net-charge segment. In these spectra, the statistics is reduced by a factor of ≈ 3.5 for the peak at 1.223 MeV. This reduction comes from the preference of absorbed γ rays of this energy to interact more than once in one crystal.
<figure><img src="image_107.png" /><figcaption>**Fig. 11.** (Color online) (a) Doppler corrected γ-ray spectra of <sup>98</sup>Zr for events where the interaction point used for Doppler correction was in a crystal with only one segment hit. Solid line is the result using the AGS with the ADL bases, dashed is from the Direct Method, dotted is for the AGS using the *in situ* bases, and dash-dotted when corrected with the segment center (i.e. without PSA). (b) Same as (a) with the energy zoomed in on the 2<sup>+</sup><sub>I</sub> → 0<sup>+</sup><sub>I</sub> transition of <sup>98</sup>Zr and only when the interaction position used for Doppler correction was in crystal 13A (see text for details).</figcaption></figure>

The reduction factor is smaller for lower γ-ray energies as they are more likely to be absorbed within one segment. Spectra produced with this extra condition are shown in fig. 11, where the top panel marked with an (a) shows the full energy range whereas the bottom panel shows a zoom on the region of interest. The interest of investigating the Direct Method comes from the fact that before γ-ray tracking about 50% of the events can be expected as one segment hit events, and hence the use of the Direct Method can reduce the CPU demand for PSA considerably. In the present architecture of AGATA, where each crystal is physically connected via optical fibers to a computer for the PSA this gain will not allow a reduction of the same order (i.e., 50%) for the needed computer hardware. For the future, where data from crystals will be transported on a standard TCP/IP computer network before the PSA, this decrease of needed computing hardware can be capitalized on. It should be noted that the choice of PSA method does not affect the statistics after γ-ray tracking, as can be seen in the full-range spectra in figs. 10 and 11.

For all data sets the FWHM has been extracted, giving a total of 48 values. The data is summarized in fig. 12. First comparing the FWHM for set I, the difference between using AGS with the ADL bases or AGS with the ADL bases and the Direct Method is small, reflecting the

<figure><img src="image_108.png" /><figcaption>**Fig. 12.** (Color online) The full width at half maximum from Gaussian fits to the peaks in the data, crystal by crystal. The left panel is for all data (set I), and crystal number indicates the crystal in which the interaction position used to define the angle for Doppler correction was recorded. For the right panel, there is the additional constraint that there was only one segment with a net charge in the crystal with the interaction used for Doppler correction (set II).</figcaption></figure>

small fraction of events where the Doppler correction was made with an interaction position determined with the Direct Method. For all crystals the difference is smaller than the uncertainty in the determination of the FWHM. Looking at the difference using AGS with the ADL bases and the *in situ* bases, the latter is performing worse for three of the crystals, 37 (12B), 39 (13A), and 41 (13C), but still about a factor of two better than when using the segment center as interaction position. Turning the attention to data set II, the pattern is repeated with the exception of crystal 41 (13C) where AGS with *in situ* basis is performing better than the Direct Method. However, considering the larger error bars from the decreased statistics, statistical scattering cannot be excluded as the reason for this.

## 4 Conclusions and outlook

Using experimental data from the AGATA@GANIL campaign, we have demonstrated the possibility to use the Jacobian method to both produce an experimental pulse-shape *in situ* basis and to perform PSA by the so-called Direct Method for events with only one net-charge segment in a crystal. Both give comparable performance for PSA as if a basis calculated with the ADL package had been used. The Direct Method is of particular interest as it allows a considerable reduction in needed computing for events with only one net-charge segment in a crystal. The results for the *in situ* experimental basis require some more comments. There is no improvement in performance, neither for the position resolution nor in the reduction of
computing power needed for the *in situ* basis as compared to the ADL basis. The slightly worse PSA performance of the *in situ* bases suggests that they are less accurate than the ADL bases. There are several possible reasons for this. In the first step of creating an *in situ* basis, the theoretical interaction point distributions are determined. To do this, assumptions about the effective segmentation of the Ge crystals are made. In this work, the segmentation used in the AGATA Geant4 package was used. An alternative would be to use a code such as ADL to better determine the segmentation borders in a hybrid approach to construct the basis for a crystal. We note that the neutron damage correction methods developed within the AGATA community, see Bruyneel et al. [43], depend on the trajectories of the charge carriers as calculated by ADL, showing the need for pulse-shape calculations even in the case of improved PSA performance with an *in situ* basis. However, an *in situ* approach still allows for effects not easily modeled to be included.

An issue not touched upon in this work, because of the effort to construct a basis from a calibration like measurement, is that of time aligning the traces before averaging. This is a critical issue for the pulse-shape analysis where a time resolution of less than the 10 ns sampling time is needed for optimal performance [31]. There is also an open question on the type of events to use to construct an *in situ* basis. In this work events (simulated and experimental) with one net-charge segment were used with an assumption of equality between number of net-charge segments and γ-ray interactions. This is clearly wrong for many γ-ray energies and an improvement in this selection process is well worth exploring. Experimental bases using gates on the Compton back-scattering edge have been produced within the context of this work but the strong reduction in statistics prohibited any conclusion as to whether this is an improvement or not.

The above mentioned issues could be corrected using a coincidence measurement between AGATA and an external fast scintillator detector (time resolution), combined with a more restrictive selection of the used events (favouring one γ-ray interaction). While technically not difficult the increase in needed measuring time is at least a factor of 20, i.e. from about a night to about a week. Remaining less time consuming then the full scanning of individual crystals, the increase in required time, together with the need of additional detectors, removes the “calibration” aspect of the method. The use of the *in situ* method for “characterisation” measurement before experimental campaigns, however, remains an interesting option to explore.

One possible approach for improving the *in situ* basis is in the choice of the grid used in the final basis. In this work, the grid for each detector was dictated by the condition of similar voxel volumes in the grid, available statistics, and the natural polar coordinate system of the crystal. However, other choices are possible [44] and several possibilities should be systematically explored and choosing a grid more closely connected to the intrinsic sensitivity of the detector is interesting.

Given the encouraging results presented in this paper, continued work exploring the *in situ* method with its inherent inclusion of electronic responses and experimental conditions is needed.

The authors would like to thank the AGATA Collaboration and the GANIL technical staff. We are also grateful to Dino Bazzacco and Francesco Recchia for fruitful discussion. Gilbert Duchêne is thanked for providing the in-beam data set.

## References

1. S. Akkoyun *et al.*, Nucl. Instrum. Methods Phys. Res. A **668**, 26 (2012).

2. I. Lee *et al.*, Nucl. Phys. A **746**, 255 (2004).

3. A. Gadea *et al.*, Nucl. Instrum. Methods Phys. Res. A **654**, 88 (2011).

4. N. Pietralla *et al.*, EPJ Web of Conferences **66**, 02083 (2014).

5. E. Clément *et al.*, Nucl. Instrum. Methods Phys. Res. A **855**, 1 (2017).

6. A. Gadea *et al.*, Eur. Phys. J. A **20**, 193 (2003).

7. J. Simpson *et al.*, Acta Phys. Hung. **11**, 159 (2000).

8. H. Wollersheim *et al.*, Nucl. Instrum. Methods Phys. Res. A **537**, 637 (2005).

9. R. Venturelli, D. Bazzacco, LNL Annual Report (2004) p. 220.

10. B. Bruyneel, B. Birkenbach, P. Reiter, Eur. Phys. J. A **52**, 70 (2016).

11. B. Bruyneel, P. Reiter, G. Pascovici, Nucl. Instrum. Methods Phys. Res. A **569**, 764 (2006).

12. B. Bruyneel, B. Birkenbach, P. Reiter, Nucl. Instrum. Methods Phys. Res. A **641**, 92 (2011).

13. B. Birkenbach *et al.*, Nucl. Instrum. Methods Phys. Res. A **640**, 176 (2011).

14. B. Bruyneel *et al.*, Nucl. Instrum. Methods Phys. Res. A **599**, 196 (2009).

15. A. Wiens *et al.*, Eur. Phys. J. A **49**, 47 (2013).

16. F. Recchia *et al.*, Nucl. Instrum. Methods Phys. Res. A **604**, 555 (2009).

17. P.-A. Söderström *et al.*, Nucl. Instrum. Methods Phys. Res. A **638**, 96 (2011).

18. T. Steinbach *et al.*, Eur. Phys. J. A **53**, 23 (2017).

19. G. Schmid *et al.*, Nucl. Instrum. Methods Phys. Res. A **430**, 69 (1999).

20. F. Recchia *et al.*, Nucl. Instrum. Methods Phys. Res. A **604**, 60 (2009).

21. C. Michelagnoli *et al.*, in preparation.

22. A. Boston *et al.*, Nucl. Instrum. Methods Phys. Res. B **261**, 1098 (2007).

23. L. Nelson *et al.*, Nucl. Instrum. Methods Phys. Res. A **573**, 153 (2007).

24. T. Ha *et al.*, Nucl. Instrum. Methods Phys. Res. A **697**, 123 (2013).

25. S. Martín, B. Quintana, D. Barrientos, Nucl. Instrum. Methods Phys. Res. A **823**, 32 (2016).

26. F. Crespi *et al.*, Nucl. Instrum. Methods Phys. Res. A **593**, 440 (2008).

27. C. Domingo-Pardo *et al.*, Nucl. Instrum. Methods Phys. Res. A **643**, 79 (2011).
28. N. Goel et al., Nucl. Instrum. Methods Phys. Res. A 652, 591 (2011).

29. M. Ginsz, Characterization of high-purity, multi-segmented germanium detectors, PhD Thesis, Université de Strasbourg, Ecole doctorale de physique et chimie physique, Institut Pluridisciplinaire Hubert Curien, UMR 7178 CNRS/IN2P3 (2015).

30. P. Désesquelles et al., Phys. Rev. C 62, 024614 (2000).

31. P. Désesquelles, Nucl. Instrum. Methods Phys. Res. A 654, 324 (2011).

32. P. Désesquelles et al., Nucl. Instrum. Methods Phys. Res. A 729, 198 (2013).

33. Second AGATA-GRETINA tracking arrays collaboration meeting, private communication (2018).

34. E. Farnea et al., Nucl. Instrum. Methods Phys. Res. A 621, 331 (2010).

35. N. Lalović et al., Nucl. Instrum. Methods Phys. Res. A 806, 258 (2016).

36. S. Pullanhiotan, M. Rejmund, A. Navin, W. Mittig, S. Bhattacharyya, Nucl. Instrum. Methods Phys. Res. A 593, 343 (2008).

37. M. Vandebrouck et al., Nucl. Instrum. Methods Phys. Res. A 812, 112 (2016).

38. M. Rejmund et al., Nucl. Instrum. Methods Phys. Res. A 646, 184 (2011).

39. J. Dudouet et al., Phys. Rev. Lett. 118, 162501 (2017).

40. B. Singh, Z. Hu, Nucl. Data Sheets 98, 335 (2003).

41. L. Bettermann et al., Phys. Rev. C 82, 044310 (2010).

42. Y.H. Kim et al., Eur. Phys. J. A 53, 162 (2017).

43. B. Bruyneel et al., Eur. Phys. J. A 49, 61 (2013).

44. I. Doxas, C. Nieter, D. Radford, K. Lagergren, J.R. Cary, Nucl. Instrum. Methods Phys. Res. A 580, 1331 (2007).
7.9 B(E2) anomalies in the yrast band of $^{170}$Os
B(E2) anomalies in the yrast band of ¹⁷⁰Os

A. Goasduff,¹,²,* J. Ljungvall,¹ T. R. Rodríguez,³ F. L. Bello Garrote,⁴ A. Etile,¹ G. Georgiev,¹ F. Giacoppo,⁵,⁶ L. Grente,⁷
M. Klintefjord,⁴ A. Kuşoğlu,¹,⁸,⁹ I. Matea,¹⁰ S. Roccia,¹ M.-D. Salsac,⁷ and C. Sotty¹,¹¹

¹CSNSM, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France

²Dipartimento di Fisica and INFN, Sezione di Padova, I-35131 Padova, Italy

³Departamento de Física Teórica and Centro de Investigación Avanzada en Física Fundamental-CIAFF, Universidad Autónoma de Madrid,
E-28049 Madrid, Spain

⁴Department of Physics, University of Oslo, N-0316 Oslo, Norway

⁵Helmholtz Institute Mainz, 55099 Mainz, Germany

⁶GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany

⁷Irfu, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France

⁸Department of Physics, Faculty of Science, Istanbul University, Vezneciler/Fatih, 34134 Istanbul, Turkey

⁹ELI-NP, Horia Hulubei National Institute of Physics and Nuclear Engineering, 077125 Magurele, Romania

¹⁰Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, France

¹¹Horia Hulubei National Institute of Physics and Nuclear Engineering-IFIN HH, 077125 Bucharest, Romania

<figure><img src="image_109.png" /></figure>

(Received 11 March 2019; revised manuscript received 30 July 2019; published 5 September 2019)

**Background:** The neutron-deficient osmium isotopic chain provides a great laboratory for the study of shape evolution, with the transition from the soft triaxial rotor in ¹⁶⁸Os to the well-deformed prolate rotor in ¹⁸⁰Os, while shape coexistence appears around *N* = 96 in ¹⁷²Os. Therefore, the study of the Os isotopic chain should provide a better understanding of shape changes in nuclei and a detailed scrutiny of nuclear structure calculations. In this paper, the lifetimes of the low-lying yrast states of ¹⁷⁰Os have been measured for the first time to investigate the shape evolution with neutron number.

**Purpose:** Lifetimes of excited states in the ground-state band of ¹⁷⁰Os are measured to investigate the shape evolution with neutron number in osmium isotopes and compare with state-of-the-art calculations.

**Methods:** The states of interest were populated via the fusion-evaporation reaction ¹⁴²Nd(³²S, 4n) at a bombarding energy of 170 MeV at the ALTO facility from IPN (Orsay, France). Lifetimes of the 2⁺₁ and 4⁺₁ states in ¹⁷⁰Os were measured with the recoil-distance Doppler-shift method using the Orsay universal plunger system.

**Results:** Lifetimes of the two first excited states in ¹⁷⁰Os were measured for the first time. A very small B(E2; 4⁺₁ → 2⁺₁)/B(E2; 2⁺₁ → 0⁺₁) = 0.38(11) was found, which is very uncharacteristic for collective nuclei. These results were compared to state-of-the-art beyond-mean-field calculations.

**Conclusions:** Although theoretical results give satisfactory results for the energy of the first few excited states in ¹⁷⁰Os and the B(E2; 2⁺₁ → 0⁺₁) they fail to reproduce the very small B(E2; 4⁺₁ → 2⁺₁), which remains a puzzle.

DOI: 10.1103/PhysRevC.100.034302

# I. INTRODUCTION

The mechanisms of shape transitions remain a challenging topic in nuclear structure calculations, but are becoming experimentally more accessible. While the transition between shapes is generally gradual, the systems of interest are those that exhibit abrupt changes in observables with the addition or subtraction of a few nucleons. The osmium isotope chain provides such a test case, as it goes from a soft triaxial rotor in ¹⁶⁸Os to a mid-shell well-deformed prolate rotor in ¹⁸⁰Os, with the appearance of shape coexistence close to *N* = 96 in ¹⁷²Os. The osmium isotopic chain is the longest continuous chain of even-even isotopes with available spectroscopic data on the

low-lying yrast states covering a mass range from *A* = 162 to *A* = 198. The evolution of the energies of the yrast 2⁺ and 4⁺ for those isotopes is reported in the upper panel of Fig. 1 together with the structural benchmark *E*₄⁺/*E*₂⁺ (*R*₄/₂) in the lower panel. A transition from vibratorlike structures for the most neutron-rich nuclei to deformed prolate rotors close to the mid-neutron shell passing by γ-unstable or triaxial shapes is suggested by the data [1–4]. Moving close to the *N* = 82 shell closure at *A* = 158, the collectivity decreases and neutron-deficient osmium isotopes pass through shape coexistence at *A* = 172 [5] to a single-particle-like excitation in ¹⁶²Os [6].

Osmium isotopes with *N* ≈ 96 lie at the edge of the region of neutron-deficient nuclei close to the *Z* = 82 shell closure where a large number of nuclei with shape coexistence [7] are found, making it fertile ground for nuclear structure research.

<footnote>*alain.goasduff@pd.infn.it</footnote>
<figure><img src="image_110.png" /><figcaption>FIG. 1. The excitation energy systematic of the 2+ and 4+ yrast states in the osmium isotopes in the upper panel. The structural benchmark $R_{4/2} = E_{4+}/E_{2+}$ is presented in the lower panel together with the empirical limits for rotation and vibrational nuclei. The theoretical values for <sup>168,170,172</sup>Os are a part of this work.</figcaption></figure>

A good example is <sup>186</sup>Pb with three 0<sup>+</sup> states close in energy [8]. Shape-coexistence phenomena have been evidenced in several nuclei in the lead region and recent lifetime measurements in Po [9], Pb [10–12], Hg [13–15], and Pt [16]. These discoveries have allowed a deeper understanding of the shape-coexistence origins. The model-independent measurements of the B(E2) values in the yrast bands have given firm experimental evidence of several low-energy configurations highly mixed at low spins.

The question of shape coexistence in the neutron-deficient osmium isotopes has been addressed several times over the last few decades. The yrast sequence of <sup>172</sup>Os shows a sharp backbend near spin 14ħ originated from the i<sub>13/2</sub> neutron alignment [17]. At a spin of 6ħ, an up-bend can be observed. The shape coexistence in <sup>170,172</sup>Os was discussed based on a three-band mixing model [18] reproducing level energies and moments of inertia. The work suggested that shape coexistence is as well present in <sup>170</sup>Os although the deformed structure responsible for the anomaly seen in the moments of inertia in <sup>172</sup>Os is shifted upwards in <sup>170</sup>Os, making its influence on the kinematic moments of inertia significantly smaller. To explain this variation in the moments of inertia around <sup>172</sup>Os several approaches were employed based on either particle alignment or phenomenological shape coexistence [17]. Although no firm conclusions could be drawn, shape coexistence is presented as a plausible explanation. The question of shape coexistence in <sup>172</sup>Os [19] was also addressed by means of lifetime measurements using the recoil-distance Doppler-shift (RDDS) method giving access to the transition quadrupole moment Q<sub>t</sub>. A strong variation in the Q<sub>t</sub> with increasing spin in the ground-state band was observed. This behavior could be explained by the model of three bands with strong mixing. Studying the spectroscopy of <sup>168</sup>Os [20]

and using a similar theoretical approach of the three-band mixing model, a conclusion similar to that for <sup>170</sup>Os is reached concerning the presence of shape coexistence as the shaping force of the low-spin spectroscopy.

More recent studies concerning neutron-deficient Os isotopes such as <sup>162</sup>Os [21], including a lifetime measurement of the 17/2<sup>+</sup> state in <sup>167</sup>Os [22] and of yrast and non-yrast states in <sup>168</sup>Os [23], give evidence for a shape transition from prolate deformation via γ-soft nuclei to spherical shapes close to the *N* = 82 shell gap. It is worth pointing out that for <sup>168</sup>Os Grahn *et al.* [23] measured a reduced transition probability for the yrast 4<sup>+</sup> resulting in *B*<sub>4/2</sub> = *B(E*2; 4<sup>+</sup> → 2<sup>+</sup>)/(*B(E*2; 2<sup>+</sup> → 0<sup>+</sup>)) = 0.34(18). A *B*<sub>4/2</sub> < 1 is very rare throughout the nuclear chart, with only a handful of examples away from closed shell nuclei, e.g., <sup>48,50</sup>Cr [24], <sup>72,74</sup>Zn [25], <sup>114</sup>Te [26], <sup>114</sup>Xe [27], <sup>166</sup>W [28], <sup>168</sup>Os [23], and <sup>172</sup>Pt [29]. These observations have not been reproduced so far by any type of state-of-the-art nuclear structure calculations, neither large-scale shell models nor beyond-mean-field models.

Beyond-mean-field calculations using the Gogny D1S force, allowing for triaxial shapes, have been used to investigate the shape coexistence phenomenon. For lighter nuclei such as Kr [30] and Se [31], it has been shown that triaxial shapes have to be included in the A ~ 70 region for a correct reproduction of the observable. The importance of the triaxial degree of freedom has also been demonstrated in neutron-rich osmium [1].

The work presented here was initiated to elucidate the question of shape coexistence and shape evolution in neutron-deficient osmium isotopes. In this paper the result of an experiment where the lifetimes of yrast states in <sup>170</sup>Os have been measured via the RDDS method are presented. The results are compared to the state-of-the-art beyond-mean-field calculations.

## II. EXPERIMENT AND RESULTS

The experiment was performed at the ALTO facility (IPN Orsay, France) using the Tandem accelerator. Excited states in <sup>170</sup>Os were populated in the reaction <sup>142</sup>Nd(<sup>32</sup>S, 4n)<sup>170</sup>Os at a beam energy of 170 MeV. The isotopically enriched <sup>142</sup>Nd target had a thickness of 1 mg/cm<sup>2</sup>. The Nd was evaporated onto a 2 mg/cm<sup>2</sup> thick Ta fronting facing the beam. The energy loss of the beam inside the Ta backing was taken into account in the determination of the bombarding energy. A 5 mg/cm<sup>2</sup> Au thick foil was used as a stopper foil for the fusion-evaporation fragments. Target and stopper were mounted on the Orsay universal plunger system (OUPS) plunger [32]. The γ rays were detected by the ORGAM germanium detector array composed of 10 Compton-suppressed high-purity germanium (HPGe) detectors distributed over two rings at backward angles (133.5° and 157.6°) and two additional detectors at forward angle (43°). The recoil velocity of the <sup>170</sup>Os nuclei was deduced from the Doppler shift of γ rays emitted in flight to be $\beta = v/c = 1.62 \pm 0.02\%$.

Data were collected for eight target-stopper separations between 18 and 740 µm. The normalization of the data for the different distances was obtained using the 278-keV line of <sup>197</sup>Au, resulting from the Coulomb excitation of the
<figure><img src="image_111.png" /><figcaption>FIG. 2. Left: Background subtracted γ-ray spectra obtained by gating on the in-flight transition of the $4_1^+ \rightarrow 2_1^+$ for the detectors at 157.6°. The γ-ray spectra show the stopped and in-flight components of the $2_1^+ \rightarrow 0_1^+$. Only the distances in the sensitive range are presented. The stopped component is indicated by an arrow in the uppermost panel, and the in-flight component with an arrow in the lowest panel. The large peak at 279 keV is the Coulomb excitation of the gold stopper. Spectra are background subtracted. The fit used to extract the integral of the two components is displayed for each distance with the red dashed line. The purple curves correspond to the variations performed by the MINOS package to find the two-sided error on τ. Right: Normalized number of counts for the distances in the sensitive range used to extract the lifetime of the $2_1^+$ state.</figcaption></figure>

stopper foil. The normalization is thus directly proportional to the integrated beam current on the target. The γ-γ coincidences were reconstructed and used to avoid the side-feeding effect on the lifetime determinations. Lifetimes of the two first excited states were obtained using γ-γ coincidence and the differential decay-curve method (DDCM) [33,34] gating on the in-flight component of the feeding transition. The γ-γ coincidences were sorted ringwise and the background subtracted projection was then summed and used to extract the lifetimes of interest. The background subtracted spectra obtained by gating on the in-flight component of the $4_1^+$ and $6_1^+$ are presented in Figs. 2 and 3 for the detectors at 157.6° and in Figs. 4 and 5 for the ones at 133.5°, respectively. Because the spectra were contaminated with peaks from other nuclei and there was not sufficient statistics to work with triple coincidences, two independent methods were used to extract the lifetimes of interest: the traditional method, in which the intensities of the peaks were extracted from the in-flight gated spectrum using analytic functions, and a Monte Carlo-based approach. For the latter, GEANT4 Monte Carlo simulations taking into account all the relevant aspects of the experimental setup such as the position and resolution of individual detectors, target and degrader thickness, reaction kinematics, etc., were used to determine the line shapes of

<figure><img src="image_112.png" /><figcaption>FIG. 3. Same as Fig. 2 for the $4_1^+ \rightarrow 2_1^+$ transition at 157.6° obtained by gating on the $6_1^+ \rightarrow 4_1^+$ in-flight transition.</figcaption></figure>

the peaks. These line shapes were later used to extract the intensities of the stopped ($I_{us}$) and in-flight ($I_s$) intensities in the spectra as a function of the lifetime ($\tau$) via the relation

$$I_{us} = \frac{dI_s}{dt}\tau. \qquad (1)$$

$I_{us}$ (red square) and $I_s$ (black triangle), after renormalization to the Coulomb excitation of the Au stopper, are given in the right-hand panels of Figs. 2 and 3 for the $2_1^+$ and $4_1^+$ states, respectively, and for the detectors placed at 157.6°. The same analysis was performed independently for the detectors at

<figure><img src="image_113.png" /><figcaption>FIG. 4. Same as Fig. 2 for the $2_1^+ \rightarrow 0_1^+$ transition gated on the in-flight transition of the $4_1^+ \rightarrow 2_1^+$ for the detectors at 133.5°.</figcaption></figure>
<figure><img src="image_114.png" /><figcaption>FIG. 5. Same as Fig. 3 for the $4_1^+ \rightarrow 2_1^+$ transition at 133.5° obtained by gating on the $6_1^+ \rightarrow 4_1^+$ in-flight transition.</figcaption></figure>

133.5° and the results are presented in Figs. 4 and 5. Lifetimes were extracted using background subtracted spectra gated on the in-flight component of the feeding transition. Using such a gated approach allows one to get rid of the problem with long lived unseen feeding. Moreover, the second approach presents the advantage of taking into account the non-Gaussian shape of the peaks due to the angular aperture of the detectors, the velocity distribution, and slowing down of the recoiling nuclei in the target or stopper. For these reasons the more robust fit given by the second approach gives a more reliable determination of the lifetimes. The lines shapes were fitted to the experimental spectra using the MINUIT2 package [35] and the asymmetric errors were extracted using the MINOS function included in MINUIT2, leaving as free parameters only the number of counts in the two components. MINOS extracts the error on either side by varying the lifetime such that $\Delta\chi^2 = 1$ while minimizing the $\chi^2$ on all other free parameters. In Figs. 2 and 3 the $\gamma$-ray spectra obtained by projecting the $\gamma-\gamma$ matrices on the in-flight component of the feeding transition ($4_1^+ \rightarrow 2_1^+$ and $6_1^+ \rightarrow 4_1^+$, respectively) are presented (solid black line) for the distance in the sensitive range for the lifetime measurement. The corresponding fits are shown (dashed red line) for $\gamma$-ray spectra with detectors at the most backward angle, representing about half of the total statistic. Purple bands corresponding to the variations done by MINOS to find the two-sided errors are also shown. It should be noted that the two methods yielded compatible results using the same background subtracted spectra. While the results using the second methods are reported in Table I, the ones employing the first methods correspond to $80_{-13}^{+11}$ ps for the $2_1^+$ and $20_{-5}^{+8}$ ps for the $4_1^+$.

Reduced electromagnetic transition probabilities were obtained from the measured lifetime ($\tau$) using the formula

$$ \tau = 8.13 \times 10^{13} E_{\gamma}^{-5} [B(E2) \downarrow]^{-1} (1 + \alpha)^{-1}, \quad (2) $$

<table><caption>TABLE I. Spin and parities of the yrast states in $^{170}$Os together with their excitation energies, lifetimes, and reduced electromagnetic transition probabilities (experimental and theoretical). The reported theoretical values are the ones obtained in this work using the symmetry-conserving configuration mixing method.</caption><thead><tr><th rowspan="2">J<sup>π</sup></th><th rowspan="2">E (keV)</th><th rowspan="2">τ (ps)</th><th rowspan="2">I<sub>i</sub><sup>π</sup> → I<sub>f</sub><sup>π</sup></th><th colspan="2">B(E2) ↓ (e<sup>2</sup>b<sup>2</sup>)</th></tr><tr><th>Expt.</th><th>Theor.</th></tr></thead><tbody><tr><td>2<sub>1</sub><sup>+</sup></td><td>287</td><td>70<sup>+6</sup><sub>-6</sub></td><td>2<sub>1</sub><sup>+</sup> → 0<sub>1</sub><sup>+</sup></td><td>0.54<sup>+0.05</sup><sub>-0.05</sub></td><td>0.53</td></tr><tr><td>4<sub>1</sub><sup>+</sup></td><td>750</td><td>18<sup>+6</sup><sub>-4</sub></td><td>4<sub>1</sub><sup>+</sup> → 2<sub>1</sub><sup>+</sup></td><td>0.21<sup>+0.07</sup><sub>-0.04</sub></td><td>0.81</td></tr></tbody></table>

where $E_γ$ is in units of keV, $B(E2) \downarrow$ in $e^2b^2$, $\tau$ in picoseconds, and $\alpha$ the total internal conversion coefficient evaluated using Ref. [36]. The results are summarized in Table I.

As this is a very unusual result the validity of the measured lifetime of the $4_1^+$ state can be questioned. The data were analyzed in an independent manner by several of the authors using more than one way of estimating the peak intensities. Results scatter slightly but within errors and the anomaly of a $B_{4/2} < 1$ remains valid.

### III. DISCUSSION

The measured $B(E2; 2_1^+ \rightarrow 0_1^+)$ of $0.54(0.05) e^2b^2$ (97(8) W.u.) is in agreement with extrapolation from less neutron-deficient osmium isotopes. It is also in good agreement with earlier theoretical estimates [37]. The variable-moment-of-inertia (VMI) model [38] with the fitted parameters [18] gives an estimate of the $B(E2; 2_1^+ \rightarrow 0_1^+)$ of $^{170}$Os, which is ~40% lower than the experimental value. A similar underestimate is obtained for $^{172}$Os; however, the VMI model reproduces correctly the evolution of the $B(E2; 2_1^+ \rightarrow 0_1^+)$ going from $^{172}$Os to $^{170}$Os. Looking at the $2_1^+$ state the $^{170}$Os behaves as a transitional nucleus with the normal decrease in collectivity moving away from the neutron mid-shell.

The $B(E2; 4_1^+ \rightarrow 2_1^+)$ of $0.21(0.05) e^2b^2$ is, in contrast to the “normal” $B(E2; 2_1^+ \rightarrow 0_1^+)$, surprisingly small, resulting in a $B_{4/2}$ ratio of $0.38(11)$. Similar results were obtained in $^{166}$W [28], $^{168}$Os [23], and $^{172}$Pt [29]. Based on those measurements, Cederwall *et al.* [29] proposed a transition at $N = 94$ from a collective regime into a senioritylike scheme as a possible explanation for the $B_{4/2} < 1$, despite the presence of a large number of valence nucleons. The position of such a phase transition at $N = 94$ is supported by the present data. However, as $^{170}$Os is rather collective the suggested explanation, i.e., a transition into a senioritylike scheme, is very surprising. Band-mixing calculations for $^{170}$Os [18] cannot explain this phenomenon, as the ground-state band should be pure at such low spins. Moreover, it is worth noticing that the $2_1^+$ states of these four nuclei follow the expected correlations between the $E(4_1^+)/E(2_1^+)$ or the product of the number of valence protons and neutrons and the $B(E2; 2_1^+ \rightarrow 0_1^+)$ [39].

To try to understand the small $B_{4/2}$ ratio, symmetry-conserving configuration mixing (SCCM) calculations were performed using the generator coordinate method framework with Hartree-Fock-Bogoliubov states found with variation after particle number projection (PN-VAP) [40,41]. In general
<figure><img src="image_115.png" /><figcaption>FIG. 6. The ratio between $B(E2; 4_1^+ \rightarrow 2_1^+)$ and the $B(E2; 2_1^+ \rightarrow 0_1^+)$ ($B_{4/2}$) for the neutron-deficient osmium isotopes. The tabulated values for $^{172,174}$Os values were taken from National Nuclear Data Center and from Refs. [43,44] for $^{176}$Os. The value reported for $^{168}$Os is the one from the work of Grahn et al. [23]. The experimental value for $^{170}$Os as well as the theoretical values for $^{168,170,172}$Os are part of this work.</figcaption></figure>

the yrast states are given as close to prolate with $\beta \approx 20^\circ$ and $\gamma \le 20^\circ$. For $^{172}$Os, the yrast band is, however, triaxial with $\gamma \approx 30^\circ$. The energies for the lowest yrast and non-yrast states for $^{168,170,172}$Os are presented in Fig. 1. The agreement between experimental and theoretical excitation energies is satisfactory (see Ref. [42] and references therein). In Fig. 6 experimentally known $B_{4/2}$ are shown together with the results of the calculations. The experimental $B_{4/2}$ are presented in Fig. 6 for $^{169-176}$Os and compared for $^{168-172}$Os to the present theoretical calculations. The $B_{4/2}$ for $^{172}$Os is well reproduced by the model; however, the ones of $^{168,170}$Os are overestimated by a factor of $\sim 4$. As shown in Table I, the $B(E2; 2_1^+ \rightarrow 0_1^+)$ of $^{170}$Os is very well reproduced, as well as those of $^{168,172}$Os. Thus the observed discrepancy on the $B_{4/2}$ for $^{168,170}$Os is solely originated by the $B(E2; 4_1^+ \rightarrow 2_1^+)$ . Indeed a similar factor of $\sim 4$ is found between the experimental and theoretical $B(E2; 4_1^+ \rightarrow 2_1^+)$ . While the experimental $B_{4/2}$ ratio is small, the resulting theoretical ratios are $\sim 1.5$, close to that of a deformed rotor. The experimental $B_{4/2}$ ratio for $^{172}$Os is 1.5(2), compatible with the present theoretical approach. The present results show that the structural change is more sudden than previously observed. Indeed the large drop in $B_{4/2}$ is already evidenced in $^{170}$Os.

A possible explanation for the observed $B_{4/2}$ ratio is that the yrast $4^+$ state does not belong to the same band as the $2_1^+$ state. The origin for this mismatch could be the presence of a shape-coexistent rotational band whose $4^+$ member would be below the $4^+$ level of the ground-state band. The SCCM method calculations performed in this work show no evidence for such a sideband. In Fig. 7 the potential energy surface (PES) obtained using the PN-VAP method, and the collective wave functions for the $0_1^+$, $2_1^+$, and $4_1^+$ states are plotted in the ($\beta_2, \gamma$) plane. The PES exhibits only one minimum at a slightly triaxial deformation ($\beta_2, \gamma) \sim (0.2, 15^\circ)$ and the collective wave functions have all the same structure, revealing that they belong to the same rotational band. The second $4^+$ in the calculations (not shown) corresponds to a state in a $\gamma$

<figure><img src="image_116.png" /><figcaption>FIG. 7. The PN-VAP potential energy surface for $^{170}$Os (top left) and collective wave functions for the ground state (top right) as well as the yrast $2^+$ (bottom left) and $4^+$ (bottom right) states. All calculated wave functions display a very similar structure.</figcaption></figure>

band. Another possibility is that the experimental yrast $4^+$ has a single-particle nature that could be produced, e.g., by the alignment of a pair at low spin as it was found in $^{44}$S [42]. In order to search for such a state, calculations were expanded by performing PN-VAP calculations including cranking and by extending the range of triaxial quadrupole deformations to $-60^\circ < \gamma < 120^\circ$ as done in Ref. [42]. The full configuration mixing was not performed due to the large computational burden. Nevertheless, a $4^+$ state with the sought-after characteristics to reproduce the low $B(E2; 4_1^+ \rightarrow 2_1^+)$ value would manifest itself as a minimum for the projected $J \ge 4$ PES's not present in the $J=0, 2$ PES's computed at non-zero intrinsic rotation (cranking) frequency, $\omega \ne 0$. Such a feature has not been found in the calculations and the origin of the observed transition probability remains unexplained within the employed formalism and/or variational space.

## IV. CONCLUSION

The lifetimes of the first excited $2^+$ and $4^+$ states in $^{170}$Os were measured for the first time using the RDDS method at the ALTO facility with the ORGAM $\gamma$-ray array coupled to the OUPS plunger. A surprisingly small $B(E2; 4_1^+ \rightarrow 2_1^+)$ value was found. To understand this value, the results were compared to the state-of-the-art beyond-mean-field calculations. The model accurately reproduced the energies of the lowest-lying yrast states and the $2^+$ reduced transition probabilities in $^{168,170,172}$Os. Although the model described correctly the properties of the yrast $4^+$ state of $^{172}$Os, the sudden structural change observed when removing two neutrons is not present in the calculation. The question of the origin of the small $B_{4/2}$ in $^{168,170}$Os remains open and merits experimental efforts
in order to validate these surprising results and expand the
known lifetimes to higher spin yrast and yrare states.

ACKNOWLEDGMENTS

The authors would like to thank the ALTO technical team
for the good quality beam that was provided during the
experiment. Dr. K. O. Zell and Dr. A. Blazhev from IKP
Köln are thanked for the excellent quality Nd targets. We
also thank the UK/France (STFC/IN2P3) Loan Pool and
GAMMAPOOL European Gamma-Ray Spectroscopy Pool
for the loan of the detectors for ORGAM. This work was

supported in part by the 2214-TUBITAK (Scientific and
Technological Research Council of Turkey) Programme, the
Scientific Research Projects Coordination Unit of Istanbul
University under Project No. 46811, and the European Com-
munity FP7 Capacities-Integrated Infrastructure Initiative-
Contract ENSAR No. 262010. This work has been partly
funded (A.G.) by the P2IO LabEx (ANR-10-LABX-0038)
in the framework Investissements d'Avenir (ANR-11-IDEX-
0003-01) managed by the French Agence Nationale de la
Recherche (ANR). T.R.R. acknowledges support from Span-
ish Grants No. FIS-2014-53434-P MINECO and Programa
Ramon y Cajal 2012 No. 11420, and computing time at
GSI-Darmstadt.

