Forward Ring Image Cherenkov Detector (RICH)
with achromatic and short focusing optics for PANDA setup.
1. Background.
For forward particle ID, two RICHs are considered so far: one is based on aerogel radiator, the
second – on the solid radiator and short focusing readout method. For the first time the focusing
method was proposed by JINR group for KEK B-factory in 1993 /1/. Later on the promising
R&D was carried out by BELLE /2/ and BaBar /3/ detectors teams. The scheme of RICH for
PANDA with achromatic optics optimized for the momentum range from 0.6 GeV/c up to 10
GeV/c and an angular range 10  220 has been investigated. The location of this detector in
PANDA setup shown on fig.1.
The basic problems of the RICH realization are:
- focusing and dispersion compensation of the Cherenkov light;
- compactness of the construction;
- problems with photo-detectors: size and density of the pixels, number of channels, fast
response, quantum efficiency and noise of the photo-detectors.
Fig.1. Proposed location of the RICH in PANDA.
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1.1 The optical scheme of the RICH.
The scheme of the RICH with achromatic and short focusing optics is shown on fig.2. There
are the disk radiator with thickness of 12 mm and compact axial symmetric focusing optics,
which serves as a dispersion compensator.
The fused silica ( n 0 , SiO2 ) is chosen with a large absorption length for the Cherenkov light.
The radiator is a disk by diameter of 2160 mm. At the centre there is a hole by diameter of 40
mm. The emitted Cherenkov light propagates to a rim of the radiator by total internal reflection
and passes through the ring-shaped lithium fluoride ( n1 , LiF) located on a perimeter of the
radiator, and goes through the fused silica ( n2 ) and methanol ( n3 , CH4O ) media. The photons
focused by a torus shaped mirror go through the fused silica window to photo-detector surface
(Focal Torus). The Avalanche photodiodes (APD) with an internal amplification more than 10 2
are supposed to be used as a photo-detectors /4/. Besides the requirement for the size of a
sensitive area of the photo-detectors (~2 мм 2 ), their insensibility to the magnetic field (~2 Tesla)
is necessary. The total number of APDs is about two hundred thousands.
Fig. 2. The optical scheme the RICH .
2
The selected materials of the optical media are chosen with the purpose to minimize losses of the
light and to compensate chromatic aberrations of the Cherenkov light in a range of the waves
from 250 nm up to 700 nm.
In addition, the ultra-pure water (alternate to methanol) is considered as a medium n3 .
Calculations with the variant n3   H 2O are marked separately.
Let's define variables:
 ,  - a polar angle and velocity of a particle;
 ,  - a polar angle and a wave-length of the Cherenkov light;
 3 - a polar angle of the Cherenkov light at an entry to a medium of methanol ( n3 ).
 3 is a function of variables n1 , n2 , n3 .
If the azimuth angles of the light and particle are in the same plane:
 n2  n2   2
 2
1
2
1 
 3  cos
n3





,



  cos   sin   n02   2  1,
where, the optical media n1 , n 2 , n3 are chosen according to the requirements of achromatization
of the Cherenkov light:
 3 (1 ,   0,   1)   3 (2 ,   0,   1)
for the waves 1 and 2 from visual and ultraviolet ranges.
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2. Simulation and analysis.

