Spitaleri CSSP05

Carpathian Summer School of Physics 2005Exotic Nuclei and Nuclear/Particle Astrophysics Mamaia-Constanta, Romania: 

C. Spitaleri Università di Catania-Italy Laboratori Nazionali del Sud- Catania-Italy Recent applications of the Trojan Horse Method to Nuclear Astrophysics Carpathian Summer School of Physics 2005 Exotic Nuclei and Nuclear/Particle Astrophysics Mamaia-Constanta, Romania

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Why indirect measurements of cross sections at astrophysically relevant energies?

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The main problem in the charged particle cross section measurements at astrophysical energies is the presence of the Coulomb barrier between the interacting nuclei Ecoul ~ Z1Z2 (MeV) tunnel effect cross sections measurements: Reactions between charged particles

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Ecoul ~ Z1Z2 (MeV) determines exponential drop in abundance curve ! reactions occur through TUNNEL EFFECT The energy available from thermal motion is lower than Coulomb barrier energy kT << Ec cross sections measurements: during quiescent burnings T ~ 15x106 K (e.g. our Sun)  kT ~ 1 keV T ~ 1010 K (Big Bang)  kT ~ 2 MeV

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range nano-picobarn cross sections in general, their direct evaluation is -severely hindered -and in some cases even beyond present technical possibilities. s(E) cross sections measurements Gamow energy Gamow energy

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range nano-picobarn cross sections s(E) cross sections measurements Gamow energy Gamow energy Possible solution

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range nano-picobarn cross sections s(E) cross sections measurements Gamow energy Gamow energy Possible solution Extrapolation

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Thermonuclear reactions in star : Gamow peak

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Examples: T ~ 15x106 K (T6 = 15) varies depending on reaction and/or temperature Gamow peak: Thermonuclear reactions in star : Gamow peak

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CROSS SECTION Experimental procedure LOG SCALE  direct measurements E0 Ecoul Coulomb barrier (E) non-resonant resonance extrapolation needed ! many orders of magnitude Experimental approach: extrapolation The extraction of the cross sections sb(E) at the astrophysical energies (Gamow energies) could be estimated by extrapolating measurements performed at higher energies

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CROSS SECTION Experimental procedure LOG SCALE  direct measurements E0 Ecoul Coulomb barrier (E) non-resonant resonance extrapolation needed ! many orders of magnitude Experimental approach: extrapolation Since the cross-section varies of several orders of magnitude, the extrapolation procedure can be quite complicate

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CROSS SECTION Experimental procedure LOG SCALE  direct measurements E0 Ecoul Coulomb barrier (E) non-resonant resonance extrapolation needed ! many orders of magnitude Experimental approach: extrapolation Astrophysical S(E)-factor is introduced.

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Cross section for non-resonant reactions geometrical factor (particle’s de Broglie wavelength) interaction matrix element Penetrability probability depends on projectile’s angular momentum  and energy E Astrophysical S(E)-factor

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Cross section for non-resonant reactions Astrophysical S(E)-Factor Astrophysical S(E)-factor

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Astrophysical energies Sb(E) is a smoothly varying function of the energy than the cross section sb(E) The Sb(E) –factor often is estimated by extrapolating measurements performed at higher energies by assumption of a theoretical model Experimental approach: extrapolation It is much easier extrapolation with the astrophysical S(E)-factor !!

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DANGER OF EXTRAPOLATION … large uncertainties in the extrapolation! cross sections measurements

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non resonant process interaction energy E extrapolation direct measurement 0 S(E) LINEAR SCALE S(E)-FACTOR -Er sub-threshold resonance Extrapolation cross sections measurements

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Experimental approach: cross sections measurements : 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,……) ALTERNATIVE SOLUTIONS

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EXPERIMENTAL SOLUTION (uncertainties in the extrapolation) - IMPROVEMENTS TO REDUCE THE BACKGROUND Use of laboratory with natural shield - ( underground physics) Use of magnetic apparatus  (Recoil Mass Separator) ALTERNATIVE SOLUTIONS Experimental approach: cross sections measurements :

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but… at astrophysical energies NEW PROBLEM Experimental approach: cross sections measurements : electron screening

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In the accurate measurements for the determination of nuclear cross-sections at the Gamow energy, in the laboratory, (Assenbaum,Langanke,Rolfs: Z.Phys.327(1987)461) Experimental approach: electron screening Enhancement flab(E) –factor in the astrophysical Sb(E)-factor has been experimentally found

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It is evident the presence of the Electron Screening between the interacting atoms (target and projectile) (Assenbaum,Langanke,Rolfs: Z.Phys.327(1987)461) Experimental approach: electron screening The atomic electron cloud surrounding the nucleus acts as a screening potential Ue For nuclear reaction induced in laboratory the target and projectile nuclei are in the form of atoms.