[1] P. R. John, V. Modamio, J. J. Valiente-Dobón, D. Mengoni, S. Lunardi, T. R. Rodríguez, D. Bazzacco, A. Gadea, C. Wheldon, T. Alexander, G. de Angelis, N. Ashwood, M. Barr, G. Benzoni, B. Birkenbach, P. G. Bizzeti, A. M. Bizzetti-Sona, S. B. M. Bowry, A. Bracco, F. Browne, M. Bunce, F. Camera, B. Cederwall, L. Corradi, F. C. L. Crespi, P. Désesquelles, J. Eberth, E. Farnea, E. Fioretto, A. Görgen, A. Gottardo, J. Grebosz, L. Grente, H. Hess, A. Jungclaus, T. Kokalova, A. Korichi, W. Korten, A. Kuşoğlu, S. Lenzi, S. Leoni, J. Ljungvall, G. Maron, W. Meczynski, B. Melon, R. Menegazzo, C. Michelagnoli, T. Mijatović, B. Million, P. Molini, G. Montagnoli, D. Montanari, D. R. Napoli, P. Nolan, C. Oziol, Z. Podolyák, G. Pollarolo, A. Pullia, B. Quintana, F. Recchia, P. Reiter, O. J. Roberts, D. Rosso, E. Sahin, M.-D. Salsac, F. Scarlassara, M. Sferrazza, J. Simpson, P.-A. Söderström, A. M. Stefanini, O. Stezowski, S. Szilner, C. Theisen, C. A. Ur, and J. Walshe, Phys. Rev. C 90, 021301 (2014).

[2] Z. Podolyák, S. J. Steer, S. Pietri, F. R. Xu, H. L. Liu, P. H. Regan, D. Rudolph, A. B. Garnsworthy, R. Hoischen, M. Górska, J. Gerl, H. J. Wollersheim, T. Kurtukian-Nieto, G. Benzoni, T. Shizuma, F. Becker, P. Bednarczyk, L. Caceres, P. Doornenbal, H. Geissel, J. Grebęosz, A. Kelic, I. Kojouharov, N. Kurz, F. Montes, W. Prokopowicz, T. Saito, H. Schaffner, S. Tashenov, A. Heinz, M. Pfützner, A. Jungclaus, D. L. Balabanski, C. Brandau, A. M. Bruce, W. N. Catford, I. J. Cullen, Z. Dombrádi, E. Estevez, W. Gelletly, G. Ilie, J. Jolie, G. A. Jones, M. Kmiecik, F. G. Kondev, R. Krücken, S. Lalkovski, Z. Liu, A. Maj, S. Myalski, S. Schwertel, P. M. Walker, E. Werner-Malento, and O. Wieland, Phys. Rev. C 79, 031305 (2009).

[3] C. Wheldon, G. D. Dracoulis, R. T. Newman, P. M. Walker, C. J. Pearson, A. P. Byrne, A. M. Baxter, S. Bayer, T. Kibédi, T. R. McGoram, S. M. Mullins, and F. R. Xu, Nucl. Phys. A 699, 415 (2002).

[4] P. D. Bond, R. F. Casten, D. D. Warner, and D. Horn, Phys. Lett. B 130, 167 (1983).

[5] P. M. Davidson, G. D. Dracoulis, T. Kibédi, A. P. Byrne, S. S. Anderssen, A. M. Baxter, B. Fabricius, G. J. Lane, and A. E. Stuchbery, Nucl. Phys. A 568, 90 (1994).

[6] D. T. Joss, K. Lagergren, D. E. Appelbe, C. J. Barton, J. Simpson, B. Cederwall, B. Hadinia, R. Wyss, S. Eeckhaudt, T. Grahn, P. T. Greenlees, P. M. Jones, R. Julin, S. Juutinen, H. Kettunen, M. Leino, A.-P. Leppänen, P. Nieminen, J. Pakarinen,

P. Rahkila, C. Scholey, J. Uusitalo, R. D. Page, E. S. Paul, and D. R. Wiseman, Phys. Rev. C 70, 017302 (2004).

[7] K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011).

[8] A. N. Andreyev, M. Huyse, P. V. Duppen, L. Weissman, D. Ackermann, J. Gerl, F. P. Hessberger, S. Hofmann, A. Kleinbohl, G. Munzenberg, S. Reshitko, C. Schlegel, H. Schaffner, P. Cagarda, M. Matos, S. Saro, A. Keenan, C. Moore, C. D. O'Leary, R. D. Page, M. Taylor, H. Kettunen, M. Leino, A. Lavrentiev, R. Wyss, and K. Heyde, Nature (London) 405, 430 (2000).

[9] T. Grahn, A. Dewald, P. T. Greenlees, U. Jakobsson, J. Jolie, P. Jones, R. Julin, S. Juutinen, S. Ketelhut, T. Kröll, R. Krücken, M. Leino, P. Maierbeck, B. Melon, M. Nyman, R. D. Page, P. Peura, T. Pissulla, P. Rahkila, J. Sarén, C. Scholey, J. Sorri, J. Uusitalo, M. Bender, and P. H. Heenen, Phys. Rev. C 80, 014323 (2009).

[10] A. Dewald, R. Peusquens, B. Saha, P. von Brentano, A. Fitzler, T. Klug, I. Wiedenhöver, M. P. Carpenter, A. Heinz, R. V. F. Janssens, F. G. Kondev, C. J. Lister, D. Seweryniak, K. A. Saleem, R. Krücken, J. R. Cooper, C. J. Barton, K. Zyromski, C. W. Beausang, Z. Wang, P. Petkov, A. M. Oros- Peusquens, U. Garg, and S. Zhu, Phys. Rev. C 68, 034314 (2003).

[11] T. Grahn, A. Dewald, O. Möller, R. Julin, C. W. Beausang, S. Christen, I. G. Darby, S. Eeckhaudt, P. T. Greenlees, A. Görgen, K. Helariutta, J. Jolie, P. Jones, S. Juutinen, H. Kettunen, T. Kröll, R. Krücken, Y. Le Coz, M. Leino, A.-P. Leppänen, P. Maierbeck, D. A. Meyer, B. Melon, P. Nieminen, M. Nyman, R. D. Page, J. Pakarinen, P. Petkov, P. Rahkila, B. Saha, M. Sandzelius, J. Sarén, C. Scholey, and J. Uusitalo, Phys. Rev. Lett. 97, 062501 (2006).

[12] T. Grahn, A. Dewald, O. Möller, R. Julin, C. W. Beausang, S. Christen, I. G. Darby, S. Eeckhaudt, P. T. Greenlees, A. Görgen, K. Helariutta, J. Jolie, P. Jones, S. Juutinen, H. Kettunen, T. Kröll, R. Krcüken, Y. L. Coz, M. Leino, A.-P. Leppänen, P. Maierbeck, D. A. Meyer, B. Melon, P. Nieminen, M. Nyman, R. D. Page, J. Pakarinen, P. Petkov, P. Rahkila, B. Saha, M. Sandzelius, J. Sarén, C. Scholey, J. Uusitalo, M. Bender, and P.-H. Heenen, Nucl. Phys. A 801, 83 (2008).

[13] L. P. Gaffney, M. Hackstein, R. D. Page, T. Grahn, M. Scheck, P. A. Butler, P. F. Bertone, N. Bree, R. J. Carroll, M. P. Carpenter, C. J. Chiara, A. Dewald, F. Filmer, C. Fransen, M. Huyse, R. V. F. Janssens, D. T. Joss, R. Julin, F. G. Kondev, P. Nieminen, J. Pakarinen, S. V. Rigby, W. Rother, P. Van Duppen,
H. V. Watkins, K. Wrzosek-Lipska, and S. Zhu, Phys. Rev. C 89, 024307 (2014).

[14] T. Grahn, A. Petts, M. Scheck, P. A. Butler, A. Dewald, M. B. Gómez Hornillos, P. T. Greenlees, A. Görgen, K. Helariutta, J. Jolie, P. Jones, R. Julin, S. Juutinen, S. Ketelhut, R. Krücken, T. Kröll, M. Leino, J. Ljungvall, P. Maierbeck, B. Melon, M. Nyman, R. D. Page, T. Pissulla, P. Rahkila, J. Sarén, C. Scholey, A. Semchenkov, J. Sorri, J. Uusitalo, R. Wadsworth, and M. Zielinska, Phys. Rev. C 80, 014324 (2009).

[15] M. Scheck, T. Grahn, A. Petts, P. A. Butler, A. Dewald, L. P. Gaffney, M. B. Gómez Hornillos, A. Görgen, P. T. Greenlees, K. Helariutta, J. Jolie, P. Jones, R. Julin, S. Juutinen, S. Ketelhut, T. Kröll, R. Krücken, M. Leino, J. Ljungvall, P. Maierbeck, B. Melon, M. Nyman, R. D. Page, J. Pakarinen, E. S. Paul, T. Pissulla, P. Rahkila, J. Sarén, C. Scholey, A. Semchenkov, J. Sorri, J. Uusitalo, R. Wadsworth, and M. Zielińska, Phys. Rev. C 81, 014310 (2010).

[16] K. A. Gladnishki, P. Petkov, A. Dewald, C. Fransen, M. Hackstein, J. Jolie, T. Pissulla, W. Rother, and K. O. Zell, Nucl. Phys. A 877, 19 (2012).

[17] R. A. Bark, G. D. Dracoulis, and A. E. Stuchbery, Nucl. Phys. A 514, 503 (1990).

[18] G. D. Dracoulis, R. A. Bark, A. E. Stuchbery, A. P. Byrne, A. M. Baxter, and F. Riess, Nucl. Phys. A 486, 414 (1988).

[19] A. Virtanen, N. R. Johnson, F. K. McGowan, I. Y. Lee, C. Baktash, M. A. Riley, J. C. Wells, and J. Dudek, Nucl. Phys. A 591, 145 (1995).

[20] D. T. Joss, S. L. King, R. D. Page, J. Simpson, A. Keenan, N. Amzal, T. Back, M. A. Bentley, B. Cederwall, J. F. C. Cocks, D. M. Cullen, P. T. Greenlees, K. Helariutta, P. M. Jones, R. Julin, S. Juutinen, H. Kankaanpaa, H. Kettunen, P. Kuusiniemi, M. Leino, M. Muikku, A. Savelius, J. Uusitalo, and S. J. Williams, Nucl. Phys. A 689, 631 (2001).

[21] D. T. Joss, N. Amzal, D. E. Appelbe, T. Bäck, C. J. Barton, M. A. Bentley, B. Cederwall, J. F. C. Cocks, D. M. Cullen, S. Eeckhautt, T. Grahn, P. T. Greenlees, B. Hadinia, K. Helariutta, P. M. Jones, R. Julin, S. Juutinen, H. Kankaanpää, A. Keenan, H. Kettunen, S. L. King, P. Kuusiniemi, K. Lagergren, M. Leino, A. P. Leppänen, M. Muikku, P. Nieminen, R. D. Page, J. Pakarinen, E. S. Paul, P. Rahkila, C. Scholey, A. Savelius, J. Simpson, M. J. Taylor, J. Uusitalo, S. J. Williams, D. D. Warner, D. R. Wiseman, and R. Wyss, J. Phys. G 31, S1593 (2005).

[22] D. O'Donnell, T. Grahn, D. T. Joss, J. Simpson, C. Scholey, K. Andgren, L. Bianco, B. Cederwall, D. M. Cullen, A. Dewald, E. Ganioglu, M. B. Gómez Hornillos, P. T. Greenlees, B. Hadinia, H. Iwasaki, U. Jakobsson, J. Jolie, P. Jones, D. S. Judson, R. Julin, S. Juutinen, S. Ketelhut, M. Labiche, M. Leino, N. M. Lumley, P. J. R. Mason, O. Möller, P. Nieminen, M. Nyman, R. D. Page, J. Pakarinen, E. S. Paul, M. Petri, A. Petts, P. Peura, N. Pietralla, T. Pissulla, P. Rahkila, P. Ruotsalainen, M. Sandzelius, P. J. Sapple, J. Saren, J. Sorri, J. Thomson, J. Uusitalo, and H. V. Watkins, Phys. Rev. C 79, 064309 (2009).

[23] T. Grahn, S. Stolze, D. T. Joss, R. D. Page, B. Sayğı, D. O'Donnell, M. Akmali, K. Andgren, L. Bianco, D. M. Cullen, A. Dewald, P. T. Greenlees, K. Heyde, H. Iwasaki, U. Jakobsson, P. Jones, D. S. Judson, R. Julin, S. Juutinen, S. Ketelhut, M. Leino, N. Lumley, P. J. R. Mason, O. Möller, K. Nomura, M. Nyman, A. Petts, P. Peura, N. Pietralla, T. Pissulla, P. Rahkila, P. J. Sapple, J. Sarén, C. Scholey, J. Simpson, J. Sorri, P. D. Stevenson, J. Uusitalo, H. V. Watkins, and J. L. Wood, Phys. Rev. C 94, 044327 (2016).

[24] D. Hertz-Kintish, L. Zamick, and S. J. Q. Robinson, Phys. Rev. C 90, 034307 (2014).

[25] C. Louchart, A. Obertelli, A. Görgen, W. Korten, D. Bazzacco, B. Birkenbach, B. Bruyneel, E. Clément, P. J. Coleman-Smith, L. Corradi, D. Curien, G. de Angelis, G. de France, J.-P. Delaroche, A. Dewald, F. Didierjean, M. Doncel, G. Duchêne, J. Eberth, M. N. Erduran, E. Farnea, C. Finck, E. Fioretto, C. Fransen, A. Gadea, M. Girod, A. Gottardo, J. Grebosz, T. Habermann, M. Hackstein, T. Huyuk, J. Jolie, D. Judson, A. Jungclaus, N. Karkour, S. Klupp, R. Krücken, A. Kusoglu, S. M. Lenzi, J. Libert, J. Ljungvall, S. Lunardi, G. Maron, R. Menegazzo, D. Mengoni, C. Michelagnoli, B. Million, P. Molini, O. Möller, G. Montagnoli, D. Montanari, D. R. Napoli, R. Orlandi, G. Pollarolo, A. Prieto, A. Pullia, B. Quintana, F. Recchia, P. Reiter, D. Rosso, W. Rother, E. Sahin, M.-D. Salsac, F. Scarlassara, M. Schlarb, S. Siem, P. P. Singh, P.-A. Söderström, A. M. Stefanini, O. Stézowski, B. Sulignano, S. Szilner, C. Theisen, C. A. Ur, J. J. Valiente-Dobón, and M. Zielinska, Phys. Rev. C 87, 054302 (2013).

[26] O. Möller, N. Warr, J. Jolie, A. Dewald, A. Fitzler, A. Linnemann, K. O. Zell, P. E. Garrett, and S. W. Yates, Phys. Rev. C 71, 064324 (2005).

[27] G. de Angelis, A. Gadea, E. Farnea, R. Isocrate, P. Petkov, N. Marginean, D. R. Napoli, A. Dewald, M. Bellato, A. Bracco, F. Camera, D. Curien, M. D. Poli, E. Fioretto, A. Fitzler, S. Kasemann, N. Kintz, T. Klug, S. Lenzi, S. Lunardi, R. Menegazzo, P. Pavan, J. L. Pedroza, V. Pucknell, C. Ring, J. Sampson, and R. Wyss, Phys. Lett. B 535, 93 (2002).

[28] B. Sayğı, D. T. Joss, R. D. Page, T. Grahn, J. Simpson, D. O'Donnell, G. Alharshan, K. Auranen, T. Bäck, S. Boening, T. Braunroth, R. J. Carroll, B. Cederwall, D. M. Cullen, A. Dewald, M. Doncel, L. Donosa, M. C. Drummond, F. Ertuğral, S. Ertürk, C. Fransen, P. T. Greenlees, M. Hackstein, K. Hauschild, A. Herzan, U. Jakobsson, P. M. Jones, R. Julin, S. Juutinen, J. Konki, T. Kröll, M. Labiche, A. Lopez-Martens, C. G. McPeake, F. Moradi, O. Möller, M. Mustafa, P. Nieminen, J. Pakarinen, J. Partanen, P. Peura, M. Procter, P. Rahkila, W. Rother, P. Ruotsalainen, M. Sandzelius, J. Sarén, C. Scholey, J. Sorri, S. Stolze, M. J. Taylor, A. Thornthwaite, and J. Uusitalo, Phys. Rev. C 96, 021301 (2017).

[29] B. Cederwall, M. Doncel, O. Aktas, A. Ertoprak, R. Liotta, C. Qi, T. Grahn, D. M. Cullen, B. S. Nara Singh, D. Hodge, M. Giles, S. Stolze, H. Badran, T. Braunroth, T. Calverley, D. M. Cox, Y. D. Fang, P. T. Greenlees, J. Hilton, E. Ideguchi, R. Julin, S. Juutinen, M. K. Raju, H. Li, H. Liu, S. Matta, V. Modamio, J. Pakarinen, P. Papadakis, J. Partanen, C. M. Petrache, P. Rahkila, P. Ruotsalainen, M. Sandzelius, J. Sarén, C. Scholey, J. Sorri, P. Subramaniam, M. J. Taylor, J. Uusitalo, and J. J. Valiente-Dobón, Phys. Rev. Lett. 121, 022502 (2018).

[30] E. Clément, A. Gorgen, W. Korten, E. Bouchez, A. Chatillon, J.-P. Delaroche, M. Girod, H. Goutte, A. Hurstel, Y. Le Coz, A. Obertelli, S. Peru, C. Theisen, J. N. Wilson, M. Zielinska, C. Andreoiu, F. Becker, P. A. Butler, J. M. Casandjian, W. N. Catford, T. Czosnyka, G. de France, J. Gerl, R.-D. Herzberg, J. Iwanicki, D. G. Jenkins, G. D. Jones, P. J. Napiorkowski, G. Sletten, and C. N. Timis, Phys. Rev. C 75, 054313 (2007).

[31] J. Ljungvall, A. Gorgen, M. Girod, J.-P. Delaroche, A. Dewald, C. Dossat, E. Farnea, W. Korten, B. Melon, R. Menegazzo, A. Obertelli, R. Orlandi, P. Petkov, T. Pissulla, S. Siem, R. P. Singh, J. Srebrny, C. Theisen, C. A. Ur, J. J. Valiente-Dobón, K. O. Zell, and M. Zielinska, Phys. Rev. Lett 100, 102502 (2008).
[32] J. Ljungvall, G. Georgiev, S. Cabaret, N. Karkour, D. Linget, G. Sedes, R. Chevrier, I. Matea, M. Niikura, M.-D. Salsac, and B. Sulignano, Nucl. Instrum. Methods Phys. Res. Sect. A **679**, 61 (2012).

[33] A. Dewald, S. Harissopulos, and P. von Brentano, Z. Phys. A **334**, 163 (1989).

[34] A. Dewald, O. Möller, and P. Petkov, Prog. Part. Nucl. Phys. **67**, 786 (2012).

[35] M. Hatlo, F. James, P. Mato, L. Moneta, M. Winkler, and A. Zsenei, IEEE Trans. Nucl. Sci. **52**, 2818 (2005).

[36] T. Kibédi, T. W. Burrows, M. B. Trzhaskovskaya, P. M. Davidson, and C. W. Nestor, Jr., Nucl. Instrum. Methods Phys. Res. Sect. A **589**, 202 (2008).

