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Study of 17 O(p, α ) 14 N reaction

53-esimo Congresso della Societa' Astronomica Italiana (SAIt) “L'Universo quattro secoli dopo Galileo”. 4 - 8 Maggio 2009, PISA. Study of 17 O(p, α ) 14 N reaction via the Trojan Horse Method for application to 17 O Nucleosynthesis. Maria Letizia Sergi LNS-INFN, Catania.

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Study of 17 O(p, α ) 14 N reaction

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  1. 53-esimo Congresso della Societa' Astronomica Italiana (SAIt) “L'Universo quattro secoli dopo Galileo” 4 - 8 Maggio 2009, PISA Studyof 17O(p,α)14N reaction via the TrojanHorseMethodforapplicationto17O Nucleosynthesis Maria Letizia Sergi LNS-INFN, Catania

  2. Role of 17O: astrophysical scenarios • It is one of the very few isotopes whose nucleosynthetic origin can be attributed to Novae, stellar explosion occurring in close binary systemthatcontain White Dwarf (WD) as a compact object and a companion star. In novae, 17O is produced in one of the two paths of CNO cycles leading to 18F production which is of special interest for gamma ray astronomy. γ-raylinefluxes measurement would shed light into the physical processes that occur in the early phases of the explosion. Nova Cygni 1992 2) The relative abundances of the oxygen isotopes have been observed at the surface of some Red Giant (RG) stars. The change in the surfacecompositionoffersanopportunityto probe the “history” of the stellar interior. Red Giant Mira

  3. 17O production & destruction In nova 17O is produced starting with the 16O isotope found at the surface of the WD progenitor. 16O nuclei can be processed in a two different competing cycles: CNO2 cycle HCNO2 cycle 16O(p,)17F(+)17O(p,)18F(p,α)15O(+)15N(p,)16O 16O(p,)17F(+)17O(p,α)14N(p,)15O(+)15N(p,)16O Production: 16O(p,)17F: reaction rate well known in literature (NACRE) Destruction: 17O(p,)18F:importantfor18F production in novae 17O(p,)14N : dominantchannelfor17O destruction C. Iliadis, Nuclear physics of Stars, 2007 Stellar temperatures of primary importance for nucleosynthesis: T=0.01-0.1 GK for red giant, AGB, and massive stars; T=0.01- 0.4 GK for classical nova explosion (peak temperatures of 0.35 GK can be easily achieved in explosion hosting very massive white dwarfs.)

  4. Energetic Region of astrophysical interest for the 17O(p,α)14N reaction T=0.01-0.4 GK: 17O(p,α)14N and 17O(p,γ)18F reaction cross section have to be precisely known in the center-of-mass energy range Ec.m.=0.017-0.37 MeV. In thisenergeticregion, tworesonantlevelsof18F are importantfor17O(p,α)14N reaction: • Ec.m. = 65.0 keV Jπ = 1- • Ec.m. = 183.3 keV Jπ = 2- correspondingtoEx = 5.673 MeVand Ex = 5.786 MeVrespectively.. Two sub-threshold levels at EX(Jπ)=5.605 MeV (1−) and EX(Jπ)=5.603 MeV (1+) could also play a significant role in the reaction rate through the high-energy tail of the levels. Possible interference effects between 5.673 MeV level and 5.605 MeV level

  5. Status of the Art In the last years several efforts to measure the cross section for the 17O(p,α)14N at astrophysical energies were made in order to reduce the indetermination on reaction rate. J.C.Blackmonet al., Phys. Rev. Lett. 74, 2642, (1995) The first direct measurement of the 17O(p,α)14N at low energy LARGE UNCERTAINTIES !! 183.3 keV To reduce the uncertainties INDIRECT MEASUREMENT 65.0 keV A. Chafa et al., Phys. Rev. C 75, 035810, (2007)

  6. 3 CD2 2 1 17O 4 5 6 Experimental Set-up 2H break-up diretto 17O+d 14N+ α +n n L.N.S - Catania p 14N 17O+p 14N+ α 17O α Trojan Horse Method Two ionization chambers filled with 60 mbar of isobuthan gas as ΔE detector were in front of PSD1 and PSD4 detector Ebeam = 41 MeV Target Thickness ~ 150 μg/cm2

  7. Selection of the 2H(17O, α14N)n reaction channel • Nparticleswereselectedwith the standard ΔE-E technique in bothtelescopes 1 and 4 • The loci events in E1vs E5 and E4vs E2 for the 2H(17O, α14N)n reactionwere deduced Good agreement with the theoretical value -1.033 MeV • Good detector calibration procedure!! • Good reaction channel selection!!

  8. Study of the presence of SD mechanism The 14N+α+nexitchannel can befedthroughdifferentreactionmechanism: or Quasi-Free mechanism (QF). Sequential Decay (SD) Study of relative energy spectra: E14N-α(MeV) E14N-n(MeV) E14N-n (MeV) Eα-n(MeV) The clear horizontal loci in E14N-αrepresentanevidencefor the formationof the 18F excitedstates.

  9. Ec.m.=183±50 keV |(ks)|2= Selection of the Quasi-Free mechanism: experimental momentum distribution An observable which turns out to be more sensitive to the reaction mechanism is the shape of the experimental momentum distribution In a energy windows of 100 keV d/dconst. dividing the resultingthree-bodycoincidenceyieldby the kinematicfactor, the p-nmomentumdistribution in arbitraryunitsisobtained The extractedexperimentalmomentumdistributioniscomparedwith the theoreticalone, givenby the Hulthénwavefunction in momentumspace: N: normalization parameter a=0.2317 fm-1 b=1.202 fm-1 |Pn| < 30 MeV/c

  10. d3σ dΩαdΩ14NdEcm dσN ∝ KF · |Φ(Ps)|2 dΩ 17O(p,α)14N cross section & angular distributions Extractionofnuclear part of the two body cross sectionbyusing the PWIA approach THM data THM data Chafa 07 Theoretical calculation based on Blatt (1952) theory Legendre polinomyal fit of direct data reported in Chafa et al., 2007 Wc.m.(θc.m.)=a1+a2P2(cosθc.m.)

  11. Trojan Horse Cross section Trojan Horse cross section: horizontal error bar refers to the integration bin while the vertical one arise for the statistics (25%) The extractedtwo-bodydifferential cross sectionhasbeenintegrated in the wholeangularrange, assumingthat in the regionwhere no experimentalangulardistribution are available, their trend isgivenby the fitof the obtainedexperimentalangulardistribution. In order to separate the different contributions on this cross section, a fit of the nuclear cross section has been performed. σNTHM (arb. un.) • Extraction of: • Resonance energies: ER1=65±5 keVandER2=183±5 keV. • Peak value of the two resonances:N1=0.170±0.025andN2=0.220±0.031,used to derive the resonancestrengthsωγ (case ofnarrowresonances). Ec.m.(MeV)

  12. Reaction rate determination KEY PARAMETER: STRENGTH OF THE RESONANCE: Wefocussed on the 0-0.3 MeVenergyregion and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strengthof the resonance at Ec.m.=65 keVbyusing the available information in literature on the wellmeasured Ec.m.=183 keVresonance. New approach σNTHM (arb. un.) The strengthof the resonance at 65 keVisgivenfrom the ratiobetween the peakvalue N1 and N2 through the relation: 2 1 La Cognata et al., PRL 101, 152501, (2008) where Mi(E) is the direct transfer reactionamplitudefor the binaryreaction17O+d->18F*+s populating the resonant state 18F* with the resonanceenergyERi; Ec.m.(MeV)

  13. Reaction rate determination II ωγ RESULTS: • Thistwovalues are in agreement • eachother; • with the value 5.5+1.8-1.0 ·10-9 eVadopted in NACRE; • with the (4.7±0.8)·10-9eVcalculatedbyusing the valueofΓα and Γpreported in Chafa’07. NACRE: C. Angulo et al., Nucl. Phys. A 656, 3-183 (1999) Moazen’07: B.H. Moazen et al., Phys. Rev. C 75, 065801, (2007) TOTAL REACTION RATE: Ratioof the THM reaction rate to the NACRE one (blu line). The THM reaction rate wascalculatedbyconsidering the valueofωγ=(4.4±1.1)x10-9 eVfor the 65 keVresonance. Ratiobetween the reaction rate evaluatedbyChafa’07 and NACRE. NACRE adoptedreaction rate.

  14. Reaction rate determination II ωγ RESULTS: • Thistwovalues are in agreement • eachother; • with the value 5.5+1.8-1.0 ·10-9 eVadopted in NACRE; • with the (4.7±0.8)·10-9eVcalculatedbyusing the valueofΓα and Γpreported in Chafa’07. NACRE: C. Angulo et al., Nucl. Phys. A 656, 3-183 (1999) Moazen’07: B.H. Moazen et al., Phys. Rev. C 75, 065801, (2007) TOTAL REACTION RATE: T=0.02-0.1 GK:the differencebetween the rate adopted in literature and the total rate calculated, ifoneconsiders the NA<σv>65THMextractedasexplainedbefore, are smallerthan 10%. Agreement between the twosetsof data

  15. Conclusions Main results: A clearevidence of both levels at Ec.m.=65 and 183 keV is present in the excitation function. Extractionofangulardistributionsforboth levels at Ec.m.=65 (for the first time!!) and 183 keV and comparison with theoretical calculation and direct measurement (only for Ec.m.=183 keV). The 17O(p,α)14N reaction rate was extracted and compared with that one reported in Chafa’07, giving a difference of less than 10%. … in progress: • A deeper analysis of contribution of sub-threshold level is needed • Our results are affected by a statistical error of 25%. Data analysis in progress A further experiment was performed at Physics Department of Notre Dame University (Indiana, USA) in November 2008 by using the same experimental apparatus adopted in the previous one.

  16. ALTRE DIAPOSITIVE

  17. Roche Model Solution of restricted three body problem Assumptions: the third mass mustbeinfinitesimal mass; The twolargemassesmustbe in circularorbit. L1,L2… L5 Lagrangepoints: pointswheretherewasnot net forceexerted on the third mass. Roche surface: equipotentialsurfacewhere the sum of the rotational and gravitationalpotentialenergyisconstant. Roche surfacethrough L1: consistsoftwo Roche lobes and form the innercriticalpotential. Ifone star completelyfillsits Roche lobethenitmay loss mattertoitscompanion star throughL1. Roche surfacethrough L2: itdefines the outercriticalpotential. If a star has a potentialgreaterthan the outercriticalpotential mass maybetransferred out of the system

  18. Kopal Classification Comparisonbetween the star potential and the innercriticalpotential. Detached system: neither star completelyfill the Roche lobe. The stars evolve separately. Semi-detached system: onlyoneof the twostarscompletelyfillsits Roche lobe.  Mass transfer (NOVA EXPLOSION). Contact system: bothstarshave the potentialsgreaterthan the innercriticalpotentialbutlessthan the outercriticalpotential. Bothcomponetesof the binaryfilltheir Roche lobe and a common envolopesurroundsbothstars.

  19. A nova is a cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a white dwarf star. Hydrogen-rich matter is tansferred via Roche lobe from a low-mass main sequence star to surface of WD. For effect of the high gravitational field created from WD, it draws on itself the matter that is in the envelope of the companion star. This transferred matter is accumulated in an accretion disc surrounding the WD with a accretion rates amount to ∼ 10-10−10−9M⊙ per year. A fraction of this matter spirals inward and accumulates on the WD surface, where is heated and compressed by the strong surface gravity. At some point the bottom layers of the WD become electronic degenerate. Hydrogen starts to fuse to helium via the p-p chains during the accretion phase and the temperature increases gradually. The electron degeneracy prevents an expansion of the envelope and eventually a thermonuclear runaway occurs near the base of the accreted layers [Iliadis07]. At this stage the nuclear burning is dominated by explosive hydrogen burning via the CNO cycle. Both the compressional heating and the energy released from the nuclear burning heat the accreted material until an explosion occurs.

  20. L’altezza del picco della i-esima risonanza è legata la rapporto tra Γαi e Γitot(ERi) della risonanza attraverso il quadrato dell’elemento di matrice che descrive il polo di break-up SiMi2(ERi): M. La Cognata at al. PRL, in press arXiv:0806.1274 σ(E)THM (arb. un.) con Si fattore spettroscopico dell’i-esimo stato dell’ 18F • Strength della resonanza: Ec.m. (MeV) Sostituendo: “single particle width” ottenuta con calcoli di ANC con

  21. σ(E)THM (arb. un.) Ec.m. (MeV) Quindi: 1 2 Dividendo membro a membro: Rapporto dei parametri “model dependent” Calcolo “model independent” !!

