Low Counting Experimental Techniques 3th lecture: Detectors for low counting experiments 1: scintillation, Cherenkov, semiconductors
Fedor Danevich Institute for Nuclear Research, Kyiv, Ukraine http://lpd.kinr.kiev.ua [email protected] [email protected]
1 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture The main sources of background, natural radioactivity
The main sources of background are: • Environmental radioactivity (mainly the natural radioactivity) • Cosmic rays • Neutron induced background • Cosmogenic activation • Artificial radioactivity • Noise, events pile-up
The most valuable gamma quanta come from 40K and daughters of 232Th, 238U
The secular equilibrium is typically broken in materials which have been subjected to physical and chemical treatment due to different physical and chemical properties of daughter elements
2 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture Main components of cosmic rays
The Electromagnetic To suppress the Muons penetrate for component can be suppressed Hadronic kilometers underground by tens cm of metal (lead, component one copper, steel) need to go 5-10 m underground
CdWO4 crystal scintillator 77 cm
no shield
GIOVE = Germanium Spectrometer with Inner and induced 5 cm lead + 10 cm copper Outer Veto (Max-Planck-Institut, muons Heidelberg) 0.5
3 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture Cosmogenic activation environmental, material of detector, in-situ
Permanent production of cosmogenic radionuclides under cosmic rays irradiation (e.g. 3H, 7Be, 10Be, 14C, 36Cl)
Cosmogenic activation of detector materials Cosmogenic activation of materials can be calculated with reasonable accuracy: COSMO, ACTIVIA packages
Cosmogenic activation in-situ (short living radioactivity, which nevertheless cannot be vetoed by anti-coincidence counters due to increase of data acquisition dead time)
4 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture Neutron induced background recoils, production of radioactive nuclides, high energy
Neutron induced recoils in the CRESST cryogenic dark matter experiment (neutron calibration data)
Neutron induced quanta (neutron caption) in gammas after CdWO cryogenic scintillating bolometer (to neutron capture 4 113 search for 02 decay) on Cd
Internal alphas
Radioactivity can be produced by neutrons in the details of experimental set-up (e.g. radioactive 116In from 115In) Main sources of neutrons: cosmic rays, spontaneous fusion of uranium, (,n) reactions
5 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture Anthropogenic radioactivity nuclear reactor disasters, bomb tests, careless handling of radioactive sources
The total activity of radioactive materials after the Chernobyl disaster is 5.2·1018 Bq (Fukushima: 0.3-0.8 ·1018 Bq, continues)
Chernobyl reactor after the disaster in 1986
Activity of 137Cs in atmosphere after the nuclear bomb tests
244 Cm (?) on ZnMoO4 crystal in the EDELWEISS set-up (Modane Underground Lab, France)
6 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Brief summary of the 2nd lecture Electronic noise, events pile-up
PMT noise in scintillation PMT noise experiments Any detector produce noise and spectrum of 14C wrong signals spectrum of 113Cd The main ways to suppress: • Pulse-shape discrimination • Stability of signal in time 2nd event Randomly coinciding events in cryogenic 1th event detector become to be the main source of background in 02 experiments with 100Mo
Randomly coinciding event in cryogenic detector
7 F.A. Danevich Univ. Tor Vergata November 24, 2015 Short baseline experiments: LSND
unexplained νe appearance in a νμ beam at a short distance