[37] W. Nazarewicz, M. Riley, and J. Garrett, Nucl. Phys. A **512**, 61 (1990).

[38] M. A. J. Mariscotti, G. Scharff-Goldhaber, and B. Buck, Phys. Rev. **178**, 1864 (1969).

[39] R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. **70**, 402 (1993).

[40] T. R. Rodríguez and J. L. Egido, Phys. Rev. C **84**, 051307(R) (2011).

[41] T. R. Rodríguez and J. L. Egido, Phys. Lett. B **705**, 255 (2011).

[42] J. L. Egido, M. Borrajo, and T. R. Rodríguez, Phys. Rev. Lett. **116**, 052502 (2016).

[43] O. Möller, P. Petkov, B. Melon, A. Dewald, A. Fitzler, J. Jolie, D. Tonev, S. Christen, B. Saha, K. O. Zell, and M. Heidemann, Phys. Rev. C **72**, 034306 (2005).

[44] B. Melon, Ph.D. thesis, University of Cologne, 2011 (unpublished).
7.10 Performance of The Advanced GAmma Track-
ing Array at GANIL
<figure><img src="image_117.png" /></figure>

ELSEVIER

Contents lists available at ScienceDirect

Nuclear Inst. and Methods in Physics Research, A

journal homepage: www.elsevier.com/locate/nima

<figure><img src="image_118.png" /></figure>

# Performance of the Advanced GAmmo Tracking Array at GANIL

J. Ljungvall<sup>a,*</sup>, R.M. Pérez-Vidal<sup>b</sup>, A. Lopez-Martens<sup>a</sup>, C. Michelagnoli<sup>c,d</sup>, E. Clément<sup>c</sup>,
J. Dudouet<sup>a,i</sup>, A. Gadea<sup>b</sup>, H. Hess<sup>f</sup>, A. Korichi<sup>a</sup>, M. Labiche<sup>j</sup>, N. Lalović<sup>e</sup>, H.J. Li<sup>c</sup>, F. Recchia<sup>g,h</sup>,
and the AGATA collaboration

<figure><img src="image_119.png" /></figure>

Check for
updates

## ARTICLE INFO

**Keywords:**

AGAMA spectrometer

GANIL facility

γ-ray tracking

Nuclear structure

HPGe detectors

## ABSTRACT

The performance of the Advanced GAmmo 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 γ-ray tracking are discussed. Recent developments of γ-ray tracking are also presented. The experimentally achieved peak-to-total is compared with simulations showing the impact of back-scattered γ rays on the peak-to-total in a γ-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 γ-ray tracking on the normalization of the angular correlations.

## 1. Introduction

In order to perform γ-ray spectroscopy nuclear structure studies in conditions of extreme neutron/proton asymmetry and/or extreme angular momentum the so-called γ-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 γ rays inside the detector medium giving maximum efficiency and an excellent energy resolution. The technique of γ-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 γ rays in the

detector, presently with a position resolution of about 5 mm FWHM [3–5]. The interaction points (hits) are grouped into events on the basis of their timestamp, i.e. the absolute time of the γ-ray interaction. The sequence of interaction points of the γ 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 γ-ray tracking algorithm. The use of digital electronics allows a higher count-rate with maintained energy resolution, and rates up to 50 kHz per crystals are routinely used during experiments. The almost continuous measurement of γ-ray emission angles, via the PSA and tracking, allows for the excellent Doppler correction seen in γ-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 analyzing data from AGATA experiments performed at GANIL.

<footnote><sup>a</sup> CSNSM, Université, Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France</footnote>

<footnote><sup>b</sup> Instituto de Física Corpuscular, CSIC - Universidad de Valencia, E-46980 Paterna, Valencia, Spain</footnote>

<footnote><sup>c</sup> GANIL, CEA/DRF-CNRS/IN2P3, BP 55027, 14076 Caen cedex 5, France</footnote>

<footnote><sup>d</sup> Institut Laue-Langevin, B.P. 156, F-38042 Grenoble cedex 9, France</footnote>

<footnote><sup>e</sup> Department of Physics, Lund University, SE-22100, Lund, Sweden</footnote>

<footnote><sup>f</sup> IKP, University of Cologne, D-50937 Cologne, Germany</footnote>

<footnote><sup>g</sup> INFN Sezione di Padova, I-35131 Padova, Italy</footnote>

<footnote><sup>h</sup> Dipartimento di Fisica e Astronomia dell'Università di Padova, I-35131 Padova, Italy</footnote>

<footnote><sup>i</sup> Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Lyon 1, CNRS-IN2P3, F-69622 Villeurbanne, France</footnote>

<footnote><sup>j</sup> STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: joa.ljungvall@csnsm.in2p3.fr (J. Ljungvall).</footnote>
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 γ-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 γ-ray tracking arrays (e.g. [15–17]) that address the questions of efficiency, peak-to-total, and, Doppler correction capabilities of γ-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 Sections 2 and 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 Fig. 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 from 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

<figure><img src="image_120.png" /><figcaption>Fig. 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. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>**Table 1**
Radioactive sources used for the measurement.</caption><thead><tr><td>Source</td><td>Activity [kBq]</td><td>t<sub>0</sub></td></tr></thead><tbody><tr><td><sup>152</sup>Eu</td><td>19.1</td><td>05/01/2016</td></tr><tr><td><sup>60</sup>Co</td><td>8.7</td><td>05/01/2016</td></tr></tbody></table>

the closest part of the imaginary sphere that touches the front of the AGATA crystals and the target position. Different standard radioactive sources were placed at the target position, see Table 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.

For each detector, the data were collected from the 36 segments as well as for two different gains of the central contact (ranges of ≈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, ≈40 pre-trigger and ≈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 µs followed by a flat top of 1 µs. 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
<figure><img src="image_121.png" /><figcaption>Fig. 2. Chains of Narval actors used for data processing. For details see text.</figcaption></figure>

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 analyzing the data. A time signal is also extracted directly from the digitizer in order to provide a γ-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 Fig. 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 “Pre-processing 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 γ-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 γ-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 γ-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 γ rays. Finally γ-ray tracking is performed. In this work the OFT γ-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.

### 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 $^{60}$Co and $^{152}$Eu 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 et al. [25,26]. The correction for the
effects of the neutron damage on the detection of the γ 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 Fig. 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 normalized 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 10⁹ 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 Fig. 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 A.3 in
Appendix). 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 Fig. 3. For the other 10 detectors good energy resolution
was achieved without the neutron-damage correction procedure.

In Fig. 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 Fig. 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.

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 γ-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

<figure><img src="image_122.png" /><figcaption>Fig. 3. Example of the peak line shapes for the 1332 keV<sup>60</sup>Co γ-ray before (red) and after (black) the neutron damage correction for the 36 segments of the crystal A002 position 12A ATC3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_123.png" /><figcaption>Fig. 4. FWHM at 1.332 MeV ($^{60}$Co) of the central contact (blue) and the sum of segments (red) before (dark colors) and after (light colors) the neutron damage correction for 20 out of the 30 capsules individually named with its position labels. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_124.png" /><figcaption>Fig. 5. FWHM at 1.332 MeV ($^{60}$Co) 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. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

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 γ-γ coincidences,
corrected for the angular correlation effects for the given geometry, and
from singles central contact data taken with $^{60}$Co and $^{152}$Eu 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 µs 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 γ-γ 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 γ-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 γ-γ coincidences analysis.

Using the 1.3 MeV transition from the decay of ⁶⁰Co the efficiency relative to a 3 in × 3 in NaI detector (i.e., 1.2 × 10⁻³ cps/Bq at 25 cm) for each detector at nominal position was extracted and is reported in Fig. 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 Fig. 7 for the nominal position of AGATA and Fig. 8 for the compact position of AGATA. Here each crystal is treated as a single detector like in a standard γ-ray detector array. The values obtained in the singles measurement are compared with the γ-γ 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 VA-MOS 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 Fig. 6, between factory measurements and measurements made within the AGATA collaboration. However, Geant4 simulations of the three differently shaped 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 Figs. 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 Figs. 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><img src="image_125.png" /><figcaption>Fig. 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.</figcaption></figure>

<figure><img src="image_126.png" /><figcaption>Fig. 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. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_127.png" /><figcaption>Fig. 8. Same as Fig. 7 for the compact configuration and with a data rate per between 300 and 500 Hz. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

## 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
<caption>**Table 2**</caption>

Table summarizing the meaning and standard ranges of the main adjustable parameters of OFT.

<table><thead><tr><td>Parameter</td><td>Definition</td><td>Typical value</td></tr></thead><tbody><tr><td>σ<sub>θ</sub></td><td>Average interaction-point position resolution (cm)</td><td>0.3–3</td></tr><tr><td>P<sub>sing</sub></td><td>Minimum probability to accept single-interaction-point clusters</td><td>0.02–0.15</td></tr><tr><td>P<sub>track</sub></td><td>Minimum figure of merit to accept multiple-interaction-point clusters</td><td>0.02–0.05</td></tr></tbody></table>

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 probability 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: ~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 explanation on the OFT algorithms see Lopez-Martens et al. [24].

**OFT parameters.** The definition and typical ranges of the main parameters of OFT are summarized in Table 2.

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 maximizes the gain in efficiency at medium and high energy while minimizing the loss of efficiency at low energy. By analyzing source and in-beam data obtained at Legnaro, GSI and GANIL, the optimal value of $\sigma_\theta$ is found to be around ~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 clusterization of interaction points in specific areas of the detector segments.

<figure><img src="image_128.png" /><figcaption>**Fig. 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 Fig. 7 is also shown. See text for details.</figcaption></figure>

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 ~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 ($\sigma_\theta = 0.8$, $P_{track} = 0.05$ and $P_{sing} = 0.05$) 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 $^{152}$Eu 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 $^{152}$Eu, 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 Fig. 9.

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 Fig. 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
<figure><img src="image_129.png" /><figcaption>**Fig. 10.** (a) γ-γ angular correlations obtained for the 121.8 keV–244.7 keV cascade in <sup>152</sup>Sm using the OFT parameter σ<sub>θ</sub> = 0.8. (b) same as (a) for the 344.3 keV–778.9 keV cascade in <sup>152</sup>Gd and in the case of σ<sub>θ</sub> = 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.</figcaption></figure>

photons when these lie too close to each other. This is clearly seen
in the plot of the γ-γ angular correlations for the 121.8–244.7 and
344.3–778.9 coincidences in <sup>152</sup>Sm and <sup>152</sup>Gd shown in Fig. 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.

Using a larger value of σ<sub>θ</sub> 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 ~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 Fig. 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 γ-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 γ 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 ± 5 keV was demanded. In this manner a γ-ray
multiplicity of one can be guaranteed for the remaining 29 detectors. In
Fig. 11 the γ-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 γ-ray tracking array is dominated
by single-interaction points accepted as events corresponding to a
direct absorption of the total γ-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

<figure><img src="image_130.png" /><figcaption>**Fig. 11.** Gamma-ray tracked spectra for 29 AGATA detectors for <sup>60</sup>Co data using a 30th AGATA detector as an 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. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_131.png" /><figcaption>**Fig. 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 γ-ray track. This for when including or excluding single point interactions.</figcaption></figure>

of peak-to-total and efficiency at 1173 keV as a function of the $P_{track}$ parameter is shown in Fig. 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 Fig. 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.

Monte Carlo simulations using the AGATA simulation package were
made in order to compare the simulated γ-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 simula-
tions 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 γ-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
<figure><img src="image_132.png" /><figcaption>**Fig. 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.</figcaption></figure>

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 Fig. 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” γ rays are very difficult to properly discriminate against as they are from the point of view of γ-ray tracking perfectly good single interaction point events in the front of the crystals.

### 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

<figure><img src="image_133.png" /><figcaption>**Fig. 14.** Gamma-ray spectra showing the 1510 keV $2_1^+ \rightarrow 0_1^+$ transition in ⁹²Mo used to estimate the in beam efficiency.</figcaption></figure>

give a useful rule of thumb to allow consistency checks when analyzing data. The in-beam efficiency for events with a higher γ-ray fold than one also depends on the angular distribution of and correlation of the γ-ray transitions used to measure it. This both via pure geometrical effects and via the lowered γ-ray tracking efficiency for γ 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 µs. 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°, 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 $2_1^+ \rightarrow 0_1^+$ γ rays per detected γ ray from the $4_1^+ \rightarrow 2_1^+$ transition was determined. Peak intensities were extracted from singles spectra and from γγ coincidence matrices. The projected gate in the γγ coincidence matrix is shown in Fig. 14. The efficiency at 1510 keV extracted using this method is after γ-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 µs 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° (as can be seen in Fig. 10 the efficiency to track two γ 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 dependent, 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 γ 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

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
<figure><img src="image_134.png" /><figcaption>Fig. 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.</figcaption></figure>

mill. Given that the recoil velocity has a very small error the position resolution can be estimated by the Doppler Broadening of the γ-ray peaks via the Doppler Shift given by (for details see, e.g., Söderström et al. [5])

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

where $E_γ$ is the energy detected in the detector, $E_{γ0}$ is the energy of the γ ray in the rest frame of the nucleus, β is the velocity of the nucleus emitting the γ ray and θ is the angle between the velocity of the emitting nucleus and the γ ray in the laboratory frame. From this we have a γ-ray peak width $\Delta E_{γ0}$ of

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

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

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

where $\vec{v}$ is the recoil velocity as detected by VAMOS and $\vec{r}$ is the position vector of the first γ-ray interaction as given by γ-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 γ-ray peaks while varying the assumed position resolution of the PSA. The experimental FWHM of the γ-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, $^{98}$Zr. A beam of $^{238}$U impinged on a 10 µm think $^{99}$Be foil. The VAMOS was positioned at 28° relative to the beam axis. Six AGATA detectors close to 112° 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 γ-ray tracking it was the interaction used for Doppler Correction that determined which detector was studied. The FWHM of the γ-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 γ-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]

$$\Delta r_i = 1.9 + 4.4 * \sqrt{100 \text{ keV}/E_i} \text{ mm FWHM} \quad (4)$$

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 γ-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 Fig. 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 Fig. 15). Note that in Fig. 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 γ decays has been investigated using source data. Two pairs of γ-γ cascades from the decay of $^{152}$Eu were used: The first pair was the 1408 keV–121.8 keV coincidence in $^{152}$Sm de-exciting the $2_1^-$ level at 1530 keV to the ground state via the $2_1^+$ level at 121.8 keV. The second pair is the 244.7 keV–121.8 keV de-exciting the $4_1^+$ level at 366.5 keV and the $2_1^+$ level, also in $^{152}$Sm.

The tracking algorithm identifies the first interaction point of each γ ray and as the position of the source is known the angle between the γ 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 Fig. 16. The main features of the two pairs of γ 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 γ rays emitted into a small solid angle, since they often will be reconstructed as one γ ray with sum energy. The angular
<figure><img src="image_135.png" /><figcaption>Fig. 16. Histograms used for angular correlation measurements using AGATA. The lower panel shows the angle between the two correlated γ rays detected in AGATA. The upper panel shows the angle between γ rays from uncorrelated events concatenated before tracking.</figcaption></figure>

correlation is then extracted by normalizing for geometrical effects and the already mentioned decrease in efficiency for two low-energy γ rays absorbed close to each other. The normalization was created by tracking events consisting of the interaction points of two events each with a total energy corresponding to one of the γ rays in the cascade of interest concatenated into one event, thus generating pairs of γ rays with the correct energies, but with no angular correlation. From the tracked events the angle between the γ rays was then again extracted. The resulting histograms for the two pairs of γ rays are shown in the upper panel of Fig. 16.

By dividing the histograms in the lower panel in Fig. 16 by the upper panel the histograms shown in Fig. 17 are created. The upper panel is for the $4_1^+ \rightarrow 2_1^+ \rightarrow 0_1^+$ cascade, the lower panel for the $2_1^- \rightarrow 2_1^+ \rightarrow 0_1^+$ cascade. For each angular correlation the expression

$$W(\theta) = 1 + a_{22} P_2(\cos(\theta)) + a_{44} P_4(\cos(\theta)) \quad (5)$$

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 $4_1^+ \rightarrow 2_1^+ \rightarrow 0_1^+$ 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 $2_1^- \rightarrow 2_1^+ \rightarrow 0_1^+$ 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.

A particularity of a γ-tracking array as compared to a classical multi-detector γ-ray spectrometer is the continuous variation in efficiency with the angle between the detected γ rays. For angular correlations this means the normalization 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 γ rays concatenated into events when constructing the normalization used to extract the angular correlations from the experimental correlations. In the top panel of Fig. 18 the histogram drawn with a black solid line shows the distribution of θ angles between uncorrelated γ rays concatenated after tracking. The histogram drawn with red dashed line shows the θ angle distribution if one instead concatenates uncorrelated events using the individual hits and then preforms the tracking. The bottom panel shows the resulting angular correlations using the two different methods of generating the normalization. It is clear that the effects of γ-ray tracking, included when events are concatenated before tracking, are needed for a correct normalization over the entire angle range. This procedure works well

<figure><img src="image_136.png" /><figcaption>Fig. 17. Gamma-gamma angular correlations measured with AGATA. The upper panel shows the angular correlation for the $4_1^+ \rightarrow 2_1^+ \rightarrow 0_1^+$ pair of transitions in $^{152}$Sm. The lower panel is for the $2_1^- \rightarrow 2_1^+ \rightarrow 0_1^+$ transitions.</figcaption></figure>

<figure><img src="image_137.png" /><figcaption>Fig. 18. Normalization histograms and angular correlations for $4_1^+ \rightarrow 2_1^+ \rightarrow 0_1^+$ using the “concatenate before tracking” and “concatenate after tracking” methods.</figcaption></figure>

for source data where the peak-to-background ratio is high and γ rays from different decays have no correlations. The application of this method to in-beam data is however more problematic due to 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 γ-ray tracking array. A total efficiency for AGATA of 3.8(1)% at 1332 keV for the nominal geometry when using γ-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 γ rays combined with the clustering stage of γ-ray tracking generates a loss of efficiency that depends on the angle between the two γ 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 a¹⁵²Eu source angular correlations have been produced and methods to properly normalize for the combined effect of geometry and γ-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 γ-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.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## CRediT authorship contribution statement

**J. Ljungvall:** Conceptualization, Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **R.M. Pérez-Vidal:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **A. Lopez-Martens:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **C. Michelagnoli:** Conceptualization, Data curation, Formal analysis, Methodology. **E. Clément:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **J. Dudouet:** Data curation, Formal analysis, Writing review & editing. **A. Gadea:** Data curation, Supervision, Writing - orginal draft, Writing review & editing. **H. Hess:** Data curation, Resources. **A. Korichi:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **M. Labiche:** Data curation, Formal analysis. Writing - orginal draft, Writing review & editing. **N. Lalović:** Data curation, Writing - orginal draft, Writing review & editing. **H.J. Li:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing. **F. Recchia:** Data curation, Formal analysis, Writing - orginal draft, Writing review & editing.

## 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

<caption>Table A.3</caption>

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.

