For more information on
the simulation code and to obtain the actual code contact Enrico Farnea
Last updated: June 3^{rd} 2004
The
configurations
The configurations for AGATA which will be compared below are
"spherically symmetrical" configurations, based on
encapsulated tapered coaxial detectors, grouped into clusters within a
single cryostats, arranged around the target position and pointing to
the target position.
As outlined in the AGATA
Technical Proposal (see p.41 and following), a method for tiling
the spherical surface with a few elementary shapes is to project a
pattern drawn on each of the faces of an enclosed regular polyhedron.
In the case of AGATA, it is convenient to start with an icosahedron,
which has 20 equilateral triangular faces and is the platonic
polyhedron with the largest number of faces; this will ensure the
maximum degree of symmetry. Covering the icosahedron faces with a
pattern of regular hexagons, the final polyhedron will be composed of
12 regular pentagons (the tips of the icosahedron) and of a number of
hexagons, which in general will
be slightly irregular and of a few different shapes.
The actual shape of the single capsule is given by the intersection of
a cylinder (80 mm diameter, 90 mm length) with an irregular polyhedron
having two parallel irregular hexagonal faces and it is
shown in the following picture:
A 1 mm thick passivated area is considered at the back
part of the detector and around the coaxial hole. The detectors are
encapsulated in an Aluminium capsule 0.7 mm thick, with a 0.5 mm
capsulecrystal spacing.
Only a few of the resulting polyhedra (that is, number of hexagons)
have been taken into consideration as a possible configuration for
AGATA, given the requirements that only a small as possible number of
hexagonal shapes should be used and that there should be a free
space of reasonable size around the target to host ancillary devices.
The polyhedra with 120 or 180 hexagons satisfy these conditions. The
180 hexagons can be grouped into triple clusters in a natural way and
no space is left in between the neighbouring clusters. This arrangement
will be referred to as A180
configuration. To achieve the
same result with 120 hexagons using triple clusters, one needs six
different crystal shapes,
obtaining what will be referred to as A120F
configuration. However, accepting a small spacing in between the
triple clusters, the number
of different shapes can be reduced to two, with an obvious gain in
development cost and modularity of the array. This arrangement will be
referred to as A120 configuration.
Actually, a more natural way to group the detectors in the case of 120
hexagons would be to consider clusters of 2 or 4 detectors; in both
cases, one ends with two different crystal shapes and one cluster type.
In the following, only the configuration with quadruple clusters will
be considered, which will be referred to as A120C4 configuration. It should be
noted that the latter configuration is less attractive than the others
from the practical point of view, due to the extra complication of
handling more objects within a single cryostat (148 signal feedthroughs
instead of 111).
The A120 configuration
is built out of 2 different capsule shapes,
grouped into 2 different triple cluster types. These clusters can be
arranged
in two different ways around the target position, depending on the way
the icosahedron is "unpacked" on a plane; in the following, only the
arrangement having the higher degree of
symmetry around the beam axis will be discussed. The performance of the
other arrangement as
a whole is similar, but it lacks the required symmetries to build
partial sections of the array, that is groups of clusters having a
border as "sharp" as possible. In the case of the symmetrical A120
configuration, the possible sections are as following:
Each section covers more solid angle than suggested by its name, which
is the price to pay to obtain "compact" sections. Notice that in order
to simplify the drawing, the intersection of each polyhedron with the
cylinder has not been sketched in the VRML files (a nice VRML viewer
can be downloaded at the Systems in Motion
web site).
The A120F configuration
is built instead out of 6 different capsule
shapes,
grouped into 2 different triple cluster types. The natural way to
arrange the
clusters is to follow the same arrangement of the A120 configuration
with the highest degree of
symmetry around the beam axis. This way, one obtains the same sequence
of sections shown for the A120 configuration:
The A120C4 configuration
is built out of 2 different capsule
shapes,
grouped into a quadruple cluster (of a single type). Given the size of
the quadruple clusters, it is very difficult to build regular sections
and what can be achieved is the following:
Given the underlying symmetry, it is not possible to arrange the
clusters
to form a compact section covering (even roughly) half of the total
solid angle.
The A180 configuration
is built out of 3 capsule shapes (grouped into a single triple cluster
type).
In this case, the sequence of sections is the following:
Also in this case, given the underlying symmetry, it is not possible to
arrange the
clusters
to form a compact section covering half of the total solid angle.
In the calculations, the pentagonal elements were not considered. Given
the cost to develop the pentagonal encapsulated segmented detectors, it
was felt that the increase in performance brought by these detector
would not be worthwhile.
Performance
considering the tracking
In the following, the performance of the
AGATA array in its various proposed configurations will be presented.
The results were obtained considering the proper
amount of passive materials (capsules and cryostats) and performing a
full reconstruction with the mgt
tracking code developed in Padova. Of course the quoted
performance depends on the performance of the tracking algorithms. The
performance of the array in the (unrealistic) case of perfect gammaray
tracking is called response function
and is given for
reference purposes in the next section.
Response function as a function of energy and recoil velocity
Demonstrator
In the demonstrator phase, 5 triple (or quadruple)
clusters will
be employed. The
following table summarizes the expected photopeak efficiency and P/T
ratios for 1 MeV photons at various multiplicities and zero recoil
velocity.
Multiplicity