[1] J. Link, Short baseline experiments , talk at TAUP 2015, Torino, Sep 7-12, 2015, http://www.taup-conference.to.infn.it/2015/day4/plenary/link.pdf
[2] C.Athanassopoulos et al., Results on νμ→νe Neutrino Oscillations from the LSND Experiment, PRL 81 (1998) 1774 8 F.A. Danevich Univ. Tor Vergata November 24, 2015 Short baseline experiments: MiniBooNE the LSND result was not confirmed
J. Link, Short baseline experiments , talk at TAUP 2015, Torino, Sep 7-12, 2015, 9 F.A. Danevich Univ. Tor Vergata November 24, 2015 Ongoing and future of short baseline experiments
J. Link, Short baseline experiments , talk at TAUP 2015, Torino, Sep 7-12, 2015, 10 F.A. Danevich Univ. Tor Vergata November 24, 2015 11 F.A. Danevich Univ. Tor Vergata November 24, 2015 Long baseline experiments: T2K, MINOS
disappearance of , appearance of e T2K MINOS
Reconstructed energy spectra for e CC candidate events in the Far Detector. The black points indicate the experimental data. The histogram indicates the expected background (unfilled area) together with the
contribution of e signal (hatched 2 area) for the best-fit value of sin (213) = 0.041
[1] P. Adamson et al., Improved Search for Muon-Neutrino to Electron-Neutrino Oscillations in MINOS Phys. Rev. Lett. 107 (2011) 181802 12 F.A. Danevich Univ. Tor Vergata November 24, 2015 Long baseline experiments: OPERA appearance of tau-neutrino
A.Palazzo Sterile neutrinos, talk at TAUP 2015, torino, Sep 7-12, 2015 http://www.taup-conference.to.infn.it/2015/day3/plenary/palazzo.pdf 13 F.A. Danevich Univ. Tor Vergata November 24, 2015 Long baseline experiments started: NOA
disappearance of , appearance of e NOA
Brian Rebel (Fermilab) The NOvA Experiment, talk at TAUP 2015, torino, Sep 7-12, 2015
14 F.A. Danevich Univ. Tor Vergata November 24, 2015 in this lecture:
• Scintillation detectors • Cherenkov counters • Semiconductor detectors
15 F.A. Danevich Univ. Tor Vergata November 24, 2015 Characteristics of detectors NaI(Tl) scintillator 60Со • Energy resolution • Time resolution • Coordinate resolution • Dead time HPGe
• Density, Zeff (detection efficiency) • Composition (presence of certain elements) • Available volume • Radiopurity • Operational stability
16 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors principle of operation , , , … escape
Scintillator
Light guide Photomultiplier: principle of operation (optional) Scintillation photons
*
Photoelectron Photo-detector (electron hole pair)
Photomultiplier: quantum efficiency 17 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors photodetectors • Photomultiplier tubes (PMT) – most commonly used in APP experiments (quantum efficiency QE ~ 20%-35%) • Photodiodes – too small working area, but very high QE ~ 70% • Silicon photomultipliers (SiPM) – started to use
76 mm 20-inch
20.5 mm 10 mm
S8664-1010 Excellent energy resolution high quantum metal package hemispherical Si Avalanche achieved with avalanche efficiency R6233- R8520-406 R1449 and R3600 photodiode photodiode (APD) 16 mm size [1] 100 [1] M. Moszynski et al., IEEE TNS 46 (1999) 880 18 F.A. Danevich Univ. Tor Vergata November 24, 2015 Silicon photomultipliers (SiPM)
avalanche photodiode array Typical size of one element is 0.02 - 0.1 mm Simple read out
Photomultiplier Tube Avalanche SiPM Active area Photodiode Quantum Efficiency 25% … 40% … 80% … 80% Single Photon • – • Resolution Operation Voltage 1 - 3 kV 100 - 500 V 20 - 80 V 4 9 5 7 Gain 10 - 10 30 - 300 10 - 10 Insensitivity to – • • Magnetic Field Miniaturization – • • Production Costs Medium Low Potentially Low http://www.ketek.net/ 19 Scintillation detectors scintillators • Organic crystals (anthracene, stilbene, p-terphenyl, …) Plastic Liquid • Inorganic
NaI(Tl), CsI(Tl), CsI(Na), BGO, CdWO4, PbWO4, YAG(Ce), GSO(Ce), LSO(Ce), CaF2(Eu), CaWO4, ZnWO4, LaBr3(Ce), CeCl3, … • Nobble gases (Xe, Ar, …) • Gaseous • Ceramic (glasses, nano-ceramic)
20 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors energy resolution NaI(Tl) crystal scintillator Energy resolution of scintillation detector [1]: 2 2 2 2 (E/E) = (sc) + (p) +(st) ,
sc intrinsic resolution of scintillator, p photoelectrons (electron-hole – pairs) statistical contribution,
st photodetector noise contribution
Intrinsic resolution (R) of scintillators [2]: RRR2 2 2 R2 La(Br,Cl) :Ce i np inh nu 3 2 R np non-proportional response of scintillator; 2 inhomogeneity of scintillator Rnp 2 Rnu non-uniformity of light collection
[1] M. Moszynski et al., IEEE TNS 46 (1999) 880 [2] P. Dorenbos, IEEE TNS 45 (1995) 2190 21 F.A. Danevich Univ. Tor Vergata November 20, 2015 Scintillation detectors decay kinetics, pulse-shape discrimination, time resolution
Decay time Rise-time
CaWO4 9 s Plastic 4 s scintillator
0.3 s
Scintillator eff (s) Liquid and plastic scintillators 0.005 Aii decay constants, = i eff A its intensities PbWO4 0.01 Ai i NaI(Tl) 0.2
CaWO4 8
ZnWO4 24
22 F.A. Danevich Univ. Tor Vergata November 24, 2015 Temperature dependence of scintillation properties
ZnWO4 [1], PbWO4 [2]
[1] H. Kraus et al., ZnWO4 scintillators for cryogenic dark matter experiments, NIMA 600 (2009) 594
[2] F.A. Danevich et al., Feasibility study of PbWO4 and PbMoO4 crystal scintillatorsforcryogenic rare eventsexperiments, NIMA A 622 (2010) 608 23 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors quenching (/ ratio)
CaWO4 [1] CdWO4 [2]
/ ratio = E / E
[1] Yu.G. Zdesenko et al., NIMA 538 (2005) 657 [2] P.G. Bizzeti et al., NIMA 696 (2012) 144
24 F.A. Danevich Univ. Tor Vergata November 24, 2015 Application of scintillation detectors inorganic scintillators Solotvina experiment: 2 decay of 116 116 Cd ( CdWO4) Plastic active shield
CdWO4
116 CdWO4 crystal ~0.5 kg
Plastic light guide
F.A.Danevich et al., Phys. Rev. C 68 (2003) 035501 25 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors energy resolution NaI(Tl) crystal scintillator Energy resolution of scintillation detector [1]: 2 2 2 2 (E/E) = (sc) + (p) +(st) ,
sc intrinsic resolution of scintillator, p photoelectrons (electron-hole – pairs) statistical contribution,
st photodetector noise contribution
Intrinsic resolution (R) of scintillators [2]: RRR2 2 2 R2 La(Br,Cl) :Ce i np inh nu 3 2 R np non-proportional response of scintillator; 2 inhomogeneity of scintillator Rnp 2 Rnu non-uniformity of light collection
[1] M. Moszynski et al., IEEE TNS 46 (1999) 880 [2] P. Dorenbos, IEEE TNS 45 (1995) 2190 26 F.A. Danevich Univ. Tor Vergata November 24, 2015 crystal scintillators 116 example of application: CdWO4
116 ( Cd) = 82% 116 CdWO4 crystal (510 g) grown in 1986 for the 116 CdWO4 scintillator 1868 g Solotvina experiment [2] Yield of crystal 87% 116 Optical transmission curve of Losses of Cd 2% 116 CdWO4 crystal before and after annealing The excellent optical and scintillation properties of the crystal were obtained thanks to the deep purification of 116Cd and W, and the advantage of the low- The crystal was cut into 3 thermal-gradient Czochralski scintillation elements technique to grow the crystal [1]
[1] A.S. Barabash et al., JINST 06( 2011) p08011 [2] F.A.Danevich et al., JETP Lettt. 49 (1989) 476 27 F.A. Danevich Univ. Tor Vergata November 24, 2015 • Experiment 116 CdWO4 scintillation detector
PMT PTFE container filled quartz light-guide Hamamats by liquid scintillator 116 u R6233 CdWO4
FWHM 5% at 2615 keV
F.A. Danevich Univ. Tor Vergata November 24, 2015 Low background DAMA R&D set-up at LNGS
An event-by-event data acquisition system based on a 1 GS/s 8 bit transient Lead 15 cm Air-tight Cu box digitizer (operated at 50 MS/s) records flushed by high Copper 10 cm the time of each event and the pulse purity N2 gas shape over a time window of 100 s 116 from the CdWO4 detectors 116 CdWO4 detectors 22 116Cd 116 Q2 Cd
Cadmium 1.5 mm Plexiglas box continuously flushed
by high purity N2 gas Polyethylene 4-10 cm
The background rate in the region of interest 2.7 2.9 MeV (after pulse-shape discrimination) is on the level T2 [2.62 0.02( stat .) 0.14( syst .)] 10 19 yr of 0.12 counts/(yr keV kg) 1/2 29 F.A. Danevich Univ. Tor Vergata November 24, 2015 DAMA/LIBRA at Gran Sasso 1996–2002: DAMA/NaI with 100 kg of NaI(Tl) 2003– till now: DAMA/LIBRA with ~240 kg NaI(Tl) • 25 radiopure NaI(Tl) 9.7 kg • Special R&D (Saint-Gobain & INFN) viewed by • two PMTs through Suprasil-B light guides
PMT NaI(Tl) PMT
light guides
[1] R. Bernabei et al., Nucl. Instr. Meth. A 592 (2008) 297 30 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors liquid scintillators KamLAND: Investigation of neutrino oscillations by measurement of neutrino flax from 56 Japanese reactors at ~ 100-200 km Liquid scintillator: 20% Pseudocumene + 80% mineral oil + 1.5 g/l PPO (1000 ton, 13 m)
Cherenkov water counter triphenylamine
Cherenkov counter PMT The radio-purest scintillator: • Registration of neutrino oscillations 40K = 70 nBq/kg 232 • Detection of geo-neutrino Th = 0.2 nBq/kg 238U = 0.04 nBq/kg 31 F.A. Danevich Univ. Tor Vergata November 24, 2015 BOREXINO Liquid scintillation detector
Liquid scintillator: Pseudocumene [1,2,4-trimethylbenzene
C6H3(CH3)3] + 1.5 g/l PPO [2,5- Diphenyloxazole, C15H11NO] Energy spectrum 32 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors loaded liquid scintillators
Daya Bay experiment to measure 13 antineutrino detector with 20 t of mixing angle (neutrino oscillations) Gadolinium loaded LS
reactors
antineutrino detectors
F. P. An et al. Phys. Rev. Lett. 108 (2012) 171803 33 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors loaded liquid scintillators: Sudbury Neutrino Observatory (SNO, Canada) The SNO+ experiment is the successor to the SNO, in heavy water is replaced by approximately 780 T of liquid scintillator (LAB). By loading the liquid scintillator with 0.3% of natural Tellurium, resulting in about 800kg of 130Te (isotopic abundance is slightly over 34 %), a competitive sensitivity to the effective neutrino mass can be reached.
34 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors plastic scintillators Project SuperNEMO: search for decay of 82Se (48Ca, 150Nd)
82Se foil
Track detector (Geiger cells) Calorimeter to detect particles and quanta (plastic scintillators)
35 F.A. Danevich Univ. Tor Vergata November 24, 2015 Calorimeter Status Matthew KauerR&D of SuperNEMO calorimeter module (plastic scintillator) 25 cm EJ200 ~ BC408
Glycerol
FWHM = 7.1% at 1 MeV
Hamamatsu R5912-MOD Super-Bialkali 8 Dynodes 36 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors plastic scintillators to measure muons after tau- interaction OPERA at Gran Sasso Lab
20 м
Main goal: search for oscillations → ( come from CERN, 730 km away) • The "target area" is made of walls filled with ECC (Emulsion Cloud Chamber) bricks interleaved with planes of plastic scintillators • data taking form 2007 (now dismounted) • data analysis is in progress Reconstruction of the first registration of -neutrino
37 F.A. Danevich Univ. Tor Vergata November 24, 2015 Application of organic crystal scintillator (Stylben) Detector HEND (High Energy Neutron Detector) at the 2001 Mars Odyssey spacecraft orbiting the planet Mars spectrometer HPGe