<table><thead><tr><th>Cluster</th><th>Crystal A</th><th>Crystal B</th><th>Crystal C</th><th>Position array</th></tr></thead><tbody><tr><td>ATC6</td><td><b>A001</b></td><td><b>B004</b></td><td><b>C010</b></td><td>00</td></tr><tr><td>ATC8</td><td>A009</td><td>B005</td><td>C008</td><td>02</td></tr><tr><td>ATC5</td><td>A005</td><td><b>B002</b></td><td>C009</td><td>03</td></tr><tr><td>ATC9</td><td>A004</td><td>B008</td><td>C013</td><td>04</td></tr><tr><td>ATC10</td><td>A010</td><td>B012</td><td>C012</td><td>05</td></tr><tr><td>ADC9</td><td>-</td><td><b>B011</b></td><td>C011</td><td>09</td></tr><tr><td>ATC2</td><td><b>A003</b></td><td><b>B003</b></td><td>C005</td><td>10</td></tr><tr><td>ATC7</td><td>A006</td><td><b>B013</b></td><td>C006</td><td>11</td></tr><tr><td>ATC3</td><td><b>A002</b></td><td><b>B010</b></td><td>C001</td><td>12</td></tr><tr><td>ATC4</td><td><b>A007</b></td><td><b>B007</b></td><td>C007</td><td>13</td></tr><tr><td>ATC1</td><td><b>A008</b></td><td><b>B001</b></td><td>C003</td><td>14</td></tr></tbody></table>

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, Spain 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. Detector and crystal positions and ids

See Table A.3.

## References

[1] S. Akkoyun, A. Algora, B. Alikhani, F. Ameil, G. de Angelis, L. Arnold, A. Astier, A. Ataç, Y. Aubert, C. Aufranc, A. Austin, S. Aydin, F. Azaiez, S. Badoer, D. Balabanski, D. Barrientos, G. Baulieu, R. Baumann, D. Bazzacco, F. Beck, T. Beck, P. Bednarczyk, M. Bellato, M. Bentley, G. Benzoni, R. Berthier, L. Berti, R. Beunard, G.L. Bianco, B. Birkenbach, P. Bizzeti, A. Bizzeti-Sona, F.L. Blanc, J. Blasco, N. Blasi, D. Bloor, C. Boiano, M. Borsato, D. Bortolato, A. Boston, H. Boston, P. Bourgault, P. Boutachkov, A. Bouty, A. Bracco, S. Brambilla, I. Brawn, A. Brondi, S. Broussard, B. Bruyneel, D. Bucurescu, I. Burrows, A. Bürger, S. Cabaret, B. Cahan, E. Calore, F. Camera, A. Capsoni, F. Carrió, G. Casati, M. Castoldi, B. Cederwall, J.-L. Cercus, V. Chambert, M.E. Chambit, R. Chapman, L. Charles, J. Chavas, E. Clément, P. Cocconi, S. Coelli, P. Coleman-Smith, A. Colombo, S. Colosimo, C. Commeaux, D. Conventi, R. Cooper, A. Corsi, A. Cortesi, L. Costa, F. Crespi, J. Cresswell, D. Cullen, D. Curien, A. Czermak, D. Delbourg, R. Depalo, T. Descombes, P. Désesquelles, P. Detistov, C. Diarra, F. Didierjean, M. Dimmock, Q. Doan, C. Domingo-Pardo, M. Doncel, F. Dorangeville, N. Dosme, Y. Drouen, G. Duchêne, B. Dulny, J. Eberth, P. Edelbruck, J. Egea, T. Engert, M. Erduran, S. Ertürk, C. Fanin, S. Fantinel, E. Farnea, T. Faul, M. Filliger, F. Filmer, C. Finck, G. de France, A. Gadea, W. Gast, A. Geraci, J. Gerl, R. Gernhäuser, A. Gianniatiempo, A. Giaz, L. Gibelin, A. Givechev, N. Goel, V. González, A. Gottardo, X. Grave, J. Grebosz, R. Griffiths, A. Grint, P. Gros, L. Guevara, M. Gulmini, A. Görgen, H. Ha, T. Habermann, L. Harkness, H. Harroch, K. Hauschild, C. He, A. Hernández-Prieto, B. Hervieu, H. Hess, T. Hüyük, E. Ince, R. Isocrate, G. Jaworski, A. Johnson, J. Jolie, P. Jones, B. Jonson, P. Joshi, D. Judson, A. Jungclaus, M. Kaci, N. Karkour, M. Karolak, A. Kaskas, M. Kebbiri, R. Kempley, A. Khaplanov, S. Klupp, M. Kogimtzis, I. Kojouharov, A. Korichi, W. Korten, T. Kröll, R. Krücken, N. Kurz, B. Ky, M. Labiche, X. Lafay, L. Lavergne, I. Lazarus, S. Leboutelier, F. Lefebvre, E. Legay, L. Legeard, F. Lelli, S. Lenzi, S. Leoni, A. Lermitage, D. Lersch, J. Leske, S. Letts, S. Lhenoret, R. Lieder, D. Linget, J. Ljungvall, A. Lopez-Martens, A. Lotodé, S. Lunardi, A. Maj, J. van der Marel, Y. Mariette, N. Marginean, R. Marginean, G. Maron, A. Mather, W. Meczyński, V. Mendéz, P. Medina, B. Melon, R. Menegazzo, D. Mengoni, E. Merchan, L. Mihailescu, C. Michelagnoli, J. Mierzejewski, L. Milechina, B. Million, K. Mitev, P. Molini, D. Montanari, S. Moon, F. Morbiducci, R. Moro, P. Morrall, O. Möller, A. Nannini, D. Napoli, L. Nelson, M. Nespolo, V. Ngo, M. Nicoletto, R. Nicolini, Y.L. Noa, P. Nolan, M. Norman, J. Nyberg, A. Obertelli, A. Olariu, R. Orlandi, D. Oxley, C. Özben, M. Ozille, C. Oziol, E. Pachoud, M. Palacz, J. Palin, J. Pancin, C. Parisel, P. Pariset, G. Pascovici, R. Peghin, L. Pellegrì, A. Perego, S. Perrier, M. Petcu, P. Petkov, C. Petrache, E. Pierre, N. Pietralla, S. Pietri, M. Pignanelli, I. Piqueras, Z. Podolyak, P.L. Pouhalec, J. Pouthas, D. Pugnère, V. Pucknell, A. Pullia, B. Quintana, R. Raine, G. Rainovski, L. Ramina, G. Rampazzo, G.L. Rana, M. Rebeschini, F. Recchia, N. Redon, M. Reese, P. Reiter, P. Regan, S.
Riboldi, M. Richer, M. Rigato, S. Rigby, G. Ripamonti, A. Robinson, J. Robin, J. Roccaz, J.-A. Ropert, B. Rossé, C.R. Alvarez, D. Roso, B. Rubio, D. Rudolph, F. Saillant, E. Sahin, F. Salomon, M.-D. Salsac, J. Salt, G. Salvato, J. Sampson, S. Sanchis, C. Santos, H. Schaffner, M. Schlarb, D. Scraggs, D. Seddon, M. Senyiğit, M.-H. Sigward, G. Simpson, J. Simpson, J. Smith, P. Sona, B. Sowicki, P. Spolaore, C. Stahl, T. Stanios, E. Stefanova, O. Stézowski, J. Strachan, G. Suliman, P.-A. Söderström, J. Tain, S. Tanguy, S. Tashenov, C. Theisen, J. Thornhill, F. Tomasi, N. Toniolo, R. Touzey, B. Travers, A. Triossi, M. Tripon, K. Tun-Lanoë, M. Turcato, C. Unsworth, C. Ur, J. Valiente-Dobon, V. Vandone, E. Vardaci, R. Venturelli, F. Veronese, C. Veyssiere, E. Viscione, R. Wadsworth, P. Walker, N. Warr, C. Weber, D. Weisshaar, D. Wells, O. Wieland, A. Wiens, G. Wittwer, H. Wollersheim, F. Zocca, N. Zamfir, M. Ziebliński, A. Zucchiatti, Agata-advanced {GAmma} tracking array, Nucl. Instrum. Methods Phys. Res. A 668 (2012) 26-58, http://dx.doi.org/10.1016/j.nima.2011.11.081, URL http://www.sciencedirect.com/science/article/pii/S0168900211021516.

[2] I.Y. Lee, M.A. Deleplanque, K. Vetter, Developments in large gamma-ray detector arrays, Rep. Progr. Phys. 66 (7) (2003) 1095, URL http://stacks.iop.org/0034-4885/66/i=7/a=201.

[3] F. Recchia, D. Bazzacco, E. Farnea, R. Venturelli, S. Aydin, G. Suliman, C. Ur, Performance of an agata prototype detector estimated by compton-imaging techniques, Nucl. Instrum. Methods Phys. Res. A 604 (1) (2009) 60-63, http://dx.doi.org/10.1016/j.nima.2009.01.079, psDB. URL http://www.sciencedirect.com/science/article/pii/S0168900209001168.

[4] F. Recchia, D. Bazzacco, E. Farnea, A. Gadea, R. Venturelli, T. Beck, P. Bednarczyk, A. Buerger, A. Dewald, M. Dimmock, G. Duchène, J. Eberth, T. Paul, J. Gerl, R. Gernhaeuser, K. Hauschild, A. Holler, P. Jones, W. Korten, T. Kröll, R. Krücken, N. Kurz, J. Ljungvall, S. Lunardi, P. Maierbeck, D. Mengoni, J. Nyberg, L. Nelson, G. Pascovici, P. Reiter, H. Schaffner, M. Schlarb, T. Steinhardt, O. Theilen, C. Ur, J.V. Dobon, D. Weisshaar, Position resolution of the prototype agata triple-cluster detector from an in-beam experiment, Nucl. Instrum. Methods Phys. Res. A 604 (3) (2009) 555-562, http://dx.doi.org/10.1016/j.nima.2009.02.042, URL http://www.sciencedirect.com/science/article/pii/S0168900209004124.

[5] P.-A. Söderström, F. Recchia, J. Nyberg, A. Al-Adili, A. Ataç, S. Aydin, D. Bazzacco, P. Bednarczyk, B. Birkenach, D. Bortolato, A. Boston, H. Boston, B. Bruyneel, D. Bucurescu, E. Calore, S. Colosimo, F. Crespi, N. Dosme, J. Eberth, E. Farnea, F. Filmer, A. Gadea, A. Gottardo, X. Grave, J. Grebosz, R. Griffiths, M. Gulmini, T. Habermann, H. Hess, G. Jaworski, P. Jones, P. Joshi, D. Judson, R. Kempley, A. Khaplanov, E. Legay, D. Lersch, J. Ljungvall, A. Lopez-Martens, W. Myczynski, D. Mengoni, C. Michelagnoli, P. Molini, D. Napoli, R. Orlandi, G. Pascovici, A. Pullia, P. Reiter, E. Sahin, J. Smith, J. Strachan, D. Tonev, C. Unsworth, C. Ur, J. Valiente-Dobón, C. Veyssiere, A. Wiens, Interaction position resolution simulations and in-beam measurements of the {AGATA} {HPGe} detectors, Nucl. Instrum. Methods Phys. Res. A 638 (1) (2011) 96-109, http://dx.doi.org/10.1016/j.nima.2011.02.089, URL http://www.sciencedirect.com/science/article/pii/S016890021100489X.

[6] A. Gadea, E. Farnea, J. Valiente-Dobón, B. Million, D. Mengoni, D. Bazzacco, F. Recchia, A. Dewald, T. Pissulla, W. Rother, G. de Angelis, A. Austin, S. Aydin, S. Badoer, M. Bellato, G. Benzoni, L. Berti, R. Beunard, B. Birkenbach, A. Bissiato, N. Blasi, C. Boiano, D. Bortolato, A. Haberman, D. Calore, F. Camera, A. Capsoni, J. Chavas, P. Cocconi, S. Coelli, A. Colombo, D. Conventi, L. Costa, L. Corradi, A. Corsi, A. Cortesi, F. Crespi, N. Dosme, J. Eberth, S. Fantinel, C. Fanin, E. Fioretto, C. Fransen, A. Giaz, A. Gottardo, X. Grave, J. Grebosz, R. Griffiths, E. Grodner, M. Gulmini, T. Habermann, C. He, H. Hess, R. Isocrate, J. Jolie, P. Jones, A. Latina, E. Legay, S. Lenzi, S. Leoni, F. Lelli, D. Lersch, S. Lunardi, G. Maron, R. Menegazzo, C. Michelagnoli, P. Molini, G. Montagnoli, D. Montanari, O. Möller, D. Napoli, M. Nicoletto, R. Nicolini, M. Ozille, G. Pascovici, R. Peghin, M. Pignanelli, V. Pucknell, A. Pullia, L. Ramina, G. Rampazzo, M. Rebeschini, P. Reiter, S. Riboldi, M. Rigato, C.R. Alvarez, D. Rosso, G. Salvato, J. Strachan, E. Sahin, F. Scarlassara, J. Simpson, A. Stefanini, O. Stezowski, F. Tomasi, N. Toniolo, A. Triossi, M. Turcato, C. Ur, V. Vandone, R. Venturelli, F. Veronese, C. Veyssiere, E. Viscione, O. Wieland, A. Wiens, F. Zocca, A. Zucchiatti, Conceptual design and infrastructure for the installation of the first agata sub-array at Inl, Nucl. Instrum. Methods Phys. Res. A 654 (1) (2011) 88-96, http://dx.doi.org/10.1016/j.nima.2011.06.004, URL http://www.sciencedirect.com/science/article/pii/S0168900211011132.

[7] C. Domingo-Pardo, D. Bazzacco, P. Doornenbal, E. Farnea, A. Gadea, J. Gerl, H. Wollersheim, Conceptual design and performance study for the first implementation of agata at the in-flight rib facility of gsi, Nucl. Instrum. Methods Phys. Res. A 694 (2012) 297-312, http://dx.doi.org/10.1016/j.nima.2012.08.039, URL http://www.sciencedirect.com/science/article/pii/S0168900212009102.

[8] N. Lalović, C. Louchart, C. Michelagnoli, R. Perez-Vidal, D. Ralet, J. Gerl, D. Rudolph, T. Arici, D. Bazzacco, E. Clément, A. Gadea, I. Kojouharov, A. Korichi, M. Labiche, J. Ljungvall, A. Lopez-Martens, J. Nyberg, N. Pietralla, S. Pietri, O. Stezowski, Performance of the {AGATA} γ-ray spectrometer in the prespec setup at {GSI}, Nucl. Instrum. Methods Phys. Res. A 806 (2016) 258-266, http://dx.doi.org/10.1016/j.nima.2015.10.032, URL http://www.sciencedirect.com/science/article/pii/S0168900215012395.

[9] E. Clément, C. Michelagnoli, G. de France, H. Li, A. Lemasson, C.B. Dejean, M. Beuzard, P. Bougault, J. Cacitti, J.-L. Foucher, G. Fremont, P. Gangnant, J. Goupil, C. Houarner, M. Jean, A. Lefevre, L. Legeard, F. Legruel, C. Maugeais,

L. Ménager, N. Ménard, H. Munoz, M. Ozille, B. Raine, J. Ropert, F. Saillant, C. Spitaels, M. Tripon, P. Vallerand, G. Voltolini, W. Korten, M.-D. Salsac, C. Theisen, M. Zielińska, T. Joannem, M. Karolak, M. Kebbiri, A. Lotode, R. Touzery, C. Walter, A. Korichi, J. Ljungvall, A. Lopez-Martens, D. Ralet, N. Dosme, X. Grave, N. Karkour, X. Lafay, E. Legay, I. Kojouharov, C. Domingo-Pardo, A. Gadea, R. Pérez-Vidal, J. Civera, B. Birkenbach, J. Eberth, H. Hess, L. Lewandowski, P. Reiter, A. Nannini, G.D. Angelis, G. Jaworski, P. John, D. Napoli, J. Valiente-Dobón, D. Barrientos, D. Bortolato, G. Benzoni, A. Bracco, S. Brambilla, F. Camera, F. Crespi, S. Leoni, B. Million, A. Pullia, O. Wieland, D. Bazzacco, S. Lenzi, S. Lunardi, R. Menegazzo, D. Mengoni, F. Recchia, M. Bellato, R. Isocrate, F.E. Canet, F. Didierjean, G. Duchêne, R. Baumann, M. Brucker, E. Dangelser, M. Filliger, H. Friedmann, G. Gaudiot, J.-N. Grapton, H. Kocher, C. Mathieu, M.-H. Sigward, D. Thomas, S. Veeramootoo, J. Dudouet, O. Stézowski, C. Aufranc, Y. Aubert, M. Labiche, J. Simpson, I. Burrows, P. Coleman-Smith, A. Grant, I. Lazarus, P. Morrall, V. Pucknell, A. Boston, D. Judson, N. Lalović, J. Nyberg, J. Collado, V. González, I. Kuti, B. Nyakó, A. Maj, M. Rudigier, Conceptual design of the agata 1π array at ganil, Nucl. Instrum. Methods Phys. Res. A 855 (Suppl. C) (2017) 1-12, http://dx.doi.org/10.1016/j.nima.2017.02.063, URL http://www.sciencedirect.com/science/article/pii/S0168900217302590.

[10] H. Savajols, Vamos: a variable mode high acceptance spectrometer, Nuclear Phys. A 654 (1) (1999) 1027c-1032c, http://dx.doi.org/10.1016/S0375-9474(00)88592-9, URL http://www.sciencedirect.com/science/article/pii/S0375947400885929.

[11] M. Rejmund, B. Lecornu, A. Navin, C. Schmitt, S. Damoy, O. Delaune, J. Enguerrand, G. Fremont, P. Gangnant, L. Gaudefroy, B. Jacquot, P. Pancin, S. Pullanhiotan, C. Spitaels, Performance of the improved larger acceptance spectrometer: Vamos++, Nucl. Instrum. Methods Phys. Res. A 646 (1) (2011) 184-191, http://dx.doi.org/10.1016/j.nima.2011.05.007, URL http://www.sciencedirect.com/science/article/pii/S0168900211008515.

[12] J. Valiente-Dobón, G. Jaworski, A. Goasduff, F. Egea, V. Modamio, T. Hüyük, A. Triossi, M. Jastrząb, P. Söderström, A.D. Nitto, G. de Angelis, G. de France, N. Erduran, A. Gadea, M. Moszyński, J. Nyberg, M. Palacz, R. Wadsworth, R. Aliaga, C. Aufranc, M. Bézard, G. Baulieu, E. Bissiato, A. Boujrad, I. Burrows, S. Carturan, P. Cocconi, G. Colucci, D. Conventi, M. Cordwell, S. Coudert, J. Deltoro, L. Ducroux, T. Dupasquier, S. Ertürk, X. Fabian, V. González, A. Grant, K. Hadyińska-Kłeł, A. Ilana, M. Jurado-Gomez, M. Kogimtzis, I. Lazarus, L. Legeard, J. Ljungvall, G. Pasqualato, R. Pérez-Vidal, A. Raggio, D. Ralet, N. Redon, F. Salliant, B. Sayğı, E. Sanchis, M. Scarcioffolo, M. Siciliano, D. Testov, O. Stezowski, M. Tripon, I. Zanon, Neda-nutron detector array, Nucl. Instrum. Methods Phys. Res. A 927 (2019) 81-86, http://dx.doi.org/10.1016/j.nima.2019.02.021, URL http://www.sciencedirect.com/science/article/pii/S0168900219301962.