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Possible solution: Electron screening THEORY

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It is evident the presence of the Electron Screening between the interacting atoms (target and projectile) (Assenbaum,Langanke,Rolfs: Z.Phys.327(1987)461) Experimental approach: electron screening The atomic electron cloud surrounding the nucleus acts as a screening potential Ue For nuclear reaction induced in laboratory the target and projectile nuclei are in the form of atoms.

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Experimental approach : Reactions between charged particles

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Bare nucleus Astrophysical Sb(E)-Factor Correction for stellar screening Enhancement fplasma-factor Shielded Nucleus Astrophyisical Ss(E)-factor (Measured ) Splasma(E) = fplasma (E) Sb(E) or splasma(E) = fplasma (E) sb(E) Experimental approach : Reactions between charged particles – Correction with Theory (approach to extract the electron screening potential Ue,)

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Example : Adiabatic approximation: If the velocity of the projectiles Vpro is lesser than the velocity of the electrons V Vproj<<V the electrons continuously rearrange their orbits while projectile and target approach each other Ue=Ec-E1-E2 E1, E2, Ec electronic binding energies of projectile, target and ‘compound system’ projectile+target Experimental approach : Reactions between charged particles –

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BUT FURTHER PROBLEM Experimental Electron screening potential (Ue)expis larger than Electron screening potential in the adiabatic approximation (Ue) ad (Ue)exp >> (Ue)ad Sistematic discrepance Experimental approach : Reactions between charged particles –  Typical Ue values

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Experimental Electron screening potential (Ue)exp compared with the Electron screening potential in the adiabatic approximation (Ue) ad Examples: Li reactions Experimental approach : Reactions between charged particles

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7Li + p  a + a S0=55  3 keV b 6Li + d  a + a S0= 16.9 MeV b 6Li+p a+3He So = 3  0.9 MeVb 6Li+d a + a 7Li+p a + a 6Li+p a + 3He R-matrix calculation

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PROBLEM Experimental Electron screening potential (Ue)expis larger than Electron screening potential in the adiabatic approximation (Ue) ad (Ue)exp >> (Ue)ad Sistematic discrepance Experimental approach : Reactions between charged particles

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Experimental approach : Reactions between charged particles (Ue)exp >> (Ue)ad Sistematic discrepance

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Electron screening NO SOLUTION Experimental approach : Reactions between charged particles – GOOD RESEARCH FIELD FOR INTERESTED STUDENTS ! Theory

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“Standard” solution: Electron screening EXTRAPOLATION Experimental approach : Reactions between charged particles –

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Bare nucleus Astrophysical Sb(E)-Factor Correction for stellar screening fplasma Shielded Nucleus Astrophyisical Ss(E)-factor (Measured ) Splasma(E) = fplasma (E) Sb(E) or splasma(E) = fplasma (E) sb(E) Experimental approach : Reactions between charged particles EXTRAPOLATION

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To avoid extrapolations, experimental techniques were improved; To extract from direct (shielded) measurements the bare astrophysical Sb(E) -factor, extrapolation were performed at higher energy After improving measurements (at very low energies), electron screening effects were discovered; Experimental approach : Reactions between charged particles

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To avoid extrapolations, experimental techniques were improved; To extract from direct (shielded) measurements the bare astrophysical Sb(E) -factor, extrapolation were performed at higher energy After improving measurements (at very low energies), electron screening effects were discovered; Experimental approach : Reactions between charged particles

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Gamow peak !! S(E) [Mev b] bare nuclei shielded nuclei 3He + 3He  2p + 4He 10 100 500 18 10 6 10-2 10-8 10-14 To extract from direct (shielded) measurements the bare astrophysical Sb(E) -factor, extrapolation were performed at higher energy