2.1 The simulation requirements.
The RICH simulation was performed under the following conditions:
- detector is disposed on the distance of 2.16 meters from the vertex (X=0,Y=0,Z=0);
- the particles emitted from point-like vertex;
- polar angle range of the emitted particles is 10  220 .
- solenoid magnetic field is 2 Tesla;
- quantum efficiency of the photo-detectors is 25 %;
- pixel size is 0.38  7.7 mm 2 ;
- absorption lengths of the optical media are given on fig. 3.
Fig. 3. The absorption lengths of the optical media.
a
b
c
d
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The refractive index for the wave in
range of 0.25 m ≤ λ ≤ 0.7 m has
been calculated according to the
formula:
b
n a  2
 d  2 .
 c
n0 , n 2
2.10491
n1
1.925388 0.004934 0.006656 0.005943
n3 ( CH 4O ) 1.74776
n3 ( H 2 O )
0.008668 0.011064 0.010516
0.006428 0.0127
1.762288 0.006338 0.01564
0.00517
0.01299
2
Coefficients a, b, c, d for the media are given in the Table 1.
Table 1
2.2 Analysis and results.
As a result of simulation, we obtained the photons spectrum registered by the photo-detectors.
Data of absorption, refraction and quantum efficiency (fig.4) were used.
Fig.4. A spectrum of the registered photons from pions with a momentum of 5 GeV/c and
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polar angle   6 0 .
The ring images of the particles on the photo-detectors surface are shown on the fig.5. The
coordinates origin are fixed on the axis of the RICH symmetry. Index a) corresponds to the ring
image generated by one pion, index b) corresponds to the ring image generated by a hundred
pions which have the same kinematical parameters. A polar angle  of the particle in its birthplace is also fixed, because the angular coordinates of the particle depend on its traversed path in
a solenoid magnetic field.
Fig. 5. The Ring Images of the detected pions with a momentum 5 GeV/c and polar angle  =6°.
Index a) corresponds to single pion, index b)- to 100 pions.
The image ring width imposes a limitation on the RICH detector resolution for separating
particles with close values of velocities. Further, to get the RICH characteristics, a radius-vector
(r) of the image point (hit) is used.
The Ring Image is divided to 1024 sectors. The radius-vector r i of the hit in every sector i has
been obtained. Based on that, the average weighted value of the radius-vectors for the entire
Ring Image ( r ) has been calculated and the normalization factors k i = r / r i for every sectors has
been assigned. These factors are used to calculate the reduced radius-vector values (r), that is
not depended on the sector’s number i . The distributions of the photons as function of the
reduced r-coordinates for Ring Images of pions are shown on fig.6. Standard deviation in these
distributions (   0.3 mm) defines the Ring Images’ width and, consequently, sets the
requirement to the photo-detector’s pixel size.
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Fig.6. The distributions of the reduced radius-vectors (r) for the registered photons in the
Ring Images for pions with 5 GeV/c momentum and a polar angle  = 6°.
Analogous distributions of reduced radius-vectors have been obtained for the kaons and protons
with same kinematical parameters (5 GeV/c,  = 6°). At known velocities of pions β(  ), kaons
β( K ) and protons β( p ) one can make scale transformation r to β for the particles with the fixed
coordinates and momentums. (It is assumed that the coordinates and momentum of the particles
are obtained using the data from the track detectors in front of RICH). Thus, as result of
simulation and processing of the Ring Images, the data on standard deviations (   ) of
reconstructed velocities (β) for pions, kaons and protons with different momentums and polar
angles have been obtained.
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On figure 7 the distributions of reconstructed velocities β for pions, kaons and protons with 5
GeV/c momentum and a polar angle  = 6˚ are shown. Also, the β-resolutions for pions, kaons,
protons are represented:   ( ),   ( K ),   ( p) .
Fig 7 . The distributions of reconstructed velocities (β) for pions, kaons and protons with 5Gev/c
momentum and a polar angle α=6°.
Figure 8 illustrates capability of the suggested RICH optical scheme for separation of particles π,
K and p at the different polar angles (  ). The characteristic value Nsigma (in units of   ) is
defined as:
Nsigma(  K ) 
mean ( )  mean ( K )
.
  ( )    ( K )
2
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Fig.8. Kaon-proton and pion-kaon separation in   units for
simulated events in RICH.
The upper bound of the momentum range in which particles can be separated more than on
4 Nsigma depends on a polar angle  shown in figure 9.
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Fig.9. Upper bound for the particles identification range.
The lower bound depends on the refractive index of the radiator, polar angle and the particle
minimum velocity for which the condition of total internal reflection of the Cherenkov light in
the radiator is fulfilled. Fig. 10 represents the low bound for the particles for which 10 photons or
more have been detected.
Fig.10. Lower bounds for the particles.
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3. Conclusion.
As the results of the above estimations, the proposed RICH scheme is fitted quite well to
PANDA setup and provides the excellent PID features.
References:
1. ‘Total Internal Reflection RICH counter for B-factory at KEK’, talk by B.Morosov at the
International Meeting for TRISTAN-II at KEK, ), Tsukuba, Japan,30-31 (1993
2. T. Kamae et al., ‘Focussing DIRC – A new compact Cherenkov ring imaging device’,
NIM A382, pp. 430-440, 1996
3. ‘Timing and detection efficiency properties of Multi-Anode PMTs for Focussing DIRC’,
talk by J. Schwiening at IEEE NSS/MIC 2003 conference, Portland, Oregon, USA,
October 20-24, 2003
4. S. Vasile at el., ‘High Gain Avalanche Photodiode Arrays for DIRC Applications’, IEEE
Transactions on Nuclear Science, vol. 46, No 4,April, 1999.
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