1

10

20

30

A120
Efficiency (%)

3.6

3.1

2.8

2.5

A120F Efficiency (%)

4.0

3.4

3.0

2.8

A120C4 Efficiency (%) 
5.7

4.7

4.2

3.8

A180
Efficiency (%) 
2.8

2.4

2.2

2.0

A120
P/T (%) 
47.6

49.8

49.5

48.7

A120F P/T (%)

50.0

50.2

49.2

48.1

A120C4 P/T (%) 
50.3

50.1

49.2

47.9

A180
P/T (%) 
49.5

49.6

49.2

48.6

The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
Positioning the demonstrator in its "standard" position along the z
axis, the FWHM of a 1 MeV peak as a function of the recoil direction
(assumed to be sharply defined) is shown in the following plots for
various recoil velocities:
The same data are displayed comparing the various configurations at
various recoil velocities, which should be compared to the reference
values at zero recoil velocity summarized in the following table:

A120

A120F

A120C4

A180

FWHM (keV)

2.46

2.48

2.49

2.46

The case of variable recoil velocity is discussed in more detail in the
following report,
where it is shown that, measuring on an eventbyevent basis the
direction of the recoils within 0.3 degrees and their velocity module
within 0.3%, the performance of the array is kept to a reasonable value
up to a 50% recoil velocity.
1
array
As explained above, 15 triple clusters are
needed to build this section for both the
A120 and A180 configurations, while 10 quadruple clusters will be
needed for the A120C4 configuration. Also in this case the
table summarizes the expected photopeak efficiency and P/T
ratios for 1 MeV photons at various multiplicities and zero recoil
velocity.
Multiplicity

1

10

20

30

A120
Efficiency (%)

11.5

9.6

8.5

7.5

A120F Efficiency (%) 
12.8

10.2

9.0

8.3

A120C4 Efficiency (%) 
11.2

8.9

8.0

7.3

A180
Efficiency (%) 
8.8

7.3

6.6

6.2

A120
P/T (%) 
52.0

53.2

50.0

47.2

A120F P/T (%) 
52.0

51.0

49.2

47.3

A120C4 P/T (%) 
50.7

50.0

48.5

46.6

A180
P/T (%) 
51.6

51.6

51.0

50.2

The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
2 array
As explained above, in the case of the
A120C4 and A180 configurations it is not really meaningful to build
this section
and only the data relative to the A180 configuration are presented for
completeness. In order to build this
section, 25 or 30 triple
clusters are needed respectively for the
A120 and A180 configurations. Also in this case the
table summarizes the expected photopeak efficiency and P/T
ratios for 1 MeV photons at various multiplicities and zero recoil
velocity.
Multiplicity

1

10

20

30

A120
Efficiency (%)

19.8

15.8

14.2

13.0

A120F Efficiency (%) 
21.9

17.2

15.2

13.8

A180
Efficiency (%) 
18.3

14.7

13.4

12.4

A120
P/T (%) 
52.6

51.0

49.0

47.1

A120F P/T (%) 
51.9

50.1

47.5

45.0

A180
P/T (%) 
52.6

51.3

50.3

48.8

The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
3 array
As explained above, in order to build
this phase 35 or 45 triple
clusters are needed respectively for the
A120 and A180 configurations, while 20 quadruple clusters are needed
for the A120C4 configuration. Also in this case the
table summarizes the expected photopeak efficiency and P/T
ratios for 1 MeV photons at various multiplicities and zero recoil
velocity.
Multiplicity

