Diapositiva 1

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23rd Bruxelles meeting between astrophysicists
and nuclear physicists, 11 December 2006
The Trojan Horse Method in Nuclear Astrophysics
Aurora Tumino
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Nuclear Astrophysics
The detailed understanding of the origin of the
chemical elements and their isotopes
combines Astrophysics And Nuclear Physics
Supernova 1054 (Crab Nubula)
Red giant Betelgeuse
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Nuclear reactions
at the heart of nuclear astrophysics they
made/make possible the nucleosynthesis of the
elements in the earliest stage of the universe as
well as in all the objects formed
thereafter Theories of nucleosynthesis have
identified the most important sites of the
element formation and also the diverse nuclear
processes involved in their production.
Overview of main nuclear processes and
astrophysical sites
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Nuclear Reactions between charged particles
at astrophysical energies
? ?picobarn ? Low signal-to-noise ratio due to
the Coulomb barrier between the interacting
nuclei 
Extrapolation from the higher energies by using
the ASTROPHYSICAL FACTOR   S(E) ?(E) E
exp(2ph) S(E) is a smoothly varying function of
the energy than the cross section ?(E)

• gt to increase the number of
  detected particles
• gt to reduce the background

but large uncertainties in the extrapolation ?
EXPERIMENTAL IMPROVEMENTS/SOLUTIONS
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but further problem at astrophysical energies
? ? ? ?
Electron Screening
S(E) enhancement experimentally found due to the
Electron Screening
S(E)s S(E)b exp(phUe/E)
3He 2H ? p 4He
In astrophysical plasma - the screening, due to
free electrons in plasma, can be different ? we
need S(E)b to evaluate reaction rates
Although we try to improve experimental
techniques to measure at very low energy ? ?
Sb(E)-factor extracted from
extrapolation of higher energy data
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• new methods are necessary
• to measure cross sections at never reached
  energies
• to get independent information on Ue

-gt -gt -gt INDIRECT METHODS

•  
• Asymptotic Normalization Coefficients (ANC)
• Coulomb dissociation
• Trojan Horse Method (THM) 

to extract direct capture cross sections using
peripheral transfer reactions
to study radiative capture reactions
to extract charged particle reaction cross
sections using the quasi-free mechanism
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Trojan Horse Method
Basic principle astrophysically relevant
two-body ? from quasi- free contribution of an
appropriate three-body reaction A a ? c C s
? ? ? A x ? c C a x ? s clusters
Quasi-free mechanism

• only x - A interaction
• s spectator (ps0)

EA gt ECoul ?
NO Coulomb suppression NO electron screening
Eq.f. EAx Bx-s intercluster motion
Eq.f. ? 0 !!!
plays a key role in compensating for the beam
energy
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Theoretical approaches to the THM
A a ? c C s ? ? ? A x ? c C

• PWIA hypotheses
• A does not interact simultaneously with x and s
• The presence of s does not influence the A-x
• interaction

KF and KF kinematical factors ???2 momentum
distribution of s inside a d?N/d? Nuclear cross
section for the Ax?Cc reaction

• DWBA formalism
• (S. Typel and H. Wolter, Few-Body Syst. 29 (2000)
  75)
• distortions introduced in the cC channel, but
  plane waves for the three-body entrance/exit
  channel
• off-energy-shell effects corresponding to the
  suppression of the Coulomb barrier are included

but No absolute value of the cross section
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What has to be done practically?
Before data taking 1) Suitable Trojan Horse
nucleus must be found e.g. 6Li (a-d structure
with Ebinding1.47MeV), d (p-n structure with
Ebinding 2.22MeV)
2) Suitable kinematical conditions which
correspond to the expected quasi free
contribution must be selected
3) Optimize beam energy kinematical conditions
in order to make the Magnifying glass effect
dominant in a chosen relative energy region
what we find there is a weak dependence of the
relative energy EA-x around the minimum at given
energies of the detected particles
Example D(Ea-d)/D(Ea) ? 1 - 2
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Typical experimental set-up
Very simple, consisting of a few
telescopes Trigger coincidence detection of two
particles
1
4
projectile ?
target
2
Telescopes
3
?E-detector Silicon detectors (10 to 30 ?m
thick) or Ionization Chambers
E-detector Position sensitive detector (500 to
1000 ?m thick)
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After data taking 4) Selection of the three
body reaction of interest. 5) Check if the quasi
free reaction mechanism is present and can be
discriminated from others (mainly sequential
decays). 6) Reconstruct s2bbare and multiply it
by the penetration factor. 7) Normalise s2bTHM
to s2bDirect above barrier. 8) Verify that
direct data are reproduced. 9) If
points 1-8 are true, we believe that THM data are
reliable where direct data are not available.
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Off-line Channel Selection
Selection of the events corresponding to the
three body reaction 2H(15N,?012C)n ? Carbon
locus in the experimental ?E-E 2D plot ? Peaks
in the Q-value spectrum
12C
Two peaks ground state of 12C (Q-value 2.74
MeV) first excited state of 12C _at_ 4.44 MeV
(Q-values -1.70 MeV) Accurate calibration
procedure!!
?1
?0
Q (MeV)
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Selection of quasi-free contribution
Angular correlation analysis
Need to select the reaction mechanism via angular
correlation analysis coincidence spectra
projected onto the Ep axis for a fixed ?p and
different ??
Example for the 3He 6Li ? ? p ? 4He-d
relative motion within 6Li in s-wave ? events
corresponding to a quasi-free mechanism show an
enhancement of the yield for p4He approaching
zero (QF angles). As expected, large background
contribution sequential decay through the 8Be
first excited state (already seen in a previous
experiment (Zadro et al. (1987))
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Subtraction of the 8Be 1st excited
state background contribution
J?2 Ex3.04 MeV FWHM ?1.5 MeV
For each pair of (??,?p) quasi free angles the
8Be contribution is subtracted by fitting the
level with a Breit-Wigner in the variable E?-?.
Further analysis with the remaining events
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Momentum Distribution
An observable which turns out to be more
sensitive to the reaction mechanism is the shape
of the experimental momentum distribution
The extracted experimental momentum distribution
is compared with the theoretical one. For p-n
system it is given by the Hulthén wave function
in momentum space
G2(ps)N
N normalization parameter a 0.2317 fm-1 b
1.202 fm-1
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Extraction of the 2-body cross section