CsI
Stylben crystal
Thermal neutrons Fast (>2 MeV) neutrons 3He proportional counters (stylben)
38 F.A. Danevich Univ. Tor Vergata November 24, 2015 Scintillation detectors liquid noble gases
• Ultra-violet light guides and PMts are needed • Xenon should be deeply purified to provide stable scintillation efficiency
39 F.A. Danevich Univ. Tor Vergata November 24, 2015 Cherenkov detectors Qualitative description polarization in dielectric by passing charge particle
- - + - + - - + - - + - - - + + + + - + - - - - + - + + + - + - - - + + + + + + - - - + + - - + - - - + + + + + + + - + - + + - - - + + - - + + - + - + - + - - -
Slow particle Symmetric polarization Fast particle Asymmetric polarization No irradiation Irradiation appear
40 F.A. Danevich Univ. Tor Vergata November 24, 2015 Cherenkov detectors
Particle pass the distance Basic formulas AB = c t 1 v Light in the media 1) cos n c pass the distance AC = c/n t Cherenkov radiation condition
1 2) min 90 n
Threshold speed: if < min, no radiation
1 3) arccos( ) max n Maximal for ultra-relativistic particles 1
41 F.A. Danevich Univ. Tor Vergata November 24, 2015 Large water Cherenkov detectors Super Kamiokande 39 41 m 50 000 ton ultra-pure water 11 200 PMTs 50 cm 2.5% at 1 GeV (16% at 10 MeV) Energy threshold 5 MeV
Search for proton decay Measurement of atmospheric neutrino oscillations Measurements of high energy solar neutrino from 8B K2K: neutrino oscillations from accelerator Search for supernova explosions 42 F.A. Danevich Univ. Tor Vergata November 24, 2015 Air Cherenkov detectors High energy cosmic rays, detection in atmosphere
http://www.astroparticle.org/
43 F.A. Danevich Univ. Tor Vergata November 24, 2015 H.E.S.S. Imaging Atmospheric Cherenkov Telescope Investigation of the origin and acceleration mechanisms of cosmic rays
Namibia
The angular resolution of the H.E.S.S array allowed for the first time to resolve the Gamma ray emission structure from the shell type supernova remnant RXJ1713 H.E.S.S. camera (PMTs) The telescope sensitive to cosmic rays 100 GeV to 100 TeV http://www.aspera-eu.org 44 F.A. Danevich Univ. Tor Vergata November 24, 2015 Pierre Auger Observatory Above the energy of 1020 eV, only one particle falls on a square kilometer in a century
10 km
1,600 particle detector stations. The detector stations ~1.5 km apart, each one filled with 12 tons of pure water
PMT
24 air fluorescence telescopes Camera 45 F.A. Danevich Univ. Tor Vergata November 24, 2015 Sudbury Neutrino Observatory
Observations of neutral current solar neutrino interactions
0.45 0.48 6 2 1 3.410.45 (stat .) 0.45 ( syst .) 10 cm s
0.05 0.09 6 2 1 e 1.760.05 (stat .) 0.09 ( syst .) 10 cm s
0.44 0.46 6 6 1 NC 5.090.43 (stat .) .043 ( syst .) 10 cm s
Event reconstruction
1000 t of heavy water (D2O) at the depth of 2,5 km in nickel mine Sudbury (Canada)
46 F.A. Danevich Univ. Tor Vergata November 24, 2015 Largest Cherenkov detector: IceCube South Pole, Antarctica
High energy neutrino events 47 F.A. Danevich Univ. Tor Vergata November 24, 2015 Future plans of a large Cherenkov detector
http://www.taup-conference.to.infn.it/2015/day4/plenary/mezzetto.pdf 48 BOREXINO anti-muon Cherenkov veto
Water
PMT viewing water
49 F.A. Danevich Univ. Tor Vergata November 24, 2015 Cherenkov light as noise source in PMT PMT noise, single electron counting
Thermionic electrons Single photoelectron peak spontaneously emitted by 2 photoelectrons photocathode and dynodes 3 photoelectrons Cherenkov light from radioactive contamination of PMT window Cherenkov light from cosmic muons
Production of PMT from low radioactive materials improves noise
50 F.A. Danevich Univ. Tor Vergata November 24, 2015 Semiconductor detectors principle of operation
HPGe detectors: reverse biased diode An excellent energy resolution NaI(Tl) scintillator Electron-Hole- 60Со Pair Creation Energies
Ordinary construction of HPGe detector HPGe
Due to the small bandgap 0.7 eV, Ge detectors are • High-Purity Germanium (HPGe) detectors impossible to operate at • Silicon Lithium-drifted (SiLi) detectors room-temperature (because • Cadmium Telluride (CdTe) and the large thermally-induced • Cadmium Zinc Telluride (CdZnTe) detectors leakage current) • Mercury Iodide (HgI2) detectors R. C. Alig and S. Bloom, Electron-Hole-Pair Creation Energies in Semiconductors, Phys. Rev. Lett. 35 (1975) 1522 Ian Rittersdorf, Gamma Ray Spectroscopy, http://www-personal.umich.edu/~ianrit/gammaspec.pdf 51 F.A. Danevich Univ. Tor Vergata November 24, 2015 GERDA: search for 02 decay of 76Ge
Bare HPGe detectors 76Ge
Phase I
Phase II
BEG detectors provide better energy resolution
52 F.A. Danevich Univ. Tor Vergata November 24, 2015 Majorana search for 02 decay of 76Ge
• 500 kg of Ge, isotopically enriched to 86% in 76Ge, in the form of ~200 segmented detectors, equipped by pulse shape analysis electronics. • A half-life sensitivity is predicted of 41027 yr Detectors in cryostat m 0.04 eV • Pulse-shape analysis to reject multi Compton scattering events
M. Green, Current Status of The Majorana Demonstrator, talk at TAUP 2015 Torino, Sep 7-12, 2015 http://www.taup-conference.to.infn.it/2015/day2/parallel/nub/1_green.pdf 53 F.A. Danevich Univ. Tor Vergata November 24, 2015 Majorana Underground production of copper
M. Green, Current Status of The Majorana Demonstrator, talk at TAUP 2015 Torino, Sep 7-12, 2015 http://www.taup-conference.to.infn.it/2015/day2/parallel/nub/1_green.pdf 54 F.A. Danevich Univ. Tor Vergata November 24, 2015 CoGent HPGe detector to search for dark matter
Background energy spectrum (very low energy threshold ~ 0.5 keV)
P-type point-contact Ge detector 443 g of mass in passive shield
C. E. Aalseth et al., CoGeNT: A search for low-mass dark matter using p-type point contact germanium detectors, PRD 88 (2013) 012002 55 F.A. Danevich Univ. Tor Vergata November 24, 2015 Silicon alpha detectors
ORTECR: Compact detector for spectroscopy
56 F.A. Danevich Univ. Tor Vergata November 24, 2015 Silicon charged particle detectors, X rays detectors
CANBERRA: CANBERRA: Silicon Lithium Si(Li) Silicon Lithium Si(Li) Detectors for X-ray detectors for charged Spectroscopy particle spectroscopy
57 F.A. Danevich Univ. Tor Vergata November 24, 2015 CdZnTe room temperature semiconductors
Stefan Zatschler, The COBRA experiment - Status and Prospects, MEDEX-2015, June 9 – 12, 2015 Prague 58 F.A. Danevich Univ. Tor Vergata November 24, 2015 Conclusions • Variety of detectors is used in astroparticle physics • Advantage of scintillation detectors: presence of element of interest, stability, good spectrometric and time properties, large volume (liquid scintillators), stability • Semiconductor detectors provide a very high energy resolution (particularly to quanta), in most of the cases they are very radiopure • Cherenkov detectors used in a case of huge mass request, allow to measure direction of particles, can use water (ice, air) as detector material • There is no “ideal” detector. Typically a combination of different detectors is used in APP experiments
59 F.A. Danevich Univ. Tor Vergata November 24, 2015
60 The next lessons
• November 25 (Wednesday) 11:00-13:00 • December 02 (Wednesday) 11:00-13:00 (Aula Grassano) • December 09 (Wednesday) 11:00-13:00 • December 16 (Wednesday) 11:00-13:00 • December 23 (Wednesday) 11:00-13:00
61 F.A. Danevich Univ. Tor Vergata November 24, 2015