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INTRODUCTION Reactions between charged particles CONCLUSION In the direct measurements at relevant astrophysical energies In any case… Extrapolation is necessary !!! Experimental approach : Reactions between charged particles

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The electron screening in laboratory Ue(lab) is DIFFERENT from electron screening in plasma Ue(plasma) GENERAL PROBLEM

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need to understand Ue(lab) (flab(E)) in the laboratory (or the enhancement flab(E) –factor in laboratory) improve calculation of Ue(plasma) (Enhancement fplasma(E) –factor in plasma)

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NEW METHODS ARE NECESSARY to measure cross sections at never reached energies Experimental approach : Reactions between charged particles TO STUDY THE ELECTRON SCREENING Independent measurements of electrom screening potential Ue are needed !!! to retrieve information on electron screening effect when ultra-low energy measurements are available. INDIRECT METHODS ARE NEEDED

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a) - Coulomb dissociation … to study radiative capture reactions (Motobayashi’s talk) b) - Asymptotic Normalization Coefficients (Anc) …to extract direct capture cross sections using peripheral transfer reactions (Tribble’s talk) d) - The Trojan Horse Method (THM) to extract charged particle reaction cross sections using the quasi-free mechanism… Main Indirect Metods c) – R-matrix (Descouvemont’s talk)

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- Trojan Horse Main application: Charged particle cross section measurements at astrophysical energies Basic idea: It is possible to extract astrophysically relevant 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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-The A nucleus present a strong cluster structure: A = x  S clusters -The S cluster acts as a spectator (it doesn’ t take part to the reaction) -The x cluster (partecipant) interacts with the nucleus B   B + x  C + D Basic Principle of Quasi-free reaction mechanism Quasi-Free mechanism

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Quasi-Free mechanism Basic Principle of Quasi-free reaction mechanism

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Quasi-Free mechanism Trojan Horse Method Basic Principle of THM

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Quasi-Free mechanism Trojan Horse Method The nucleus A can be brought into nuclear field of nucleus B and the cluster x induces the reaction B + x  C + D Coulomb effects and electron screening are negligible G.Baur: Phys. Lett. B178,(1986),135 The incoming energy EA of the incident particle is larger than the Coulomb barrier energy (EAB)Coul. Bar. EA > (EAB)Coulomb Barrier

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Eqf. = EBx– Bx-S ± intercluster motion EBx is the beam energy in the center of mass of the two body reaction Bx-S binding energy of the two clusters inside the Trojan Horse plays a key role in compensating for the beam energy (under proper kinematical conditions) Eqf~ 0 Prescription for the energy in the two-body channel

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EBA >Eb EB Trojan Horse nucleus x S x x x B EB = Coulomb Barrier between the nucleus target B and the projectile nucleus A EBA> EB S A nuclear field Quasi-Free mechanism Trojan Horse Method

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S x B EB = Coulomb Barrier between the nucleus target B and the projectile nucleus A EBA> EB C A D nuclear field Quasi-Free mechanism Trojan Horse Method

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In Plane Wave Impulse Approximation (PWIA) the cross section of the three body reaction can be factorized into two terms corresponding to the two vertices Theoretical cross section for Quasi-Free mechanism PWIA (or MPWBA)

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Theoretical cross section for Quasi-Free mechanism PWIA (or MPWBA) 

Indirect Two-body cross section : 

Indirect Two-body cross section Measured KF |F(q xs)| 2  Calculated = =

Indirect Two-body cross section : 

Indirect Two-body cross section Measured KF |F(q xs)| 2  Calculated below the Coulomb barrier =

Indirect Two-body cross section : 

Indirect Two-body cross section Measured KF |F(q xs)| 2  Calculated below the Coulomb barrier Direct 2-body cross section Above Coulomb barrier = =

Typel & Wolter Few Body Systems 29, 7 (2000)Typel & Baur (2002) ,Ann. Phys.305,228 (2003): 

Typel & Wolter Few Body Systems 29, 7 (2000) Typel & Baur (2002) ,Ann. Phys.305,228 (2003) T matrix formalism

What has to be done practically? : 

What has to be done practically? - Before data taking - After data taking

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Before data taking Suitable “Trojan Horse nucleus” must be found Suitable kinematical conditions which correspond to the expected quasi free contribution must be found What has to be done practically? (1)

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After data taking 3) Selection of the three body reaction of interest. 4) Check if the quasi free reaction mechanism is present and can be discriminated from others. 5) Reconstruct s2bbare and multiply it by the penetration factor. 6) Normalise s2bTHM to s2bDirect above barrier. 7) Verify that all direct data are reproduced - excitation functions including resonances -angular distributions 8) If points 1-7 are true, we believe that THM data are reliable where direct data are not available. What has to be done practically? (3) (4) (results) (2)

Suitable “Trojan Horse nucleus” must be found: 

Suitable “Trojan Horse nucleus” must be found (1) “Trojan Horse nuclei” -The A nucleus must present a strong cluster structure: A = x  S clusters The binding energy of the x  S clusters must be “low”

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From study of the quasi-free reactions at low energies Interclusters- l- relative l= 0 l= 0 l= 0 l= 0 l= 0 l= 1 l= 1

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IN PRINCIPLE: It is possible to study nuclear reactions induced by light nuclear particles (both stable and unstable). n, d, 3H, p, d, 3He d, 3H, 3He, 6Li t, 7Li 3He, 7Be a, 6Li, 7Li, 7Be, 9Be 5He 9Be “Indirect Beam” Beam

Selection of the three body reaction of interest.: 

Selection of the three body reaction of interest. (2) I- Example of application : study of the reaction 11B + p  ao + 8Be via the 11B + d  ao + 8Be + n II- Example of application: study of the reaction 6Li + d  a + a via the 6Li + 6Li  a + a + a

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I- Example of application: study of the reaction 11B + p  ao + 8Be via the 11B + d  ao + 8Be + n Trojan Horse Nucleus d = p  n 8Be reconstruction and selection of the α0+8Be+n channel

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I- Example of application: study of the reaction 11B + p  ao + 8Be via the 11B + d  ao + 8Be + n Trojan Horse Nucleus d = p  n Relative energy between the two ’s

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I- Example of application: study of the reaction 11B + p  ao + 8Be via the 11B + d  ao + 8Be + n Trojan Horse Nucleus d = p  n Q-value corresponding to the three body reaction (Qth=6.36 MeV)

II- Example of application: study of the reaction 6Li + d  a+ a via the 6Li + 6Li  a + a + a: 

II- Example of application: study of the reaction 6Li + d  a+ a via the 6Li + 6Li  a + a + a Trojan Horse Nucleus 6Li = d  n

Check if the quasi free reaction mechanism is present and can be discriminated from others.: 

Check if the quasi free reaction mechanism is present and can be discriminated from others. (3) Necessary conditions for the existence of the quasi-free mechanism! 2- The theoretical momentum distribution of spectator s-cluster inside A-nucleus must be reproduced the experimental momentum distribution of the s-cluster inside de A-nucleus 1- The yield of the angular correlation of the energy spectra must present a maximum for the quasi-free angles and must decreases while moving far from this condition. If l = 0 the yield must present the maximum for the spectator momentum pS=0

Check if the quasi free reaction mechanism is present and can be discriminated from others.: 

Check if the quasi free reaction mechanism is present and can be discriminated from others. (3) Necessary conditions for the existence of the quasi-free mechanism! 1- The coincidence yield of the angular correlation of the energy spectra must attains a maximum for the quasi-free angles and must decreases while moving far from this condition. If l = 0 the yield must present the maximum for the spectator momentum pS=0

Check if the quasi free reaction mechanism is present and can be discriminated from others.: 

Check if the quasi free reaction mechanism is present and can be discriminated from others. (3) Necessary conditions for the existence of the quasi-free mechanism! 1- The coincidence yield of the angular correlation of the energy spectra must attains a maximum for the quasi-free angles and must decreases while moving far from this condition. 1- 9Be(3He,a a)4He 4MeV 2- 6Li(6Li,a a)4He 6MeV 3- 2H(t, d d)n 35.5 MeV 4- 6Li(3He,a p)4He 5MeV

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Quasi free angles Study of angular correlations energy spectra: Necessary condition for existence of the quasi-free mechanism A.Kasagi . et al. :Nucl. Phys.A,239(1975),233 1- 9Be(3He,a a)4He 4MeV

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Quasi free angles Study of angular correlations energy spectra: Necessary condition for existence of the quasi-free mechanism 2- 6Li(6Li,a a)4He 6MeV

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Quasi free angles Study of angular correlations energy spectra: Necessary condition for existence of the quasi-free mechanism S.Blagus . et al. :Z.Phys. 337,(1990),297 3- 2H(t, d d)n 35.5 MeV

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Quasi free angles Study of angular correlations energy spectra: Necessary condition for existence of the quasi-free mechanism 4- 6Li(3He,a p)4He 5MeV

Check if the quasi free reaction mechanism is present and can be discriminated from others.: 

Check if the quasi free reaction mechanism is present and can be discriminated from others. (3) Necessary conditions for the quasi-free mechanism! 2- The theoretical momentum distribution of the spectator s-cluster inside the A-nucleus must be reproduced by the experimental momentum distribution of the s-cluster inside the A-nucleus 1- 11Be(d,a0 8Be)n 27MeV 2- 6Li(6Li,a a)4He 6MeV 3- 2H(t, d d)n 35.5 MeV 4- 6Li(3He,a p)4He 5MeV

Check if the quasi free reaction mechanism is present and can be discriminated from others.: 

Check if the quasi free reaction mechanism is present and can be discriminated from others. (3) Necessary conditions for the quasi-free mechanism! 2- The theoretical momentum distribution of spectator s-cluster inside A-nucleus must be reproduced the experimental momentum distribution of the s-cluster inside de A-nucleus Example - 11Be(d,a0 8Be)n 27MeV

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Selected Momentum range (-40 – 40) Mev/c PS(MeV/c) EαBe(MeV) EaBe~ const. Study of experimental momentum distribution neutron-proton system EXPERIMENTAL Neutron Momentum Distribution 11B + p  ao + 8Be

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Selected Momentum range (-40 ÷ 40) Mev/c Necessary condition for the existence of the quasi-free reaction mechanism 11B + p  ao + 8Be

Verify that all direct data are reproduced  - excitation functions including resonances -angular distributions: 

Verify that all direct data are reproduced - excitation functions including resonances -angular distributions Necessary conditions for the polar approximation ! (4)

- Validity tests of the Polar Approximation are necessary: 

- Validity tests of the Polar Approximation are necessary Comparison between direct and indirect -excitation functions angular distributions 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 The behaviour of the excitation function s(E)THM is compared with the behaviour of the excitation function s(E)Direct of the two-body reaction ABOVE and BELOW COULOMB BARRIER

- Validity tests of the Polar Approximation are necessary: 

- Validity tests of the Polar Approximation are necessary Comparison between direct and indirect -excitation functions angular distributions ABOVE COULOMB BARRIER Direct 2-body cross section

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Direct-indirect excitation function 7Li(p,a)4He studied through the 7Li(d,aa)n reaction 28-48 MeV Resonances reproduced quite well PWIA M. Zadro et al.: Phys.Rev.C 40,(1989),181

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Resonances reproduced PWIA Direct-indirect excitation function6Li(p,a)3He studied through the 6Li(d,a 3He)n reaction 21.6-33.6 MeV G. Calvi et al.: Phys.Rev.C 41,(1990),1848

Slide85: 

Validity test for the THM in MDWBA above the Coulomb barrier Study of the quasi-free scattering 12C(a,a)12C via the 3-body-reaction 12C(6Li,a12C)2H 6Li 12C + a  a + 12C ELi=18 MeV Dynamitron-Bochum (1997) Tandem Catania – INFN LNS (1998) a DirectData • C.S. et al: E.P.J A 7,(2000),181 THM

- Validity tests of the Polar Approximation are necessary: 

- Validity tests of the Polar Approximation are necessary Comparison between direct and indirect -excitation functions angular distributions ABOVE COULOMB BARRIER Direct 2-body cross section Direct 2-body cross section

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Tandem Daresbury p(t,t) p studied through the d(t,t p )n reaction 35.5 MeV PWIA t + p  t + p direct data THM La Cognata et al ..submitted d t n t p p

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1H(11B, ao )2Be studied through the 2H(11B,a 2Be)n reaction 27 MeV Tandem Catania – INFN LNS C.Spitaleri et al. Phys. Rev C 2004 Excitation function Angular distributions

- Validity tests of the Polar Approximation are necessary: 

- Validity tests of the Polar Approximation are necessary Comparison between direct and indirect -excitation functions angular distributions 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 The behaviour of the excitation function s(E)THM is compared with the behaviour of the excitation function s(E)Direct of the two-body reaction ABOVE and BELOW COULOMB BARRIER

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6Li(p,a)3He studied through the 6Li(d,a 3He)n reaction 14, 25 MeV Resonances reproduced very well Tandem Catania – INFN LNS Dynamitron-DTL - Bochum ELi = 14, 25 MeV Typel & Wolter Few Body Systems 29,(2000),75

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Main problem to extract data 6Li 3He a p d a 3He 6Li p a 3He + d  a + p (3He + 6Li  a + p + a) 1-Example Sequential Decay Quasi-free 8Be* a ~3.5 MeV

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Main problem to extract data p d 7Li n a a 8Be* 7Li + p  a + a 7Li + d  a + a + n 2-Example Sequential Decay Quasi-free QF SD ~7 MeV

RESULTS: 

RESULTS

Astrophysical ApplicationDepletion lights nuclei :Li, B, BeLi reactions : 

Astrophysical Application Depletion lights nuclei : Li, B, Be Li reactions INDIRECT REACTIONS 7Li + p  a + a 7Li + p  a + a 6Li + d  a + a 6Li + p  a + 3He 7Li + d  a + a + nspett. 7Li + 3He  a + a + dspett. 6Li + 6Li  a + a + aspett. 6Li + d  a + 3He + nspett.

Slide95: 

Li reactions 7Li + p  a + a S0=55  3 keV b 6Li + d  a + a S0= 16.9 MeV b 6Li+p a+3He So = 3  0.9 MeVb 6Li+d a + a 7Li+p a + a 6Li+p a + 3He R-matrix calculation

Slide96: 

Li reactions 7Li + p  a + a S0=55  3 keV b 6Li + d  a + a S0= 16.9 MeV b 6Li+p a+3He So = 3  0.9 MeVb 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 Unchanged astrophysical implications !!!

Slide97: 

Li reactions 6Li+d a + a 7Li+p a + a 6Li+p a + 3He R-matrix calculation 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. Unchanged astrophysical implications !!!

Comparison of three-body cross section for coincidences between detectors PSD1-PSD4 and PSD2-PSD5(Ebeam=20 MeV): 

Comparison of three-body cross section for coincidences between detectors PSD1-PSD4 and PSD2-PSD5 (Ebeam=20 MeV) Extracted S(E) factor for the 7Li(p,a)4He reaction at different beam energies (after normalization) 7Li(p,a)4He 7Li(p,a)4He

Comparison of data extracted from target and projectile break-up: 

Comparison of data extracted from target and projectile break-up Projectile break-up data Target break-up data Musumarra et al.: Phys.Rev.C64,(2001),068801 6Li + d  a + a MPWBA 6Li (projectile) 6Li (projectile) 6Li target a a a a QF projectile QF target Experimental set-up: 3 PSD. (1cm x 5cm) in coincidence  DQa = DQa = 0.4o 1 Monitor Target: lithium oxide (enriched in 6Li) Tandem Zagreb – IRB Ebeam= 5.9 MeV

COMPARISON Result 6Li + p  a + 3He: 

COMPARISON Result 6Li + p  a + 3He direct data QF +THM 6Li + p  a + 3He MPWBA Tandem Catania – INFN LNS Dynamitron-DTL_ Bochum Tandem Catania – INFN LNS A.Tumino . et al. :Phys.Rev.C 67,(2003), 065803 G. Calvi et al.: Phys.Rev.C 41,(1990),1848 (1988) (2002) PWIA 6Li + p  a + 3He indirect data

Astrophysical ApplicationDepletion lights nuclei :Li, B, BeB reactions : 

Astrophysical Application Depletion lights nuclei : Li, B, Be B reactions INDIRECT REACTIONS 11B + p  ao + 8Be 10B + p  ao + 7Be 11B + d  ao + 8Be + nspett. 10B + d  ao + 7Be + nspett.

Slide102: 

2H p 11B n 8Be α I II Experiment carried on at LNS (Tandem & Camera2000); Ebeam(11B)=27 MeV & Ibeam(11B)=2-5 nA; S(0)THMMPWBA=1.091 ± 0.101 ± sist (MeV b) S(0)dir=2.1 (MeV b) (Becker et al., 1987) 11B PSD4

Slide103: 

Experiment carried on at LNS (Tandem & Camera2000); Ebeam(11B)=27 MeV & Ibeam(11B)=2-5 nA; S(0)THMMPWBA=1.091 ± 0.101 ± sist (MeV b) S(0)dir=2.1 (MeV b) (Becker et al., 1987)

Astrophysical ApplicationDepletion lights nuclei :Li, B, BeBe Reactions studied: 

Astrophysical Application Depletion lights nuclei : Li, B, Be Be Reactions studied INDIRECT REACTIONS 9Be + p  a + 6Li 9Be + p  a + 6Li + nspett

Slide105: 

Laboratory: Tandem: LNS INFN-Catania Energy: E 9Be = 22 MeV

Slide106: 

Laboratory: Tandem: LNS INFN-Catania Energy: E 9Be = 22 MeV

Astrophysical ApplicationThe Fluorine problem in the AGB stars:Reactions Studied: 

Astrophysical Application The Fluorine problem in the AGB stars: Reactions Studied INDIRECT REACTIONS 15N + p  ao + 12C 15N + d  ao + 12C + nspett

Slide108: 

Laboratory: Cyclotron- Texas A & M University Energy: E 15N ˜ 60 MeV Beam on target ˜ 1mm 15N IC (DE) + PSD3 (E) PSD2 PSD1 CD2 Mon.

Astrophysical ApplicationThe Fluorine problem in the AGB stars:Reactions to be studied 2006-2007: 

Astrophysical Application The Fluorine problem in the AGB stars: Reactions to be studied 2006-2007 INDIRECT REACTIONS 18O + p  a + 15N 19F + a  22Ne + p 18O + d  a + 15N + nspett. 19F + 6Li  22Ne + p + aspett.

Astrophysical ApplicationPrimordial nucleosyntesis :Reactions Studied: 

Astrophysical Application Primordial nucleosyntesis : Reactions Studied INDIRECT REACTIONS 3He + d  a + p d + d  p + t p + t  d + d 3He + 6Li  a + p + aspett d + 6Li  p + t + aspett d + t  d + d + nspett

Slide112: 

3He 6Li d p α d Ue = 180  40 eV

Slide113: 

THM Direct data Astrophysical Factor S(E) d+ d  p+ 3H via d+ 6Li  p+ 3H + a 6Li d a 3He d p Sequential decay contributions Tandem Catania INFN LNS Tandem Bochum – DTL– E =14, 20 MeV d+ d  p+ 3H Report LNS-INFN 2003

New validity test for polar approximation 7Li + p  a + a: 

New validity test for polar approximation 7Li + p  a + a Comparation s(E) of the virtual reaction 7Li + p  a + a via the 7Li + d  a + a + nvia the 7Li + 3He  a + a + d 3He 7Li d p a a d 7Li n a a p

Slide115: 

Pole Invariance Test

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The Experiment Cyclotron – Academy of Science, Rez (Prague), Czech Rep 4 DE/E detectors (with a PSD as E stage) 1 Monitor Target: deuterated polyethilene Beam energy (3He): 33 MeV Studying the reaction via the 7Li + p  a+ a 7Li + 3He a + a + d p d clusters

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Selection of detected particles with DE/E technique and identification of the kinematic locus 3-body reaction identification Q=11.85 MeV 7Li + 3He a + a + d Q-value 3body

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2. Momentum distribution: comparison with theoretical distribution. Only events with |ps|<30 MeV/c will be considered. --- funzione di Hulthèn Quasi-free mechanism selection 1. Angular Correlation (necessary condition for the quasi-free mechanism). 7Li + 3He a + a + d

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After normalization to direct data agreement shows up regardless of the Trojan Horse nucleus (3He in the present experiment). Resonances are well reproduced. VALIDITY TEST PERFORMED!! Measured Calculated Extracted The penetrability factor must be taken into account at sub-coulomb energies:

New validity test for polar approximation 7Li + p  a + a: 