1

10

20

30

A120
Efficiency (%)

28.0

21.7

19.4

17.7

A120F Efficiency (%) 
31.6

24.0

21.1

19.2

A120C4 Efficiency (%) 
23.4

18.3

16.2

14.9

A180
Efficiency (%) 
28.0

21.9

20.0

18.6

A120
P/T (%) 
52.6

49.4

47.3

45.2

A120F P/T (%) 
52.4

48.5

46.0

44.3

A120C4 P/T (%) 
51.0

49.4

47.2

45.4

A180
P/T (%) 
52.6

49.6

48.3

47.3

The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
Full array
In this phase, 40 or 60 triple clusters are needed
respectively for the
A120 and A180 configurations. The following table summarizes some of
the relevant geometrical characteristics of the configurations:

A120

A120F

A120C4

A180

Number
of crystals

120

120

120

180

Number
of crystal shapes

2

6

2

3

Number
of cluster types

2

2

1

1

Covered solid angle (%)

70.97

77.79

78.0

78.36

Volume
of Germanium (cm^{3})

43590

42225

43160

70243

Mass
of Germanium (kg)

232

225

230

374

Initial
mass of Germanium (kg)

289

289

289

434

Fractional
loss of Germanium (%)

19.7

22.1

20.4

13.8

Centre
to Detector face distance (cm)

19.7

18.0

18.5

24.6

The values for the partial sections can be obtained by scaling to the
number of clusters composing the section.
The
following table summarizes the expected photopeak efficiency and P/T
ratios for 1 MeV photons at various multiplicities and zero recoil
velocity:
Multiplicity

1

10

20

30

A120
Efficiency (%)

32.9

25.2

22.4

20.5

A120F Efficiency (%) 
36.9

27.7

24.3

22.0

A120C4 Efficiency (%) 
36.4

27.5

24.3

22.1

A180
Efficiency (%) 
38.8

29.6

27.0

25.1

A120
P/T (%) 
52.9

48.8

46.5

44.9

A120F P/T (%) 
53.0

48.4

45.9

43.7

A120C4 P/T (%) 
51.8

47.5

45.3

43.4

A180
P/T (%) 
53.2

48.4

47.3

46.1

The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plot:
The same quantity is shown in the case of various recoil velocities:
Response function
In the following, the response function of
the AGATA array in
its various proposed configurations will be presented for comparison
with the data obtained with the tracking procedure. The response
function is obtained by considering individual photons (multiplicity 1) interacting with the
array as a whole and considering the total energy deposition (that is,
using the array as a single "conventional" detector). The response
function gives the performance of the array in the limit of perfect
gammaray tracking. The results were
obtained considering the proper
amount of passive materials (capsules and cryostats).
Response function at
1 MeV
The response function at 1 MeV for the different sections of the four
considered configurations is given in the following two tables. For the
exact meaning of the different rows please refer to the numbering used
in the first section of this document.
Photopeak
efficiency (%)


A120G

A120F

A120C4

A180

1

3.8

4.2

5.9

2.8

2

12.2

13.5

11.8

9.1

3

21.5

23.7

25.1

30.0

4

30.8

34.6

32.0



5

36.5

40.4

39.6

42.2

Peaktototal
ratio (%)


A120G

A120F

A120C4

A180

1

46.5

46.3

46.9

46.6

2

49.3

48.9

47.8

49.2

3

51.4

50.9

50.0

53.2

4

53.0

52.7

51.0



5

54.2

53.7

52.1

55.5

Response
function as a function of energy and recoil velocity
In the following plots, the response function is given as a function of
energy (in the 80 keV  2.7 MeV range) and recoil velocity (in the
0%50% range).
Demonstrator
The response of the array to a regular rotational
cascade at zero
recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:
1
array
The response of the array to a regular
rotational cascade at zero
recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:
2 array
The response of the array to a regular
rotational cascade at zero
recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:
3 array
The response of the array to a regular rotational cascade at zero
recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:
Full array
The response of the array to a regular rotational
cascade at zero
recoil velocity is shown in the following plots:
The same quantities are shown in the case of various recoil velocities:
