Diapositiva 1

1
VI INCONTRO NAZIONALE GRUPPO ITALIANO
ASTROFISICA NUCLEARE TEORICA e SPERIMENTALE
(GIANTS) Perugia 27-28 Novembre 2006
LESPERIMENTO ASFIN
APPLICAZIONI DEL METODO DEL CAVALLO DI TROIA

• Claudio Spitaleri
• Universita di Catania-Italy
• Laboratori Nazionali del Sud- Catania-Italy

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NUCLEAR ASTROPHYSICS
PERCHE MISURE DI SEZIONI D?URTO CON METODI
INDIRETTI IN ASTROFISICA NUCLEARE ?
3
NUCLEAR REACTIONS BETWEEN CHARGED PARTICLES
The main problem in the charged particle cross
section measurements at astrophysical energies is
the presence of the interacting Coulomb barrier
between the nuclei
tunnel effect
kT 8.6 x 10-8 TK keV
T 15x106 K (e.g. our Sun) ? kT 1 keV T
1010 K (Big Bang) ? kT 2 MeV
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EXTRAPOLATION
CROSS SECTIONS Gamow energy
3He(a,g)7Be
s(E) n b

• range nano-picobarn

Ecm (Mev)
Gamow energy
Extrapolation
in general, their direct evaluation is -severely
hindered -and in some cases even beyond present
technical possibilities.
Possible solution
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EXTRAPOLATION
Astrophysical S(E)-factor
Cross-section bare nucleus
Astrophysical factor bare nucleus
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I- EXPERIMENTAL SOLUTION
(uncertainties in the extrapolation)

• - IMPROVEMENTS TO INCREASE THE NUMBER OF
  DETECTED PARTICLES
• 4 p detectors
• New accelerator at high beam intensity

Problem of targets (gas target,)
7
II- EXPERIMENTAL SOLUTION
(uncertainties in the extrapolation)
- IMPROVEMENTS TO REDUCE THE BACKGROUND

• Use of laboratory with natural shield -
• ( underground physics) LUNA
• Use of magnetic apparatus 
• (Recoil Mass Separator) ERNA
  

GRAN SASSO
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ELECTRON SCREENING
but at astrophysical energies NEW PROBLEM
The second relevant source of uncertainty in
extrapolating the S(E)-factor at astrophysical
energies (down to zero energy) is the
enhancement due to the electron screening effect
!!!!

(Assenbaum,Langanke,Rolfs Z.Phys.327(1987)461)
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ELECTRON SCREENING

• Enhanced cross section at low energies

Enhancement flab(E) factor in the astrophysical
Sb(E)-factor
(Assenbaum,Langanke,Rolfs Z.Phys.327(1987)461)
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7Li(p,a)4He
Ss(E)
S(E) (MeV b)
Ss(E)
E (KeV)
Evidences of electron screening
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11B(p,a)8Be
Ss(E)
S(E) (MeV b)
Sb(E)
Ecm (keV)
Evidences of electron screening
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ELECTRON SCREENING POSSIBLE THEORETICAL SOLUTION
POSSIBLE THEORETICAL SOLUTION of ELECTRON
SCREENING PROBLEM
If it is known a theorical approach to
extract the electron screening potential Ue,
It will be possible to extract the
astrophysical bare nucleus S(E)b-factor from
measured astrophysical shielded nucleus
Ss(E)-factor
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Experimental approach
Reactions between charged particles

Examples Li reactions
Experimental Electron screening potential
(Ue)exp compared with the Electron screening
potential in the adiabatic approximation (Ue) ad

(Ue)exp gtgt (Ue)ad Sistematic discrepance
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ELECTRON SCREENING Li reactions
6Li d ? a a S0 16.9 MeV b
6Lid? a a
7Li p ? a a S055 ? 3 keV b
R-matrix calculation
7Lip? a a
6Lip a3He So 3 ? 0.9 MeVb
6Lip? a 3He
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ELECTRON SCREENING
(Ue)exp gtgt (Ue)ad Sistematic discrepance
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ELECTRON SCREENING
Electron screening
Theory
NO SOLUTION
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ELECTRON SCREENING
Cross sections at Gamow energies Standard
solution
EXTRAPOLATION
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EXTRAPOLATION
To avoid extrapolations, experimental techniques
were improved
After improving measurements (at very low
energies), electron screening effects were
discovered
In any case Extrapolation is necessary
To extract from direct (shielded) measurements
the bare astrophysical Sb(E) -factor,
extrapolation were performed at higher energy
19
GENERAL PROBLEM
ASTROPHYSICAL APPLICATION
The electron screening in laboratory Ue(lab) is
DIFFERENT from electron screening in plasma
Ue(plasma)
Shielded Nucleus Astrophyisical Ss(E)-factor
(Measured )