New validity test for polar approximation 7Li + p  a + a Comparation s(E) of the virtual reaction 7Li + p  a + a via the 7Li + d  a + a + nvia the 7Li + 3He  a + a + d 3He 7Li d p a a d 7Li n a a p

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Concluding remarks-Test 7Li Polar approximation validity test has been performed for 7Li + 3He a + a + d. Resonances were reproduced and a good agreement with direct data shows up. 3He can be used as a Trojan Horse Nucleus as well as deuterium or 6Li

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Comparison between direct-indirect excitation function 7Li(p,a)4He studied through the 7Li(d,aa)n reaction ………………MeV Resonances reproduced PWIA Comparison between direct-indirect excitation function 6Li(n,a)3H studied through the 6Li(d,a 3H)p reaction MeV E6Li=14 MeV Li6+n direct data THM n Tumino et al., EPJ 2005

CONCLUSIONS: 

CONCLUSIONS

Main limitations of the method: 

Main limitations of the method A- Preliminary study of quasi-free mechanism and tests of validity are necessary. - Presence of different 3-body reaction mechanisms (Sequential Decay – Quasi-Free) B- No absolute cross section is measurable: -The excitation functions at energies below Coulomb barrier must be known from direct measurements; C- Measurements with high angular and energy resolutions are needed;   D-Theoretical analysis is needed: - PWIA, MPWBA, DBWA (???)

The advantages of the THM: 

The advantages of the THM A -  It is possible measure the bare nucleus cross section sb ( or the bare nucleus Astrophysical Factor Sb(E) ) at Gamow energy   No extrapolation B - It is possible to measure excitation function in a “ relatively” short time because typical order of magnitude for a three- body cross- section is mb; D - Informations on electron screening effect can be extracted ; No electron screening effects are present; E - Possibility of application to the radioactive beam measurements;

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G - It is possible to study many nuclear reactions induced light nuclear projectiles (both stable and unstable). e.g. : p, n, d, t, 3He, a, 5He F - No complex experimental apparatus.

Typical examples of experimental apparatus: 

Typical examples of experimental apparatus

I- Example of application: 

d = p  n p= participant n= spectator E 11B = 27 MeV TANDEM – LNS Catania I- Example of application

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2000 Chamber 3 Position Sensitive Detectors. (1cm x 5cm) in coincidence  1 Dual Position Sensitive Detectors. No DE detectors necessary 1 Monitor Target: deuterated polyethylene CD2 target (about 220 μg/cm2) Experimental set-up:

II- Example of application: 

II- Example of application 6Li = d  n d = participant α = spectator E 6Li = 6 MeV TANDEM – IRB Zagabria

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Reaction Chamber Detectors: 3 Position Sensitive centered at quasi free angular couples 1 Monitor Target: LiF Experimental set-up:

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Useful information on low energy reactions of astrophysical interest can be obtained by using different INDIRECT METHODS NOT ONLY BUT ALSO Conclusions Short !!!

COLLABORATION: 

COLLABORATION

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Giovanni Domenico TIEPOLO Italian painter, Venetian school (b. 1727, Venezia, d. 1804, Venezia)

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C.S., A.Tumino , M.Gulino, M.La Cognata, M.Lamia, A.Musumarra, R.G.Pizzone S. Cherubini, S.Romano, S.Tudisco I N F N, Laboratori Nazionali del Sud, Catania, Italy Università di Catania, Italy F.Strieder, C.Rolfs  Institut für Experimentalphysik III- Ruhr Universität Bochum, Germany S.Typel GSI-Germany R.Tribble, L.Trace, A.Mukhamedzanov, G.Tabacaru Texas A & M University , College Station, USA V.Kroha, V.Burjan Cyclotron- Czeck- Praga- Rep. Ceca G. Baur Forschungzentrum, Jülich, Germany S. Blagus, M. Milin, Ð. Miljanić, N.Soić Ruđer Bošković Insitute , Zagreb, Croatia

Theoretical cross section for Quasi-Free mechanism in MPWBA (Below Barrier): 

Theoretical cross section for Quasi-Free mechanism in MPWBA (Below Barrier) Typel & Wolter Few Body Systems 29, 7 (2000) Typel & Baur (2002) ,Ann. Phys.305,228 (2003) The basic theory of the THM is developed starting from a post-form distorted wave Born approximation (DWBA) of the T-matrix element.

END: 

END