[13] J. Scheurer, M. Aiche, M. Aléonard, G. Barreto, F. Bourgine, D. Boivin, D. Cabaussel, J. Chemin, T. Doan, J. Goudour, M. Harston, A. Brondi, G.L. Rana, R. Moro, E. Vardaci, D. Curien, Improvements in the in-beam γ-ray spectroscopy provided by an ancillary detector coupled to a ge γ-spectrometer: the diamanturogam ii example, Nucl. Instrum. Methods Phys. Res. A 385 (3) (1997) 501-510, http://dx.doi.org/10.1016/S0168-9002(96)01038-8, URL http://www.sciencedirect.com/science/article/pii/S0168900296010388.

[14] J. Gál, G. Hegyesi, J. Molnár, B. Nyakó, G. Kalinka, J. Scheurer, M. Aléonard, J. Chemin, J. Pedroza, K. Juhász, V. Pucknell, The vxi electronics of the diamant particle detector array, Nucl. Instrum. Methods Phys. Res. A 516 (2) (2004) 502-510, http://dx.doi.org/10.1016/j.nima.2003.08.158, URL http://www.sciencedirect.com/science/article/pii/S0168900203025075.

[15] A. Korichi, T. Lauritsen, A. Wilson, J. Dudouet, E. Clément, N. Lalović, R. Perez-Vidal, S. Pietri, D. Ralet, O. Stézowski, Performance of a gamma-ray tracking array: Characterizing the agata array using a 60co source, Nucl. Instrum. Methods Phys. Res. A 872 (2017) 80-86, http://dx.doi.org/10.1016/j.nima.2017.08.020, URL http://www.sciencedirect.com/science/article/pii/S0168900217308781.

[16] T. Lauritsen, A. Korichi, S. Zhu, A.N. Wilson, D. Weisshaar, J. Dudouet, A.D. Ayangeakaa, M.P. Carpenter, C.M. Campbell, E. Clément, H.L. Crawford, M. Cromaz, P. Fallon, J.P. Greene, R.V.F. Janssens, T.L. Khoo, N. Lalović, I.Y. Lee, A.O. Macchiavelli, R.M. Perez-Vidal, S. Pietri, D.C. Radford, D. Ralet, L.A. Riley, D. Seweryniak, O. Stezowski, Characterization of a gamma-ray tracking array: A comparison of GRETINA and Gammaspheare using a $^{60}$Co source, Nucl. Instrum. Methods Phys. Res. A 836 (2016) 46-56, URL http://dx.doi.org/10.1016/j.nima.2016.07.027, URL http://www.sciencedirect.com/science/article/pii/S0168900216307434.

[17] D. Weisshaar, D. Bazin, P.C. Bender, C.M. Campbell, F. Recchia, V. Bader, T. Baugher, J. Belarge, M.P. Carpenter, H.L. Crawford, M. Cromaz, B. Elman, P. Fallon, A. Forney, A. Gade, J. Harker, N. Kobayashi, C. Langer, T. Lauritsen, I.Y. Lee, A. Lemasson, B. Longfellow, E. Lunderberg, A.O. Macchiavelli, K. Miki, S. Momiyama, S. Noji, D.C. Radford, M. Scott, J. Sethi, S.R. Stroberg, C. Sullivan, R. Titus, A. Wiens, S. Williams, K. Wimmer, S. Zhu, The performance of the γ-ray tracking array GRETINA for γ-ray spectroscopy with fast beams of rare isotopes, Nucl. Instrum. Methods Phys. Res. A 847 (2017) 187-198, http://dx.doi.org/10.1016/j.nima.2016.12.001, URL http://www.sciencedirect.com/science/article/pii/S0168900216312402.

[18] A. Wiens, H. Hess, B. Birkenbach, B. Bruyneel, J. Eberth, D. Lersch, G. Pascovici, P. Reiter, H.-G. Thomas, The {AGATA} triple cluster detector, Nucl. Instrum. Methods Phys. Res. A 618 (1-3) (2010) 223-233, http://dx.doi.
org/10.1016/j.nima.2010.02.102, URL http://www.sciencedirect.com/science/article/pii/S0168900210003384.

[19] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce, M. Asai, D. Axen, S. Banerjee, G. Barrand, F. Behner, L. Bellagamba, J. Boudreau, L. Broglia, A. Brunengo, H. Burkhardt, S. Chauvie, J. Chuma, R. Chytracek, G. Cooperman, G. Cosmo, P. Degtyarenko, A. Dell'Acqua, G. Depaola, D. Dietrich, R. Enami, A. Feliciello, C. Ferguson, H. Fesefeldt, G. Folger, F. Foppiano, A. Forti, S. Garelli, S. Giani, R. Giannitrapani, D. Gibin, J.G. Cadenas, I. González, G.G. Abril, G. Greeniaus, W. Greiner, V. Grichine, A. Grossheim, S. Guatelli, P. Gumplinger, R. Hamatsu, K. Hashimoto, H. Hasui, A. Heikkinen, A. Howard, V. Ivanchenko, A. Johnson, F. Jones, J. Kallenbach, N. Kanaya, M. Kawabata, Y. Kawabata, M. Kawaguti, S. Kelner, P. Kent, A. Kimura, T. Kodama, R. Kokoulin, M. Kossov, H. Kurashige, E. Lamanna, T. Lampén, V. Lara, V. Lefebure, F. Lei, M. Liendl, W. Lockman, F. Longo, S. Magni, M. Maire, E. Medernach, K. Minamimoto, P.M. de Freitas, Y. Morita, K. Murakami, M. Nagamatu, R. Nartallo, P. Nieminen, T. Nishimura, K. Ohtsubo, M. Okamura, S. O'Neale, Y. Oohata, K. Paech, J. Perl, A. Pfeiffer, M. Pia, F. Ranjard, A. Rybin, S. Sadilov, E.D. Salvo, G. Santin, T. Sasaki, N. Savvas, Y. Sawada, S. Scherer, S. Sei, V. Sirotenko, D. Smith, N. Starkov, H. Stoecker, J. Sulkimo, M. Takahata, S. Tanaka, E. Tcherniaev, E.S. Tehrani, M. Tropeano, P. Truscott, H. Uno, L. Urban, P. Urban, M. Verderi, A. Walkden, W. Wander, H. Weber, J. Wellisch, T. Wenaus, D. Williams, D. Wright, T. Yamada, H. Yoshida, D. Zschiesche, Geant4-a simulation toolkit, Nucl. Instrum. Methods Phys. Res. A 506 (3) (2003) 250-303, http://dx.doi.org/10.1016/S0168-9002(03)01368-8, URL http://www.sciencedirect.com/science/article/pii/S0168900203013688.

[20] E. Farnea, F. Recchia, D. Bazzacco, T. Kröll, Z. Podolyák, B. Quintana, A. Gadea, Conceptual design and Monte Carlo simulations of the (AGATA) array, Nucl. Instrum. Methods Phys. Res. A 621 (1-3) (2010) 331-343, http://dx.doi.org/10.1016/j.nima.2010.04.043, URL http://www.sciencedirect.com/science/article/pii/S0168900210008922.

[21] D. Barrientos, M. Bellato, D. Bazzacco, D. Bortolato, P. Cocconi, A. Gadea, V. Gonzalez, M. Gulmini, R. Isocrate, D. Mengoni, A. Pullia, F. Recchia, D. Rosso, E. Sanchis, N. Toniolo, C.A. Ur, J.J. Valiente-Dobon, Digital FPGA-based front-end electronics for the GALILEO array, IEEE Trans. Nucl. Sci. 62 (6) (2015) 3134-3139, http://dx.doi.org/10.1109/tns.2015.2480243, URL https://doi.org/10.1109%2Ftns.2015.2480243.

[22] R. Venturelли, D. Bazzacco, Adaptive Grid Search as Pulse Shape Analysis Algorithm for γ-Tracking and Results, LNL Annual Report, 2004, p. 220.

[23] B. Bruyneel, B. Birkenbach, P. Reiter, Pulse shape analysis and position determination in segmented hge detectors: The agata detector library, Eur. Phys. J. A 52 (3) (2016) 70, http://dx.doi.org/10.1140/epja/i2016-16070-9, URL http://dx.doi.org/10.1140/epja/i2016-16070-9.

[24] A. Lopez-Martens, K. Hauschild, A. Korichi, J. Roccaz, J.-P. Thibaud, γ-Ray tracking algorithms: a comparison, Nucl. Instrum. Methods Phys. Res. A 533 (3) (2004) 454-466, http://dx.doi.org/10.1016/j.nima.2004.06.154, URL http://www.sciencedirect.com/science/article/pii/S0168900204014779.

[25] B. Bruyneel, P. Reiter, A. Wiens, J. Eberth, H. Hess, G. Pascovici, N. Warr, D. Weisshaar, Crosstalk properties of 36-fold segmented symmetric hexagonal (HPGe) detectors, Nucl. Instrum. Methods Phys. Res. A 599 (2-3) (2009) 196-208, http://dx.doi.org/10.1016/j.nima.2008.11.011, URL http://www.sciencedirect.com/science/article/pii/S0168900208015921.

[26] B. Bruyneel, P. Reiter, A. Wiens, J. Eberth, H. Hess, G. Pascovici, N. Warr, S. Aydin, D. Bazzacco, F. Recchia, Crosstalk corrections for improved energy resolution with highly segmented hge-detectors, Nucl. Instrum. Methods Phys. Res. A 608 (1) (2009) 99-106, http://dx.doi.org/10.1016/j.nima.2009.06.037, URL http://www.sciencedirect.com/science/article/pii/S0168900209012455.

[27] B. Bruyneel, B. Birkenbach, J. Eberth, H. Hess, G. Pascovici, P. Reiter, A. Wiens, D. Bazzacco, E. Farnea, C. Michelagnoli, F. Recchia, Correction for hole trapping in agata detectors using pulse shape analysis, Eur. Phys. J. A 49 (5) (2013) 61.

[28] T.J. Ross, C.W. Beausang, I.Y. Lee, A.O. Macchiavelli, S. Gros, M. Cromaz, R.M. Clark, P. Fallon, H. Jeppesen, J.M. Allmond, Neutron damage tests of a highly segmented germanium crystal, Nucl. Instrum. Methods Phys. Res. A 606 (3) (2009) 533-544, http://dx.doi.org/10.1016/j.nima.2009.04.024, URL http://www.sciencedirect.com/science/article/pii/S0168900209008250.

[29] D. Radford, Radware. URL https://radware.phy.ornl.gov/main.html.

[30] J. Eberth, J. Simpson, From ge(ii) detectors to gamma-ray tracking arrays-50 years of gamma spectroscopy with germanium detectors, Prog. Part. Nucl. Phys. 60 (2) (2008) 283-337, http://dx.doi.org/10.1016/j.ppnp.2007.09.001, URL http://www.sciencedirect.com/science/article/pii/S0146641007000828.

[31] H. Utsunomiya, H. Akimune, K. Osaka, T. Kaihori, K. Furutaka, H. Harada, Surface channel effect on γ-ray response functions of coaxial germanium detectors, Nucl. Instrum. Methods Phys. Res. A 548 (3) (2005) 455-463, http://dx.doi.org/10.1016/j.nima.2005.04.062, URL http://www.sciencedirect.com/science/article/pii/S0168900205010508.

[32] S. Paschalis, I. Lee, A. Macchiavelli, C. Campbell, M. Cromaz, S. Gros, J. Pavan, J. Qian, R. Clark, H. Crawford, D. Doering, P. Fallon, C. Lionberger, T. Loew, M. Petri, T. Stezelberger, S. Zimmermann, D. Radford, K. Lagergren, D. Weisshaar, R. Winkler, T. Glasmacher, J. Anderson, C. Beausang, The performance of the gamma-ray energy tracking in-beam nuclear array gretina, Nucl. Instrum. Methods Phys. Res. A 709 (2013) 44-55, http://dx.doi.org/10.1016/j.nima.2013.01.009, URL http://www.sciencedirect.com/science/article/pii/S0168900213000508.

[33] F. Recchia, D. Bazzacco, M. Bellato, D. Borolato, E. Farnea, D. Mengoni, Efficency and Energy Resolution of the Agata Demonstartor at High Count Rate, Tech. rep. LNL, 2010.
7.11 Pulseshape calculations using the AGATAGeFEM
code and applications

UNDER EDITING
# Pulseshape calculations using the AGATAGeFEM code and applications

J. Ljungvall¹

CSNSM, Univ Paris-Sud, CNRS/IN2P3, F-91405 Orsay, France

**Abstract.** A code, AGATAGeFEM, that models segmented High-purity Gemernium detectors is presented. It is discussed how the geometry is implemented, and how the electric and weighting fields are calculted. Further more are the models used for charge carrier velocity described and the solution for charge-carrier transport is shown. To code allows simple application of electroical response functions and linear and differential cross-talk. As an example of application the code is used to investigate the impact of noise and cross-talk on the achivied position resolution in AGATA detectors.

**PACS.** 21.10.Tg In-beam γ-ray spectroscopy

## 1 Introduction

In nuclear-structure physics, as in many other fields of research, the development of better instrumentation and the discoveries of new physics have been closely linked. One of the most powerful techniques to study atomic nuclei is and have been that of gamma-ray spectroscopy combined with in-beam production of the species of interest. However, the present stable-beam facilities using classical gamma-ray spectrometers based on Compton suppressed germanium detectors, such as EUROBALL [1] and GAMMASPHERE [2], have severe limitations as the nuclear physics community explores the atomic nuclei under more and more extreme conditions. In order too overcome these limitations several radioactive beam facilities are under construction, or have recently been constructed, in the world, e.g., Spiral2, FAIR, RIKEN, FRIB and HEISOLDE. High intensity stable beams are also foreseen for the future. To maximize the return in terms of physics on these investments the detection systems also need to be improved. They need to be more efficient, have higher resolving power and withstand higher counting rates. For gamma-ray spectrometers the answer to these demands lie in co called gamma-ray tracking arrays. During the last decade the gamma-ray spectroscopy community has been deeply involved in the development of two gamma-ray tracking arrays, AGATA [3], and GRETA [4].

The use of digital electronics combined pulse-shape analysis (PSA) with will allow an increase of the solid angle covered by germanium and in the maximum count rate for each germanium crystal. This without a better peak-to-total and higher efficiency. The main characteristics of these spectrometers are the lack of Compton suppression shields, which has been replaced with gamma-ray tracking: The track of the gamma-ray through the arrays

is reconstructed using interaction points given by pulse-shape analysis. For this method to be efficient and have a high probability to reject tracks from gamma-rays that were not fully absorbed it is crucial that the pulse-shape analysis giving the interaction positions and energies are accurate. The accuracy of the PSA will depend of how well the detector response is determined, and to a lesser degree to the algorithm used for the PSA. The characterisation of the used HPGe detectors are hence of great importance, and represents at the same time a difficult problem. In this paper a computer code written to model the 36 times segmented HPGe germanium detectors used in AGATA and GRETA will be described, together with the application of this code to the problem of detector characterisation and pulse-shape analysis.

Extensive work has been done to model the response of these highly segmented germanium detectors.

We will begin with describing the AGATAGeFEM code and the models and assumptions made in section 4. The use of the code to benchmark the effect of cross talk and noise for on two pulse-shape algorithms covered in section 6. Finally, conclusions will be drawn in section 7.

## 2 A short introduction to the generation of pulse shapes in semiconductor detectors

The pulse-shape formation in any detector based on the motion of charge carriers can be calculated using the Shockley-Ramo theorem [5, 6], which states that the induced charge on an electrode due to moving charges can be calculated as

$$ \frac{dQ(t)}{dt} = e [N_h v_h(r_h) \cdot W(r_h) - N_e v_e(r_e) \cdot W(r_e)] \quad (1) $$
where $W(\mathbf{r}_{e,h}) = -\nabla\Phi_W(\mathbf{r}_{e,h})$ is the weighting field, $N_{e,h}$ are the number of charge carriers for electrons and holes, and $v_{e,h}(\mathbf{r}_{e,h})$ are the charge carrier velocities, which are functions of the electric field $E(\mathbf{r})$. The electric field is calculated from the electric potential as $E(\mathbf{r}) = -\nabla\Phi(\mathbf{r})$. Since the electric and weighting fields are two fundamental quantities, the calculation of pulse shapes for any semiconductor detector begins with solving the two differential equations

$$ \nabla^2 \Phi(\mathbf{r}) = - \frac{\rho(\mathbf{r})}{\epsilon_{Ge}} \qquad (2) $$

and

$$ \nabla^2 \Phi_W(\mathbf{r}) = 0 \qquad (3) $$

known as the Poisson and Laplace equations. They describe the electric and weighting potentials, respectively. In equation 2, $\rho(\mathbf{r})$ is the free charge distribution in the detector and $\epsilon_{Ge}$ the dielectric constant for germanium. The weighting potential $\Phi_W(\mathbf{r})$ is not an electric potential but a “tool”\ used to calculate the current on the collecting electrode. It is calculated by setting it to one on the collecting electrode and zero on all other contacts and then solving the Laplace equation.

One of the major difficulties one trying to solve equation 1 is to find the correct dependence for the charge carrier velocities $v_{e,h}(\mathbf{r}_{e,h})$ as a function of the electric field $E(\mathbf{r})$. For detector cold to liquid nitrogen temperatures operating with electric field in the order of $10^5$ V/m the charge carriers will no longer follow a trajectory parallel to the electric field, this due to the anisotropy of the charge carrier velocity. The physics and the models used in this work will be discussed in section 3.

The final part of producing a realistic detector response it the application of a filter to reproduce the effects of the limited band with of the electronics and other effects such as electronic cross talk. This could in principle be done by measuring the response of the system using a pulse generator. Such an approach is however often not practical since single germanium crystals can be used with different electronics. It is often sufficient and always more practical to approximate the true response of the electronics with analytical function.

## 3 Charge carrier motion in high purity germanium detectors

Several models are developed for carrier mobilities in germanium crystals cooled down to liquid nitrogen temperatures (≈ -175° Celsius). For the electrons the model of Nathan [7] as described by Mihailescu [8] is used in this work. This model describes the anisotropy of the electron drift velocity observed in germanium with high accuracy, and is used to model the drift of electrons in AGATAGeFEM.