EXTRAPOLATION
Bare nucleus Astrophysical Sb(E)-Factor
Correction for stellar screening fplasma
Splasma(E) fplasma (E) Sb(E) or splasma(E)
fplasma (E) sb(E)
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GENERAL PROBLEM
ASTROPHYSICAL APPLICATION
need to understand Ue(lab) in the laboratory (or
the enhancement flab(E) factor in laboratory)
improve calculation of Ue(plasma) (or the
enhancement fplasma(E) factor in in plasma)
Shielded Nucleus Astrophyisical Ss(E)-factor
(Measured )

EXTRAPOLATION
Bare nucleus Astrophysical Sb(E)-Factor
Correction for stellar screening fplasma
Splasma(E) fplasma (E) Sb(E) or splasma(E)
fplasma (E) sb(E)
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INDIRECT METHODS ARE NEEDED
TO STUDY THE ELECTRON SCREENING
Independent measurements of electrom screening
potential Ue are needed !!!

• NEW METHODS ARE NECESSARY
• to measure cross sections at never reached
  energies

• to retrieve information on electron screening
  effect when ultra-low energy measurements are
  available.

INDIRECT METHODS ARE NEEDED
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NAIN INDIRECT METHODS
a) - Coulomb dissociation
b) - Asymptotic Normalization Coefficients (Anc)

• - Transfer reactions

d) - The Trojan Horse Method (THM)
e) b-delayed particle emission
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- Trojan Horse Method
Main application to extract bare nucleus
cross sections for two-body charged particle
reactions (no capture cross sections) using the
quasi-free mechanism
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QUASI-FREE REACTION MECHANISM Generality
Three body reactions
A B ? C D S
-The upper pole describes the virtual break up
of the target nucleus A into the cluster x
(partecipant) and S
Can be described by a Feynmam diagram
-The S cluster acts as a spectator to x B ? C
D virtual reaction which takes place in the
lower pole
-The A nucleus present a strong cluster
structure A x ? S clusters
This description is called impulse approximation
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THREE-BODY CROSS SECTION IN THE PLANE WAVE
IMPULSE APPROXIMATION (PWIA)
The cross section of the three body reaction can
be factorized into two terms corresponding to the
two vertices
Off energy shell
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THREE-BODY CROSS SECTION IN THE PLANE WAVE
IMPULSE APPROXIMATION (PWIA)
Second pole
Off energy shell
?
KF is a kinematical factor containing the final
state phace-space and it is a function of the
masses, momenta and angles of the outgoing
particles
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THREE-BODY CROSS SECTION IN THE PLANE WAVE
IMPULSE APPROXIMATION (PWIA)
Second pole
Off energy shell
?
F(qxS)2 describes the intercluster (x-S)
momentum distribution F(qxS) is the Fourier
transform of the radial wave function c(r) for
the x-S intercluster motion (Hanchel, Eckart and
Hulthen functions)
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THREE-BODY CROSS SECTION IN THE PLANE WAVE
IMPULSE APPROXIMATION (PWIA)
Off energy shell
?
Second pole
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THREE-BODY CROSS SECTION IN THE PLANE WAVE
IMPULSE APPROXIMATION (PWIA)
Off energy shell
?
Second pole
( ds/dW) Ec.m. is given in postcollision
prescription by
Ecm Ec-C - Q2b Q2b is the two-body Q-value
of the x B? C D reaction Ec-C is the
relative energy between the outgoing particles c
and D
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INDIRECT TWO-BODY CROSS SECTION
It is possible to extract two-body cross section
? B x ? C D
from quasi- free contribution of an appropriate
three-body reaction A B
? C D S
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- VALIDITY TESTS OF THE POLAR APPROXIMATION
The behaviour of the angular distribution s(q)THM
is compared with the behaviour of the angular
distribution s(q)Direct of the two-body reaction
Comparison between direct and indirect
angular distributions
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FIRST VALIDITY TEST. 1970- IPN- ORSAY
angular distributions
Comparison between direct and indirect
DWBA
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- VALIDITY TESTS OF THE POLAR APPROXIMATION
The behaviour of the angular distribution s(E)THM
is compared with the behaviour of the
excitation functions s(E)Direct of the two-body
reaction
Comparison between direct and indirect
excitation functions
34
Direct-indirect excitation function
7Li(p,a)4He studied through the 7Li(d,aa)n
reaction 28-48 MeV
PWIA
7Li(d,aa) n 28-48 MeV
7Li(p,a)4He
M. Zadro et al. Phys.Rev.C 40,(1989),181
35
Direct-indirect excitation function6Li(p,a)3He
studied through the 6Li(d,a 3He)n reaction
21.6-33.6 MeV
RISULTATI
6Li(d,a3He)n 21.6-33.6 MeV
PWIA
7Li(p,a)4He
6Li p ? a 3He
G. Calvi et al. Phys.Rev.C 41,(1990),1848
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Direct-indirect excitation function 12C(a,a)12C
studied through the 3-body quasi-free reaction
12C(6Li,a12C)2H
RISULTATI
12C a ? a 12C
12C(6Li,a12C)2H ELi18 MeV
MPWBA