• Monte Carlo simulation of the three-body cross
  section under the assumptions
• - PWIA/DWBA approach
• Quasi-free contribution is the only reaction
  mechanism
• a ps window of 20 MeV/c is considered

Coincidence yield
?bare(E)
KF ?(ps)2 P0-1
Spitaleri et al, P.R.C 69,55806 (2004)
The indirect THM cross section ?bare(E) is
normalized to the direct data at high energies,
where the electron screening is negligible
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Reactions recently studied
6Li d ? a a via 6Li6Li ? aaa S0 16.9
MeV b
6Lid? a a
7Lip ? aa via 7Lid ? aa n S0 55 ? 3 keV
b
R-matrix calculations
7Lip? a a
6Lip ? a 3He via 6Lid ? a 3Hen So 3.? 0.9
MeV b
6Lip? a 3He
C. Spitaleri et al., PRC60 (1999)055802 C.
Spitaleri et al., PRC63 (2001) 005801 A. Tumino
et al., PRC67 (2003) 065803
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Li reactions

• 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
  
• 4. The isotopical independence of the electron
  screening effect is confirmed.

The Lithium depletion problem not at the nuclear
physics level !!!
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...reactions recently studied
11B p ? ?o 8Be via 11B d ? ?o
8Be n _at_ 27 MeV
10B p ? ?o 7Be via 10B d ? ?o
7Be n _at_ 27 MeV

• B importance
• The determination of the surface abundance of B
  together with Li and Be acts as a probe for the
  internal stellar structure and it can give
  additional information about the mixing
  mechanisms acting inside (T64.5 K)

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...reactions recently studied
15N p ? ? 12C via 15N d ? ?
12C n _at_ 60 MeV
it can affect the production of 19F since it
removes protons and 15N nuclei from 19F
production chain
18O p ? ? 15N via 18O d ? ?
15N n _at_ 60 MeV reaction belonging to the 19F
production path

• The importance of 19F in astrophysics
• its abundance observed in red giants can
  constrain AGB star models
• Open problem
• fluorine abundance in red giants is enhanced by
  large factors with respect to the solar one

This would imply C/O values much larger than what
experimental data suggest
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11B(p,?0)8Be direct and indirect data

• Astrophysical factor

Direct reaction at astrophysical energies
proceeds through an intermediate state of 12C at
16.1 MeV ? Very important result resonance
reproduced through the indirect approach!
S(0)b 0.41 ? 0.09 MeV b
C. Spitaleri et al., PRC 69 (2004) 055806 S.
Romano et al., NPA (2004)
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10B(p,?0)7Be direct and indirect data
L. Lamia et al., NPA (2006) in press
The Resonance at Ecm 10 keV corresponding to
the 11C (8.70 MeV) decay has been reproduced
S(0)THM 562 168 (Mevb)
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The 15N p ? ? 12C Astrophysical S-factor

• Results reported in terms of S(E) factors
• - THM data as red dots
• Direct data from NACRE as
• black open dots