Crucial for all pulse shape calculations are good models for the charge carrier velocities as a function of the electric field. A commonly used function [9] to describe the charge carrier velocity is

$$ \mathbf{v}(\mathbf{r}) = \frac{\mu_0 \mathbf{E}(\mathbf{r})}{(1 + (E(\mathbf{r})/E_0)^\gamma)^{1/\gamma}} - \mu_n \mathbf{E}(\mathbf{r}), \qquad (4) $$

where $E_0$, $\gamma$, $\mu_n$, and $\mu_0$ are experimentally adjusted parameters. This parametrision is valid when the electric field is parallel to one of the symmetry axes <100>, <110> or <111>. In all other cases the charge carrier velocity will not be parallel to the electric field (the apparent breaking of the conservation of momentum is absorbed by crystal). For the hole mobility B. Bruyneel et al. [10] have developed a model based on the so-called "streaming motion" concept where the holes are accelerated to a threshold energy where the holes emit an optical phonon, losing most of its energy, and is then re-accelerated in the applied electric field to the threshold energy and so on. In this work however, another model based on the assumption that the variation in carrier velocity as a function of the electric field can be described by the fraction of holes populating the light-hole band and the heavy-hole band and a field dependent relaxation time. The anisotropy is given by the effective masses being the second derivative of the energy of the hole bands. While not completely founded to the much higher energy of the light compared to the heavy hole band, this model do reproduce experimental data for hole drift velocities. For holes the surfaces of equal energy in the conduction bands are not ellipsoids, which means that the reciprocal effective mass tensor will depend on the direction of the wave vector $\mathbf{k}$. Here the assumption was made that the wave vector is parallel to the applied electric field. The hole energy functions are [11]

$$ \epsilon_h(k) = Ak^2 \pm [B^2k^4 + C^2(k_x^2k_y^2 + k_y^2k_z^2 + k_z^2k_x^2)]^{1/2} \quad (5) $$

where the positive (negative) sign is for the light (heavy) hole band. Using equation

$$ \left(\frac{1}{m^*}\right)_{\mu\nu} = \frac{1}{\hbar^2} \frac{d^2\epsilon(k)}{dk_\mu dk_\nu} \equiv \bar{\Gamma} \qquad (6) $$

to calculate the reciprocal effective mass tensor, we have

$$ v_h = q\mathcal{T}(E) \left[ \mathcal{F}(E) \bar{\Gamma}_h^{\text{heavy}} + (1 - \mathcal{F}(E)) \bar{\Gamma}_h^{\text{light}} \right] \mathbf{E}. \quad (7) $$

Comparing equation 7 with

$$ \mathbf{v} = qt\bar{\Gamma}\mathbf{E}, \qquad (8) $$

the factor $\mathcal{T}(E)$ in the latter equation corresponds to $t$ in the former and should thus be considered an electric-field dependent relaxation time. $\mathcal{F}(E)$ is the fraction of the holes moving in the heavy hole band and it is also assumed to be field dependent. Equation 4 can now, as in the case for electrons, be used to calculate the hole drift velocities in the <100> and <111> directions. Using these velocities one can solve for $\mathcal{T}(E)$ and $\mathcal{F}(E)$ for
the electric-field strength in question. A big difference for
holes as compared to electrons is that the reciprocal effec-
tive mass tensor now will change as the direction of the
electric field changes. In figure 1 the anisotropy of charge
carrier transport is illustrated. Here a deficiency of the
model can be noted looking at the $v_{\phi}^h$ shown in the bot-
tom right corner. There should be no anisotropy in any of
the <100>, <110>, or <111> directions as they are sym-
metry axis in germanium, as is the case for the electrons
shown in the left column. If there has been no anisotropy
the top row would have shown perfect spheres in one color
and the second and third row have shown zero velocities.
It should be noted that nor the drift model for electrons
nor for holes tries to model the effects of crystal tempera-
ture or impurity concentrations on the charge carrier drift
velocities although these effects do modify the drift ve-
locity [12]. The effect of varying the hole drift velocities
have been studied within the GRETINA collaboration [13]
where it was concluded that for the moment the position
resolution is not limited by how the hole mobility is mod-
eled.

<figure><img src="image_138.png" /><figcaption>**Fig. 1.** Plot of charge carrier velocities as a function of the direction of the electric field. The column to the right is for electrons whereas the column to the right is for holes. The three rows show the $\hat{r}$, $\hat{\theta}$, $\hat{\phi}$ components of the velocities, respectively.</figcaption></figure>

## 4 The AGATAGeFEM code

There are several codes and program packages that have
been developed to calculate pulse shapes from HPGe de-
tectors such as the detector elements that build up AGATA.
Some examples are MGS [14], JASS [15, 15, 16] and ADL
[17, 10, 18]. Although they differ in details they all have in
common that they use methods based on finite difference
to solve the partial differential equations (Laplace equa-
tion) needed to calculate the electric field in the detector
and the weighting potentials used to calculate the pulse
shapes from the different electrodes of the detector. How-
ever, the complex shapes of the AGATA crystals does not

allow for an exact reproduction of their geometry using
a finite difference scheme. This is a problem that can be
circumvented using finite element methods (FEM). It is
not within the scope of this paper to describe FEM, and
we refer to [19] and references therein.

AGATAGeFEM is an effort to use FEM to calculate
the electric and weighting potentials of AGATA type ger-
manium detectors, relying heavily on high quality open
source software. The program is written in C++ and lever-
age quite heavily both object orientation and the template
features of C++ (but very little C++11). For charge car-
rier transport the ordinary differential equation solvers of
the Gnu Scientific Library [20] were chosen. The geome-
try is described to machine precision for charge transport
and mesh generation. Earlier versions of the program used
mainly a library called dealii [21,22]. This is a very flex-
ible code that allows an iterative refinement of the FEM
mesh in a very simple way. However, the mesh cell geom-
etry is limited to quadrilaterals and hexahedra. This is
from solving the partial differential equations very good
choices. However, as I not want to project down the solu-
tions to a regular grid when using them in charge carrier
transport process and calculations of the induced signals
via the Shockley-Ramo theorem. Laying behind this is the
idea that the refinement procedure tells where high gran-
ularity is needed and all projection to regular grid deteri-
orates this information. The problem is then that to find
the correct cell in an irregular mesh requires at some point
to ask cells if a points belongs to them and hexahedra
cells have boundaries that are curved making these cal-
culations quite complicated. As a result the first version
of AGATAGeFEM was capable of calculating about 2-3
pulse shapes/s. While this is enough to calculate a basis
for use with PSA it is far from enough for using the code in
fitting of parameters used in the pulse shape calculations
or to use it in a complete Monte Carlo simulation chain. I
therefore moved the FEM part of the program into using
the libmesh library [23]. It uses tetrahedra with each side
defined by three points making the calculation whether a
point is inside a cell or not much faster. I further more
restrained to the use of only linear basis function in the
solution. This way the code reproduced the results from
before but a factor of almost 100 faster.

Other features of the AGATAGeFEM is that it is fully
parallelized using both threads and the MPI interface to
allow field calculations as well as for pulse-shape calcula-
tions and for fitting the parameters that enter into pulse-
shape calculations using $\chi^2$ fitting based on the Minuit
and Minuit2 [24] that comes with ROOT [25]. It further
has an interface allowing calculating both fields and pulses
and displaying these inside the chosen detector geometry
from the ROOT interpreter interface (the cint and cling in-
terpreter). It has further a very simple server client mecha-
nism allowing other programs to ask the server to calculate
pulse shapes for it.

There further exists needed miscellaneous codes for
applying pre-amplifier response (defined in time domain),
cross talk, to re-sample pulse shapes, compare pulse shapes,
calculate pulse shapes from the output of the Agata geant4 MC [26] etc.

## 4.1 AGATA Detector model

### 4.1.1 Geometry

The AGATA crystals are 90 mm long and have an diameter of 80 mm. They have been produced in four different shapes. Symmetric hexagonal prototypes and three different non-symmetric hexagonal shapes for use in the AGATA. The non-symmetric shapes are needed to be able to close pack the crystals in an spherical geometry. For details of the AGATA crystal geometries, see [3]. In figure 2 the geometry of a "A" type AGATA crystal is shown. For the generation of the FEM mesh OpenCASCADE models of the detectors where generated whereas for the charge transportation the detector geometries where implemented in C++ as the union of a cylinder and six planes or using the CSG geometry of geant4 [27]. The hole corresponding to the core contact was modeled with the possibility of changing the radius of at the bottom of the hole. The two different geometrical models of the detectors are equivalent, and both flexible enough to allow off-centered bore holes, bore holes with angles, etc if this would have to be tested. Examples of the geometry are shown in figures 3 and 4.

### 4.1.2 Calculations of the electric fields and weighting fields

AGATAGeFEM uses a total of 40 fields when calculating the pulse shapes. The first 37 corresponds to the weighting fields for the 36 segments and the core. These are, expect for the central contact which is trivial, defined either using the limiting depth values and start and stop angle or using the intersection between the detector surface and four planes. The segments to not have to cover the hole surface of the detector, but presently no implementation of suitable boundary conditions for the electric field calculations are present in the code limiting the value of this option.

To calculate the electric field while solving the charge transport equations AGATAGeFEM uses three fields. The first one is the solution to the Laplace equation with 0 V on the surface of the detector and $V_{bias}$ V on the central contact. The second one is the solution of the Poisson equation assuming $(\partial 0) / \partial n$ V on both the surface and the central contact but with an impurity contribution of 1 at the front of the detector that decreases linearly as a function of depth to the back of the detector. The third and final field is like the second but reversing the slope of the impurity concentration. This allows varying the effective impurity concentration and its effect on the electric field in the detector without recalculating the fields, important when trying to fit detector parameters to experimental signals.

For solving the Laplace equation and the Poisson equation AGATAGeFEM uses the libmesh library [23].

### 4.1.3 Solving the charge transport equation

The detector pulses are calculated by first transporting the point representing electrons and the point representing holes from the point of origin using

$$ \frac{dr_{e,h}}{dt} = v_{e,h}(E). \qquad (9) $$

This pair of equations are solved separately for the holes and the electrons using a solver algorithm with an adaptive time step. The program AGATAGeFEM allows the user to choose between any of the possible algorithms provided by GSL, but the default choice is that of the embedded Runge-Kutta Prince-Dormand method. The paths of the electrons and the paths are sampled at a given frequency, by default a timestep of 1 ns is used. As the charge carriers approaches the boundary of the detector this time step is adapted to allow an accurate description of the pulse shapes.

In the next step the charge on electrode i is calculated using

$$ Q_i(t) = q(\Phi_W^i(r_e(t)) - \Phi_W^i(r_h(t))) \qquad (10) $$

for all 37 signals. It should be noted that the core signal has the opposite polarity of the segment signals and that the sum of all signals should be identical to zero.

### 4.1.4 Convoluting with response function

The signals can be optionally be convoluted with the response of the electronics. In this work the response of the electronics have been modeled by convoluting the calculated signals with the function shown (in time-domain) in figure 5. The effect of so-called crosstalk, both linear and differential, can also be included in the response function if needed. For in-depth discussion concerning crosstalk in segmented germanium detectors, see [28,29]. An example of the signals calculated with and without response function is given in figure 6. The effect of linear and derivative cross talk is also shown.

## 5 Scan of parameter sensitivity

In order to understand the impact of different parameters that enter into the calculations of pulse shapes the sensitivity of the pulse shapes to each parameter was calculated for a large number of points inside a detector. In figure 7 the extraction of the sensitivity which is defined as the second derivative of the square sum of the difference between a reference pulse and the a pulse calculated with a parameter changed a fraction.

In figure 8 is shown at how many positions in the detector that each parameter has the largest sensitivity. It can be seen that at most points it is the parameters that parameterise the velocity of the charge carriers in the <100> direction that is dominating. Looking at figure 9 one can
notice however that the highest average sensitivity for the dominating positions is found for the crystal orientation followed by the parameterization of the hole mobility in the <111> direction. This would suggest that these parameters are most likely to make a signal change "net-charge segment". In figure 10 the sensitivity as a function of position in the detector volume is shown for the $\mu_e^{<100>}$ parameter. It is quite homogeneous inside the volume although the projection on the XY plane shows that, apart from the volume effect, is an increase in sensitivity close to the <100> directions. This is normal as the parameterization of the charge carrier velocity only depends on parameters corresponding to that direction. A similar pattern can be seen for the $\mu_h^{<100>}$ parameter in figure 11, but with the maximum shifted towards lower radii corresponding to pulses in which the hole drift contributes more to the pulse shapes. For the parameters $\mu_e^{<111>}$ and $\mu_h^{<111>}$, shown in figures 12 and 13 the situation is a bit different. For the electrons the pattern is what can be expected, i.e. parameters concerning the <111> direction show sensitivity in the region where charge transport is parallelle to the <111> direction. For the holes the situation seems less clear. The pattern is not reflecting the <111> direction in the crystal. This is not needed in the model as it, unlike the model for the electrons, do not impose that the charge carriers when the electric field is parallel to a symmetry axis are moving parallel with the axis, which by symmetry arguments has to be wrong. This can also be seen in figure 1 where the $\phi$ component of the hole velocity is non zero in the xy-plane <100> directions. It is based on this clear that the hole velocity model used should be changed for future work as comparisons with experimental in order to fit parameters would be difficult.

## 6 Evaluation of effects of cross talk and noise for different PSA using Monte Carlo simulation data

Using the code AGATAGeFEM the resolution for Grid-search methods and the Singular Value Decomposition methods as a function of noise and inclusion of differential and linear crosstalk have also been investigated. Assuming that the detector physics of a segmented germanium detector is well known, the problem of determining the coordinates of an $\gamma$-ray interaction in a large volumes HPGe detector dependence closely on the knowledge of the response of the electronics and on the signal-to-noise ratio. These two aspects have been studies by performing PSA on a dataset calculated using the same code as that used to calculate the reference dataset of pulse shapes used by the PSA code. On this reference set of shapes different amount of noise have been added. Each position where then analysed 20 times, each time with different noise added. Also added are linear and differential crosstalk. This have been done both for the gridsearch method and for the matrix method [30]. The results are summarized in table 1. It should be noticed that according to this work the crosstalk has a very limited influence on the resolution, neither on

the average reconstructed position nor by introducing systematic errors. In figures 14 and 15 two-dimensional projections of the by the two different PSA algorithms determined interaction positions are shown. For both cases both linear and differential crosstalk have been included in the simulated events but not in the database used for the PSA. Looking at figure 14 and 15 a striking difference shows up for large noises. The gridsearch algorithm tends to cluster points towards the segment boundaries whereas the matrix method seems to move the points towards the most likely point, i.e. the barycenter of the segment.

In the work by Söderström et al. [31], the experimental position resolution has been investigated as a function of the energy deposited at the interaction point. Data from the work of Söderström et al. work is presented together with the result of pulse shape analysis performed on simulated traces done with-in the scope of this work in figure 17. It is interesting to note that the extensive gridsearch is doing better on simulated data than what has been experimentally for energies above about 50 keV whereas the Matrix inversion using SVD decomposition to suppress increase the signal-to-noise ratio is performing better at very low interaction energies.

## 7 Conclusions

A C++ based code called AGATAGeFEM aimed at modeling segmented high-purity detectors has been developed. It allows the implementation of the detector geometry and segmentation schemes to with in machine precision and uses state-of-the-art Finite Element Methods to solve the Laplace and Poisson equations. The resulting fields are calculated using the basis functions and support points of the actual FEM grid, i.e. function evaluation rather than interpolation.

The charge transport equations are solved using time adaptive Runge-Kutta methods from the GNU Scientific Libraray. To the induced charge signals linear and differential cross talk is added together with the preamplifier response function modeled in time domain. The model use in AGATAGeFEM for hole charge carrier velocity has to be improved.

As an example of applications AGATAGeFEM is used to invesitgate the impact of cross talk and noise for the grid search pulse shape method and for the SVD PSA method. The result suggest that cross talk at the level of what is found in AGATA has no real impact on the result of the PSA.

## Acknowledgement

The author would like to thank the AGATA collaboration.

## References

1. J. Simpson, The euroball spectrometer, Zeitschrift für Physik A Hadrons and Nuclei 358 (2) (1997) 139–143.
<table><caption>**Table 1.** Full width at half maximum for different amount of noise for an inclusive gridsearch on a 1x1x1 mm³ basis and using the SVD matrix method with the same basis.</caption><thead><tr><th colspan="2">No crosstalk</th><th colspan="2"></th></tr><tr><th>Noise</th><th></th><th>GS [mm]</th><th></th></tr><tr><th>[% rms]</th><th>Δx</th><th>Δy</th><th>Δz</th></tr></thead><tbody><tr><td>0.6</td><td>1.3</td><td>1.4</td><td>1.3</td></tr><tr><td>3.1</td><td>2.4</td><td>2.5</td><td>2.4</td></tr><tr><td>6.1</td><td>4.2</td><td>4.7</td><td>4.2</td></tr><tr><td>12</td><td>8.8</td><td>10</td><td>8.9</td></tr><tr><td>18</td><td>13</td><td>14</td><td>13</td></tr><tr><td>37</td><td>20</td><td>19</td><td>17</td></tr><tr><th colspan="2"></th><th>SVD [mm]</th><th></th></tr><tr><th></th><th>Δx</th><th>Δy</th><th>Δz</th></tr><tr><td>0.6</td><td>2.4</td><td>2.5</td><td>1.8</td></tr><tr><td>3.1</td><td>5.5</td><td>5.7</td><td>4.2</td></tr><tr><td>6.1</td><td>7.5</td><td>7.8</td><td>5.9</td></tr><tr><td>12</td><td>10</td><td>10</td><td>8.4</td></tr><tr><td>18</td><td>12</td><td>12</td><td>10</td></tr><tr><td>37</td><td>16</td><td>16</td><td>13</td></tr><tr><th colspan="2">Full crosstalk</th><th colspan="2"></th></tr><tr><th>Noise</th><th></th><th>GS [mm]</th><th></th></tr><tr><th>[% rms]</th><th>Δx</th><th>Δy</th><th>Δz</th></tr><tr><td>0.6</td><td>1.4</td><td>1.4</td><td>1.3</td></tr><tr><td>3.1</td><td>2.4</td><td>2.5</td><td>2.4</td></tr><tr><td>6.1</td><td>4.3</td><td>4.7</td><td>4.2</td></tr><tr><td>12</td><td>8.8</td><td>10</td><td>8.9</td></tr><tr><td>18</td><td>13</td><td>14</td><td>13</td></tr><tr><td>37</td><td>20</td><td>20</td><td>17</td></tr><tr><th colspan="2"></th><th>SVD [mm]</th><th></th></tr><tr><th></th><th>Δx</th><th>Δy</th><th>Δz</th></tr><tr><td>0.6</td><td>2.8</td><td>2.8</td><td>2.0</td></tr><tr><td>3.1</td><td>5.5</td><td>5.7</td><td>4.3</td></tr><tr><td>6.1</td><td>7.4</td><td>7.7</td><td>5.9</td></tr><tr><td>12</td><td>10</td><td>10</td><td>8.4</td></tr><tr><td>18</td><td>12</td><td>12</td><td>10</td></tr><tr><td>37</td><td>16</td><td>16</td><td>13</td></tr></tbody></table>

doi:10.1007/s002180050290.
URL http://dx.doi.org/10.1007/s002180050290

2. M. A. Deleplanque, R. M. e. Diamond, 1987 gammasphere proposal preprint lbnl-5202, Tech. rep., LBNL (1987).

3. S. Akkoyun, A. Algora, B. Alikhani, F. Ameil, G. de Angelis, L. Arnold, A. Astier, A. Ataç, Y. Aubert, C. Aufranc, A. Austin, S. Aydin, F. Azaiez, S. Badoer, D. Balabanski, D. Barrientos, G. Baulieu, R. Baumann, D. Bazzacco, F. Beck, T. Beck, P. Bednarczyk, M. Bellato, M. Bentley, G. Benzoni, R. Berthier, L. Berti, R. Beunard, G. L. Bianco, B. Birkenbach, P. Bizzeti, A. Bizzeti-Sona, F. L. Blanc, J. Blasco, N. Blasi, D. Bloor, C. Boiano, M. Borsato, D. Bortolato, A. Boston, H. Boston, P. Bourgault, P. Boutachkov, A. Bouty, A. Bracco, S. Brambilla, I. Brawn, A. Brondi, S. Broussard, B. Bruyneel, D. Bucurescu, I. Burrows, A. Bürger, S. Cabaret, B. Cahan, E. Calore, F. Camera, A. Capsoni, F. Carrió, G. Casati, M. Castoldi, B. Cederwall, J.-L. Cercus, V. Chambert, M. E. Chambit, R. Chapman, L. Charles, J. Chavas, E. Clément, P. Cocconi, S. Coelli, P. Coleman-Smith, A. Colombo, S. Colosimo, C. Commeaux, D. Conventi, R. Cooper, A. Corsi, A. Cortesi,