d
6Li
a
12C
12C
C.Spitaleri et al E.P.J A 7,(2000),181 M.G.
Pellegriti et al. NPA688,543 (2001)
a
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from QUASI-FREE REACTIONS to TROJAN-HORSE
METHOD
Ecm EC-D - Q2b gt Coulomb Barrier x-B
Ecm EC-D - Q2b lt Coulomb Barrier x-B
38

Quasi-Free mechanism Trojan Horse Method
In the quasi-free kinematical regime, the
incoming Trojan horse particle A is
accelerated at energies EA above the Coulomb
barrier energy (EAB)Coul. Bar. EA gt
(EAB)Coulomb Barrier
After penetrating through the Coulomb barrier,
nucleus A undergoes breakup leaving particle x
(partecipant) to interact with target A while
projectile S (spectator) flies away
B x ? C D
G.Baur Phys. Lett.B178,(1986),135
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Quasi-Free mechanism Trojan Horse Method
EB Coulomb Barrier between the nucleus
target B and the projectile nucleus A EBAgt
EB
Troja nucleus B
Troja Walls Coulomb barrier
Trojan Horse A nucleus
S
A
S
x
x
x
nuclear field
x
EB
B
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Quasi-Free mechanism Trojan Horse Method
EB Coulomb Barrier between the nucleus
target B and the projectile nucleus A EBAgt
EB
Troja nucleus B
Trojan Horse A nucleus
A
S
nuclear field
x
c
B
D
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Quasi-Free mechanism Trojan Horse Method
The main advantages of the THM are that the
extracted cross section of the binary subprocess
does not contain the Coulomb barrier factor
No Coulomb barrier effects
TH cross section can be used to determine the
energy dependence of the astrophysical factor,
S(E), of the binary process x B? c
C, down to zero relative kinetic energy of the
particles x and B without distortion due to
electron screening.
  No extrapolation
No electron screening effects
42
MAIN LIMITATIONS OF THE METHOD
A- Preliminary study of quasi-free mechanism.
Tests of validity are necessary. - Presence
of different 3-body reaction mechanisms
(Sequential Decay) C- Measurements with
high angular and energy resolutions are
needed   D-Theoretical analysis is needed -
PWIA, MPWBA, DBWA, ..
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Quasi-Free mechanism Trojan Horse Method
The absolute value of S(E) must be found by
normalization to direct measurements at higher
energies.
At low energies where electron screening becomes
important, comparison of the astrophysical factor
determinated from the TM Method to the direct
result provides a determination of the screening
potential.
44
What has to be done practically?
WHAT HAS TO BE DONE PRACTICALLY ?
Before data taking
MUST BE FOUND SUITABLE

• Trojan Horse nucleus ? 3-body reaction

2) Suitable kinematical conditions
45
Interclusters- l- relative
l 0
l 0
l 0
l 0
l 1
l 1
l 0
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IN PRINCIPLE It is possible to study
nuclear reactions induced by light nuclear
particles (both stable and unstable).
Indirect Beam Beam
n, d, 3H, p, d, 3He d,
3H, 3He, 6Li t, 7Li 3He,
7Be a, 6Li, 7Li, 7Be, 9B
5He 9Be
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MUST BE FOUND SUITABLE

• Trojan Horse nucleus ? 3-body reaction

virtual reaction 7Li p ? a a
3He
d

p
a
7Li
a
7Li 3He ? a a d
48
Direct-indirect excitation function
7Li(p,a)4He studied through the
7Li(3He,aa)d reaction E3He MeV (2000)
7Li(d,aa)n reaction Eli 28-48 MeV (1979)
7Li p ? a a
PWIA
Direct excitation function
Zadro et al. PRC. 40,(1989)181
A.Tumino et al. ,Epj (2005)
Resonances are reproduced l
49
6Li(p,a)3He studied through the 6Li(d,a 3He)n
reaction 14, 25 MeV
Resonances reproduced very well
Typel Wolter Few Body Systems 29,(2000),75
Tandem Catania INFN LNS Dynamitron-DTL -
Bochum ELi 14, 25 MeV
50
Direct-indirect excitation function
6Li(p,a)3He studied through the
6Li(d,a3He)n reaction ELi 2 MeV (1979)
6Li(3He,a3He)d reaction ELi 2 MeV (2005)
Barrier below
above
6Li p ? a 3He
MPWBA
PWIA
6Li p ? a 3He
THM QF
VERY PRELIMINARY RESULTS !
A.Tumino et al. PRC 67,(2003),065803
51
After data taking
What has to be done practically?

• Selection of the three body reaction of interest.
• 4) Check if the quasi free reaction mechanism
  is present and
• can be discriminated from others.
• Reconstruct s2bbare and multiply it by the
  penetration factor.
• 6) Tests of validity of the Pole Approximation
• Verify that all direct data are reproduced
• - excitation functions including
  resonances
• -angular distributions

52
1-
How to discriminate the quasi-free contribution?
9Be(3He,a a)4He 4MeV
Study of angular correlations energy spectra
coincidence spectra projected for a fixed ??1 and
different ??2 Events corresponding to a
quasi-free mechanism Coincidence yield attains
a max. for pn approaching zero and decreases
while moving far from this condition
??
Quasi free angles
Necessary condition for existence quasi-free
mechanism
A.Kasagi . et al. Nucl. Phys.A,239(1975),233
53
EXPERIMENTAL Momentum distribution neutron
2-
How to discriminate the quasi-free contribution?
11B p ? 8Be ao
PWIA
Hulthen wave function
a0.2317 fm-1 ß1.202 fm-1
Selected Momentum range (-40 40) Mev/c
Necessary condition for existence quasi-free
mechanism
FWHM 60 MeV/c
54
Main problem to extract data
1-Example

3He d ? a p
Quasi-free
(3He 6Li ? a p a)
6Li
a
d
a
p
3He
p
3He
a
8Be
a
6Li
Sequential Decay
55
Indirect Two-body cross section
d3s

Measured
Exper.
ds
?
dO
KF F(q xs) 2
x B? C D
Indirect 2-body cross section
Calculated
below the Coulomb barrier with
regular and irregular Coulomb wave
functions w

56
11B p ? 8Be ao
E.5 .1 MeV
E.7 .1 MeV
THM
Direct data
E.9 .1 MeV
2H(11B ,8Be ao )n
Spitaleri et al, P.R.C 69,55806 (2004)
57
OFF-ENERGY-SHELL CORRECTION
Recently calculations Energy dependence of the
off-shell (red dashed line) and on-shell (black
solid line) astrophysical factors for (a) the
7Li(p,a)4He reaction (b) 6Li(d,a)4He
reaction are the same !
7Li(p,a)4He
6Li(d,a)4He
ARxIVNUCL-TH/0602001 v1 1 Feb 2006
on shell.
off shell.
ds(E)
ds(E)
?
dO
dO
x B? C D
x B? C D
Sezione durto 2 corpi diretta
Sezione durto 2 corpi indiretta
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Astrophysical Applications of the THM

• Depletion of light nuclei (Li, Be, B)
• (Talk R.G. Pizzone)
• - Novae
• The Fluorine problem in the AGB
• (Talk M.La Cognata)

59
Depletion lights nuclei Li, B, Be
INDIRECT REACTIONS 7Li d ? a a
nspett. 7Li 3He ? a a
dspett 6Li 6Li ? a a
aspett. 6Li d ? a 3He
nspett. 6Li 3He ? a a dspett
DIRECT REACTIONS 1- 7Li p ? a a 2-
6Li d ? a a 3- 6Li p ? a 3He
11B d ? 8Be a nspett. 10B p ?
7Be a nspett. 9B d ? 6Li a
nspett.
4- 11B p ? 8Be a 7- 10B p ?
7Be a 8- 9B p ? 6Li a
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Li reactions
6Li d ? a a S0 16.9 MeV b
6Lid? a a
7Li p ? a a S055 ? 3 keV b
R-matrix calculation
7Lip? a a
6Lip a3He So 3 ? 0.9 MeVb
6Lip? a 3He
(Ue)exp gtgt (Ue)ad
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Li reactions
6Li d ? a a S0 16.9 MeV b

• Present extrapolations are confirmed for the
  studied reactions
• 2. The measured Ue agrees with direct
  measurements
• 3. The systematic discrepancy, experiment-theory,
  for Ue is confirmed

7Li p ? a a S055 ? 3 keV b
6Lip a3He So 3 ? 0.9 MeVb
Unchanged astrophysical implications !!!
62
10B(p,?)7Be
Astrophysical factor S(E)
extrapolation
10B p ? a 7Be
S(0)THM 562 168 (Mevb)
The Resonance at Ecm 10 keV corresponding to
the 11C (8.70 MeV) decay has been reproduced
GAMOV ENERGY
PRELIMINARY RESULTS
63
The Fluorine problem in the AGB
INDIRECT REACTIONS 11- 15N p ? a 12C
12 - 18O p ? a 15N
INDIRECT REACTIONS 15N d ? a 12C
nspett. 18O d ? a 15N nspett.
Talk. Marco La Cognata
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The Fluorine problem in the AGB
INDIRECT REACTIONS
INDIRECT REACTIONS 19F 6Li ? 22Ne p
dspett.
19F a ? 22Ne p (FSU)
Experiment December 2006
65
Novae
INDIRECT REACTIONS 18Fp ? 15O
a (CNS-Riken Tokio) 17O p ? 14N a
(LNS-Catania)
18Fd ? 15O a n 17O d ? 14N
a nspett.
66
Deuteron-Beam as a virtual Neutron-beam
n
(Talk M. Gulino)
67
Comparison between direct-indirect excitation
function 7Li(p,a)4He studied through the
7Li(d,aa)n reaction MeV
Comparison between direct-indirect excitation
function 6Li(n,a)3H studied through the 6Li(d,a
3H)p reaction MeV E6Li14 MeV
THM
Tandem- LNS
direct data
PWIA
6Lin
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LABORATORY
-ACCELERATOR - LNS
Catania
(Italy) Tandem -
DTL Bochum (Germania)
Tandem -TAMU College Station
(USA) Ciclotrone -REZ
Praga (Rep. Ceca)
Ciclotrone-ATOMKI Debrecen
(Ungheria) Ciclotrone-RIKEN
Tokyo (Giappone)
Ciclotrone-IF San Paolo
(Brasile) Tandem
- CIAE Beijing (Cina)
Tandem - FSU
Talasse (USA)
Tandem
69
S. CHERUBINI, V.CRUCILLÀ, M.GULINO, M.LA
COGNATA, M.LAMIA,F.MUDÒ, R.G.PIZZONE, S.PUGLIA,
G.RAPISARDA, S.ROMANO, L.SERGI, C.SPITALERI,
S.TUDISCO, A.TUMINO I N F N, Laboratori Nazionali
del Sud, Catania, Italy and Università di
Catania, Italy C.ROLFS  Institut für
Experimentalphysik III- Ruhr Universität Bochum,
Germany S.TYPEL GSI-Germany A.MUKHAMEDZHANOV,
B.TRIBBLE, L.TRACE,V.GOLDBERG Ciclotron
Institute, Texas AM University,
Usa S.KUBONO CNS, Tokio,Japan A.COC, CSNSM,
Orsay,France F.HAMMACHE IPN, Orsay,
France V.BURJAN, V.KROHA Nuclear Physics
Institute, Academic of Science,Rez, Czech
Rep. T.MOTOBAYASHI RIKEN , Tokio,Japan Z.ELEKES,
Z.FULOP, G.GYURKY, G.KISS, E.SOMORJAI Inst. of
Nuclear Research ofAcademic of Science
Debrecen,Ungaria G.ROGACHEV FSU, USA N.CARLIN,
M.GAMEIRO MUNHOZ, M.GIMENEZ DEL SANTO, R.LIGUORI
NETO, M.DE MOURA, F.SOUZA, A.SUAIDE, E.SZANTO,
A.SZANTO DE TOLEDO Dipartimento de Fisica
Nucleare, Universidade de Sao Paulo,Brasil
70
TheTrojan Horse in the Art
Grazie
Giovanni Domenico TIEPOLO Italian painter,
Venetian school (b. 1727, Venezia, d. 1804,
Venezia)