The error bars include both statistical and
normalization uncertainties
R-matrix fit assuming a destructive interference
between the 300 keV, 962 keV (12.44 and 13.09
MeV states of 16O) resonances and a subthreshold
one (16O level at Eexc 9.58 MeV), all of them
with J? 1-
Sbare(0)62 ? 10 MeVb
Data very well reproduced!
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18O p ? ? 15N recent experiment at
TAMU
Reaction path to 19F in the He intershell
18O(p,?)15N(?,?)19F
PRELIMINARY RESULTS
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6Li(n,?)3H via 6Li(d,?3H)p reaction E6Li 14 MeV
The good agreement between THM and direct data
suggests that no off-energy shell effects other
than those deriving from the Coulomb barrier,
when present, should be considered
THM
direct data
? arb.units
New results from a recent experiment magnifying
glass effect in the resonant region
Deuteron-Beam as a virtual Neutron-beam
A. Tumino et al., EPJ A (2005) 1
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11Bp ? 8Be? via 11Bd ?
8Be?n (in particular the 8Be?1
channel) 9Bep ? 6Li? via 9Be d ? 6Li?n
(magnifying lens effect) 19F? ? 22Nep via
19F6Li ? p22Ned (19F burning)
December 2006 18Fp ? ?15O via
18Fd ? ?15On beam-time already scheduled
at Riken (Wako Shi Tokyo)
Near future
radioactive nuclei
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The collaboration
C. SPITALERI, S. CHERUBINI, V.CRUCILLÀ, M.GULINO,
M. LA COGNATA, M.LAMIA, F.MUDÒ, R.G.PIZZONE,
S.PUGLIA, G.G. RAPISARDA, S.ROMANO, M.L.SERGI,
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, T.
MOTOBAYASHI CNS and RIKEN, 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. 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
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Electron Screening
but further problem at astrophysical energies
? ? ? ?
Due to the ? cloud, the interacting ions see a
potential which is lower than the pure Coulomb
one.

• The penetration of a shielded Coulomb potential
  is equivalent to that of bare nuclei at energy
  Eeff E Ue
• Enhancement in the S(E) factor
• S(E)screen. S(E)bareexp(phUe/E)

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...Electron Screening
? Example of theoretical estimates for
Ue Adiabatic approximation If VprojltltV? the
electrons continuously rearrange their orbits
while projectile and target approach each
other UeEc-E1-E2 E1, E2, Ec electronic
binding energies of projectile, target and
compound system projectiletarget
? Some Ue teoretical values
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...Electron Screening
S(E) enhancement experimentally found
S(E)s S(E)b exp(phUe/E)
Systematic discrepancy UexpgtUtheo Why?? Energy
loss below 100 keV ? Theoretical models for
Ue? Extrapolations of S(E)bare ?
3He 2H ? p 4He
In astrophysical plasma - the screening, due to
free electrons in plasma, can be different ? we
need S(E)b to evaluate reaction rates
Although we do our best to improve experimental
techniques in order to measure at very low energy
? ? Sb(E)-factor
extracted from extrapolation of higher energy
data
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Study of the Reaction Mechanism I
15N d? 12C a n
?-n vs 12C-? and 12C-n vs 12C-? relative energy
plots Horizontal loci marked by yellow dashed
lines ? excited states of 13C at 6.684 MeV, 7.49
MeV, 7.55 MeV, 7.67 MeV (where the last three
levels are not resolved) Negligible
contribution!!
very clear vertical loci marked by red and green
lines ? excited states of 16O at 12.44 MeV, 13.09
MeV and 13.26 MeV Sequential decays or QF
contribution??
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Study of the Reaction Mechanism II
15N d? 12C a n
Disentangle the QF from SD mechanisms
? correlation between the coincidence yield as a
function of Ec.m. ( E12C-? - Qtwo-body) and the
momentum ps for all coincidence events
? necessary condition for the dominance of the
quasi-free mechanism in the region approaching
zero spectator momentum (s-wave relative motion)
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What has to be done practically?
Before data taking 1) Suitable Trojan Horse
nucleus must be found e.g. 6Li (a-d structure
with Ebinding1.47MeV), d (p-n structure with
Ebinding 2.22MeV)
35
what has to be done practically?
2) Suitable kinematical conditions which
correspond to the expected quasi free
contribution must be selected
36
Typel Wolter Few Body Systems 29, 7
(2000)Typel Baur (2002) ,Ann. Phys.305,228
(2003)
T matrix formalism
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...reactions recently studied
3He d ? ? p via 3He 6Li ? ? p
? _at_ 5,6 MeV
Key reaction in the Big Bang nucleosynthesis
network
Electron screening effects these reactions show
a very pronounced enhancement in the
cross-section at low energy significantly larger
than could be accounted for from the adiabatic
limit
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Sbare(0) and Ue for the 3He(d,p)4He
The THM data (full dots) agree quite well with
the direct behaviour (open dots), and the 200 keV
resonance associated with the 5Li level at 16.87
MeV is reproduced.
M. La Cognata et al., PRC72 (2005) 065802
Sbare(0) from a fit on THM data is performed
Sbare(E)3.30 12.67 E - 28.8 E2 0.2
exp(E-E0)2/2?2
Ue by fitting Sscreen(E) from low-energy direct
data using the following fitting function
Sbare(0)6.4 ? 1.3 MeVb
Sscreen(E) Sbare(E) x exp(??Ue/E)
Ue155?34 eV