L. Costa, F. Crespi, J. Cresswell, D. Cullen, D. Curien, A. Czermak, D. Delbourg, R. Depalo, T. Descombes, P. Désesquelles, P. Detistov, C. Diarra, F. Didierjean, M. Dimmock, Q. Doan, C. Domingo-Pardo, M. Doncel, F. Dorangeville, N. Dosme, Y. Drouen, G. Duchêne, B. Dulny, J. Eberth, P. Edelbruck, J. Egea, T. Engert, M. Erduran, S. Ertürk, C. Fanin, S. Fantinel, E. Farnea, T. Faul, M. Filliger, F. Filmer, C. Finck, G. de France, A. Gadea, W. Gast, A. Geraci, J. Gerl, R. Gernhäuser, A. Giannatiempo, A. Giaz, L. Gibelin, A. Givechev, N. Goel, V. González, A. Gottardo, X. Grave, J. Grebosz, R. Griffiths, A. Grint, P. Gros, L. Guevara, M. Gulmini, A. Görgen, H. Ha, T. Habermann, L. Harkness, H. Harroch, K. Hauschild, C. He, A. Hernández-Prieto, B. Hervieu, H. Hess, T. Hüyük, E. Ince, R. Isocrate, G. Jaworski, A. Johnson, J. Jolie, P. Jones, B. Jonson, P. Joshi, D. Judson, A. Jungclaus, M. Kaci, N. Karkour, M. Karolak, A. Kaşkaş, M. Kebbiri, R. Kempley, A. Khaplanov, S. Klupp, M. Kogimtzis, I. Kojouharov, A. Korichi, W. Korten, T. Kröll, R. Krücken, N. Kurz, B. Ky, M. Labiche, X. Lafay, L. Lavergne, I. Lazarus, S. Leboutelier, F. Lefebvre, E. Legay, L. Legeard, F. Lelli, S. Lenzi, S. Leoni, A. Lermitage, D. Lersch, J. Leske, S. Letts, S. Lhenoret, R. Lieder, D. Linget, J. Ljungvall, A. Lopez-Martens, A. Lotodé, S. Lunardi, A. Maj, J. van der Marel, Y. Mariette, N. Marginean, R. Marginean, G. Maron, A. Mather, W. Meczyński, V. Mendéz, P. Medina, B. Melon, R. Menegazzo, D. Mengoni, E. Merchan, L. Mihailescu, C. Michelagnoli, J. Mierzejewski, L. Milechina, B. Million, K. Mitev, P. Molini, D. Montanari, S. Moon, F. Morbiducci, R. Moro, P. Morrall, O. Möller, A. Nannini, D. Napoli, L. Nelson, M. Nespolo, V. Ngo, M. Nicoletto, R. Nicolini, Y. L. Noa, P. Nolan, M. Norman, J. Nyberg, A. Obertelli, A. Olariu, R. Orlandi, D. Oxley, C. Özben, M. Ozille, C. Oziol, E. Pachoud, M. Palacz, J. Palin, J. Pancin, C. Parisel, P. Pariset, G. Pascovici, R. Peghin, L. Pellegri, A. Perego, S. Perrier, M. Petcu, P. Petkov, C. Petrate, E. Pierre, N. Pietralla, S. Pietri, M. Pignanelli, I. Piqueras, Z. Podolyak, P. L. Pouhalec, J. Pouthas, D. Pugnère, V. Pucknell, A. Pullia, B. Quintana, R. Raine, G. Rainovski, L. Ramina, G. Rampazzo, G. L. Rana, M. Rebeschini, F. Recchia, N. Redon, M. Reese, P. Reiter, P. Regan, S. Riboldi, M. Richer, M. Rigato, S. Rigby, G. Ripamonti, A. Robinson, J. Robin, J. Roccaz, J.-A. Ropert, B. Rossé, C. R. Alvarez, D. Rosso, B. Rubio, D. Rudolph, F. Saillant, E. Sahin, F. Salomon, M.-D. Salsac, J. Salt, G. Salvato, J. Sampson, E. Sanchis, C. Santos, H. Schaffner, M. Schlarb, D. Scraggs, D. Seddon, M. Şenyiğit, M.-H. Sigward, G. Simpson, J. Simpson, M. Slee, J. Smith, P. Sona, B. Sowicki, P. Spolaore, C. Stahl, T. Stanios, E. Stefanova, O. Stézowski, J. Strachan, G. Suliman, P.-A. Söderström, J. Tain, S. Tanguy, S. Tashenov, C. Theisen, J. Thornhill, F. Tomasi, N. Toniolo, R. Touzery, B. Travers, A. Triossi, M. Tripon, K. Tun-Lanoë, M. Turcato, C. Unsworth, C. Ur, J. Valiente-Dobon, V. Vandone, E. Vardaci, R. Venturelli, F. Veronese, C. Veyssiere, E. Viscione, R. Wadsworth, P. Walker, N. Warr, C. Weber, D. Weisshaar, D. Wells, O. Wieland, A. Wiens, G. Wittwer, H. Wollersheim, F. Zocca, N. Zamfir, M. Ziebliński, A. Zucchiatti, Agata-advanced {GAmma} tracking
array, Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Det-
tectors and Associated Equipment 668 (2012) 26 – 58.
doi:http://dx.doi.org/10.1016/j.nima.2011.11.081.
URL http://www.sciencedirect.com/science/
article/pii/S0168900211021516

4. I. Y. Lee, M. A. Deleplanque, K. Vetter, Developments in large gamma-ray detector arrays, Reports on Progress in Physics 66 (7) (2003) 1095.
URL http://stacks.iop.org/0034-4885/66/i=7/a=201

5. S. Ramo, Proc. IRE 27 (1939) 584.

6. W. Shockley, J. Appl. Phys. 9 (1938) 635.

7. M. I. Nathan, Anisotropy of the conductivity of n-type germanium at high electric fields, Phys. Rev. 130 (1963) 2201-2204. doi:10.1103/PhysRev.130.2201.
URL http://link.aps.org/doi/10.1103/PhysRev.130.2201

8. L. Mihailescu, W. Gast, R. Lieder, H. Brands, H. Jäger, The influence of anisotropic electron drift velocity on the signal shapes of closed-end {HPGe} detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 447 (3) (2000) 350 – 360. doi:http://dx.doi.org/10.1016/S0168-9002(99)01286-3.
URL http://www.sciencedirect.com/science/article/pii/S0168900299012863

9. G. Knoll, Radiation Detection and Measurement, Wiley, 2000.

10. B. Bruyneel, P. Reiter, G. Pascovici, Characterization of large volume {HPGe} detectors. part i: Electron and hole mobility parameterization, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 569 (3) (2006) 764 – 773. doi:http://dx.doi.org/10.1016/j.nima.2006.08.130.
URL http://www.sciencedirect.com/science/article/pii/S0168900206015166

11. C. Kittel, Introduction to Solid State Physics, Wiley, 1996.
URL https://books.google.fr/books?id=1X8pAQAAMAAJ

12. H. Mei, D.-M. Mei, G.-J. Wang, G. Yang, The impact of neutral impurity concentration on charge drift mobility in p-type germanium, Journal of Instrumentation 11 (12) (2016) P12021-P12021. doi:10.1088/1748-0221/11/12/p12021.
URL https://doi.org/10.1088%2F1748-0221%2F11%2F12%2Fp12021

13. V. Prasher, M. Cromaz, E. Merchan, P. Chowdhury, H. Crawford, C. Lister, C. Campbell, I. Lee, A. Macchiavelli, D. Radford, A. Wiens, Sensitivity of gretina position resolution to hole mobility, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 846 (2017) 50 – 55. doi:https://doi.org/10.1016/j.nima.2016.11.038.
URL http://www.sciencedirect.com/science/article/pii/S0168900216311925

14. [link].
URL http://www.iphc.cnrs.fr/-MGS-.html

15. M. Schlarb, R. Gernhäuser, S. Klupp, R. Krücken, Pulse shape analysis for γ-ray tracking (part i): Pulse shape simulation with jass, The European Physical Journal A

47 (10) (2011) 132. doi:10.1140/epja/i2011-11132-2.
URL http://dx.doi.org/10.1140/epja/i2011-11132-2

16. M. Schlarb, R. Gernhäuser, R. Krücken, Simulation and real-time analysis of pulse shapes from hpge detectors, Tech. rep. (2008).

17. B. Bruyneel, B. Birkenbach, P. Reiter, Pulse shape analysis and position determination in segmented hpge detectors: The agata detector library, The European Physical Journal A 52 (3) (2016) 1–11. doi:10.1140/epja/i2016-16070-9.
URL http://dx.doi.org/10.1140/epja/i2016-16070-9

18. B. Bruyneel, B. Birkenbach, P. Reiter, Pulse shape analysis and position determination in segmented hpge detectors: The agata detector library, The European Physical Journal A 52 (3) (2016) 70. doi:10.1140/epja/i2016-16070-9.
URL http://dx.doi.org/10.1140/epja/i2016-16070-9

19. S. C. Brenner, L. R. Scott, The Mathematical Theory of Finite Element Methods, 2nd Edition, Vol. 15 of Texts in Applied Mathematics, Springer, 2002.

20. G. P. Contributors, GSL - GNU scientific library - GNU project - free software foundation (FSF), http://www.gnu.org/software/gsl/ (2010) [cited 2010-06-20 22:49:12].
URL http://www.gnu.org/software/gsl/

21. W. Bangerth, R. Hartmann, G. Kanschat, deal.II – a general purpose object oriented finite element library, ACM Trans. Math. Softw. 33 (4) (2007) 24/1–24/27.

22. G. Alzetta, D. Arndt, W. Bangerth, V. Boddu, B. Brands, D. Davydov, R. Gassmoeller, T. Heister, L. Heltai, K. Kornmann, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin, D. Wells, The deal.II library, version 9.0, Journal of Numerical Mathematics 26 (4) (2018) 173–183. doi:10.1515/jnma-2018-0054.

23. B. S. Kirk, J. W. Peterson, R. H. Stogner, G. F. Carey, libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations, Engineering with Computers 22 (3-4) (2006) 237-254, http://dx.doi.org/10.1007/s00366-006-0049-3.

24. M. Hatlo, F. James, P. Mato, L. Moneta, M. Winkler, A. Zsenei, Developments of mathematical software libraries for the lhc experiments, IEEE Transactions on Nuclear Science 52 (6) (2005) 2818-2822. doi:10.1109/TNS.2005.860152.

25. I. Antcheva, M. Ballintijn, B. Bellenot, M. Biskup, R. Brun, N. Buncic, P. Canal, D. Casadei, O. Couet, V. Fine, L. Franco, G. Ganis, A. Gheata, D. G. Machine, M. Goto, J. Iwaszkiewicz, A. Kreshuk, D. M. Segura, R. Maunder, L. Moneta, A. Naumann, E. Offermann, V. Onuchin, S. Panacek, F. Rademakers, P. Russo, M. Tadel, Root — a c++ framework for petabyte data storage, statistical analysis and visualization, Computer Physics Communications 180 (12) (2009) 2499 – 2512, 40 YEARS OF CPC: A celebratory issue focused on quality software for high performance, grid and novel computing architectures. doi:https://doi.org/10.1016/j.cpc.2009.08.005.
URL http://www.sciencedirect.com/science/article/pii/S0010465509002550

26. E. Farnea, F. Recchia, D. Bazzacco, T. Kröll, Z. Podolyák, B. Quintana, A. Gadea, Conceptual design and monte carlo simulations of the {AGATA} array, Nuclear
Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 621 (1-3) (2010) 331 – 343.
doi:http://dx.doi.org/10.1016/j.nima.2010.04.043.
URL http://www.sciencedirect.com/science/article/pii/S0168900210008922

27. S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce, M. Asai, D. Axen, S. Banerjee, G. Barrand, F. Behner, L. Bellagamba, J. Boudreau, L. Broglia, A. Brunengo, H. Burkhardt, S. Chauvie, J. Chuma, R. Chytracek, G. Cooperman, G. Cosmo, P. Degtyarenko, A. Dell'Acqua, G. Depaola, D. Dietrich, R. Enami, A. Feliciello, C. Ferguson, H. Fesefeldt, G. Folger, F. Foppiano, A. Forti, S. Garelli, S. Giani, R. Giannitrapani, D. Gibin, J. G. Cadenas, I. González, G. G. Abril, G. Greeniaus, W. Greiner, V. Grichine, A. Grossheim, S. Guatelli, P. Gumplinger, R. Hamatsu, K. Hashimoto, H. Hasui, A. Heikkinen, A. Howard, V. Ivanchenko, A. Johnson, F. Jones, J. Kallenbach, N. Kanaya, M. Kawabata, Y. Kawabata, M. Kawaguti, S. Kelner, P. Kent, A. Kimura, T. Kodama, R. Kokoulin, M. Kossov, H. Kurashige, E. Lamanna, T. Lampén, V. Lara, V. Lefebure, F. Lei, M. Liendl, W. Lockman, F. Longo, S. Magni, M. Maire, E. Medernach, K. Minamimoto, P. M. de Freitas, Y. Morita, K. Murakami, M. Nagamatu, R. Nartallo, P. Nieminen, T. Nishimura, K. Ohtsubo, M. Okamura, S. O'Neale, Y. Oohata, K. Paech, J. Perl, A. Pfeiffer, M. Pia, F. Ranjard, A. Rybin, S. Sadilov, E. D. Salvo, G. Santin, T. Sasaki, N. Savvas, Y. Sawada, S. Scherer, S. Sei, V. Sirotenko, D. Smith, N. Starkov, H. Stoecker, J. Sulkimo, M. Takahata, S. Tanaka, E. Tcherniaev, E. S. Tehrani, M. Tropeano, P. Truscott, H. Uno, L. Urban, P. Urban, M. Verderi, A. Walkden, W. Wander, H. Weber, J. Wellisch, T. Wenaus, D. Williams, D. Wright, T. Yamada, H. Yoshida, D. Zschiesche, Geant4—a simulation toolkit, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 506 (3) (2003) 250 – 303. doi:https://doi.org/10.1016/S0168-9002(03)01368-8.
URL http://www.sciencedirect.com/science/article/pii/S0168900203013688

28. B. Bruyneel, P. Reiter, A. Wiens, J. Eberth, H. Hess, G. Pascovici, N. Warr, D. Weisshaar, Crosstalk properties of 36-fold segmented symmetric hexagonal {HPGe} detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 599 (2-3) (2009) 196 – 208.
doi:http://dx.doi.org/10.1016/j.nima.2008.11.011.
URL http://www.sciencedirect.com/science/article/pii/S0168900208015921

29. A. Wiens, H. Hess, B. Birkenbach, B. Bruyneel, J. Eberth, D. Lersch, G. Pascovici, P. Reiter, H.-G. Thomas, The {AGATA} triple cluster detector, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 618 (1-3) (2010) 223 – 233.
doi:http://dx.doi.org/10.1016/j.nima.2010.02.102.
URL http://www.sciencedirect.com/science/article/pii/S0168900210003384

30. P. Désesquelles, T. M. H. Ha, K. Hauschild, A. Korichi, F. Le Blanc, A. Lopez-Martens, A. Olariu, C. M. Petuche, Matrix formalism and singular-value decomposition

for the location of gamma interactions in segmented hge detectors, The European Physical Journal A 40 (2) (2009) 237-248. doi:10.1140/epja/i2008-10749-4.
URL http://dx.doi.org/10.1140/epja/i2008-10749-4

31. P.-A. Söderström, F. Recchia, J. Nyberg, A. Al-Adili, A. Ataç, S. Aydin, D. Bazzacco, P. Bednarczyk, B. Birkenbach, D. Bortolato, A. Boston, H. Boston, B. Bruyneel, D. Bucurescu, E. Calore, S. Colosimo, F. Crespi, N. Dosme, J. Eberth, E. Farnea, F. Filmer, A. Gadea, A. Gottardo, X. Grave, J. Grebosz, R. Griffiths, M. Gulmini, T. Habermann, H. Hess, G. Jaworski, P. Jones, P. Joshi, D. Judson, R. Kempley, A. Khaplanov, E. Legay, D. Lersch, J. Ljungvall, A. Lopez-Martens, W. Meczynski, D. Mengoni, C. Michelagnoli, P. Molini, D. Napoli, R. Orlandi, G. Pascovici, A. Pullia, P. Reiter, E. Sahin, J. Smith, J. Strachan, D. Tonev, C. Unsworth, C. Ur, J. Valiente-Dobón, C. Veyssiere, A. Wiens, Interaction position resolution simulations and in-beam measurements of the {AGATA} {HPGe} detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 638 (1) (2011) 96 – 109.
doi:http://dx.doi.org/10.1016/j.nima.2011.02.089.
URL http://www.sciencedirect.com/science/article/pii/S016890021100489X

32. M. R. Dimmock, A. J. Boston, J. R. Cresswell, I. Lazarus, P. Medina, P. Nolan, C. Parisel, C. Santos, J. Simpson, C. Unsworth, Validation of pulse shape simulations for an agata prototype detector, IEEE Transactions on Nuclear Science 56 (4) (2009) 2415-2425. doi:10.1109/TNS.2009.2021842.

33. M. R. Dimmock, A. J. Boston, H. C. Boston, J. R. Cresswell, L. Nelson, P. J. Nolan, C. Unsworth, I. H. Lazarus, J. Simpson, Characterisation results from an agata prototype detector, IEEE Transactions on Nuclear Science 56 (3) (2009) 1593-1599. doi:10.1109/TNS.2009.2019103.
<figure><img src="image_139.png" /></figure>

<figure><img src="image_140.png" /><figcaption>Fig. 3. A symmetric prototype crystal.</figcaption></figure>

<figure><img src="image_141.png" /></figure>

<figure><img src="image_142.png" /><figcaption>Fig. 4. A "C" type AGATA crystal. Half the volume is hidden to show the central contact.</figcaption></figure>

<figure><img src="image_143.png" /></figure>

<figure><img src="image_144.png" /><figcaption>Fig. 5. Response function of the electronics shown in time domain.</figcaption></figure>

<caption>Fig. 2. Views of a "A" type AGATA crystal.</caption>