  22. Some details on used Blatt theoretical calculation Consider the reaction A+X->Y+b NOTATION Before collision: -channel index α(defines the type of incoming particles and the state of struck nucleus) -channel spin s (total spin angular momentum in the channel; it is the vector sum of intrinsic spin i of the incoming particle and the spin I of the struck nucleus) -orbital angular momentum l • After collision: • channel index α’ (defines the type of outgoing particles and quantum state of the residual nucleus) • -channel spin s’ (it is the vector sum of intrinsic spin i of the outgoing particle and the spin I of the residual nucleus) • -outgoing orbital momentum l’

  23. where If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J0 and parity Π0, the cross section for the α->α’ reaction is given by

  24. PL are the Legendre polynomials If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J0 and parity Π0, the cross section for the α->α’ reaction is given by where

  25. NOTATION where W is the Racah coefficients defined in Racah 1942

  26. , where Γαsl is the partial widths of the resonant level. NOTATION

  27. ξl is the phase shifts for the potential scattering, in the hard sphere approximation, defined by equation , where Γαsl is the partial widths of the resonant level. where Fl(R) and Gl(R) are the regular and irregular Coulomb wave function (R is the channel radius and σl is the phase shift for Coulomb scattering from an impenetrable sphere of radius R) NOTATION

  28. First consideration PSD1-PSD6 and PSD4-PSD3 coincidences: PSD3 and PSD6 were placed in the scattering chamber to have an investigation of the whole kinematical locus reaction channel even if far away from the astrophysically relevant energy range. PSD1 The same for PSD4 Ec.m.>500 keV ps> 30 MeV/c Not possible to use coincidence 1-4 !! E1 and E4 obtained by kinematical calculation! E (MeV) Run 86 Run 56 Run 79

  29. Reaction Rate Cross sectionis necessary input to know the stellar reaction rate: whereσBWis the Breit-Wigner cross section StatisticalfactordependingbynuclearspinofcompoundnucleusJC*, target JX and projectileJa Foranisolated and narrowresonance: The productof the statisticalfactorω and the widthratioγ=Γ1Γ2/Γisreferredas the strengthof the resonance: Г1 and Г2 represent the partial widths describing the formation and the decay of the compound nucleus. Г= Г1+Г2 is the total width

  30. Reaction Rate Cross sectionis necessary input to know the stellar reaction rate: whereσBWis the Breit-Wigner cross section StatisticalfactordependingbynuclearspinofcompoundnucleusJC*, target JX and projectileJa Foranisolated and narrowresonance: The productof the statisticalfactorω and the widthratioγ=Γ1Γ2/Γisreferredas the strengthof the resonance: KEY PARAMETER FOR NUCLEAR RATE DETERMINATION!!

  31. Consideration on the extraction of the ωγ parameter for the 65 keV resonant level The first step of the reaction rate calculation is to evaluate the strengths of the resonances Wefocussed on the 0-0.3 MeVenergyregion and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strengthof the resonance at Ec.m.=65 KeVbyusing the available information in literature on the wellmeasured Ec.m.=183 keVresonance. Tothisaim, the extractedtwo-bodydifferential cross sectionhasbeenintegrated in the wholeangularrange, assumingthat in the regionwhere no experimentalangulardistribution are available, their trend isgivenby the fitof the obtainedexperimentalangulardistribution.

  32. Reaction Rate calculation I In the narrowresonanceapproximation, the reaction rate isdeducedby relation whereNA<σv>Risexpressed in cm3 mol-1 sec-1, ER and ωγ in MeV and S(O) in MeV b. Z1 and Z2 are the projectile and the target atomicnumberrespectively. In the calculation of the 17O(p,α)14N reaction rate, we followed the same procedure adopted in Chafa’07 by using for the resonance at Ec.m.=65 keV the two value of ωγ extracted as explained before.

  33. New approach to extract the ωγ parameter for a resonance I The THM cross sectionfor the A+a(x+s)->c+C+s reactionproceedingthrough a resonanceFiin the subsystem F=A+x=C+c is: A. M. Mukhamedzhanovet al., J. Phys. G: Nucl. Part. Phys. 35 (2008) 014016 • where • Mi(E) is the direct transfer reactionamplitudefor the binaryreaction A+a->Fi+spopulating the resonant state Fiwith the resonanceenergyERi; • Γcci(E) is the partialresonancewidthfor the decayFi -> C+c; • Γiis the total resonancewidthofFi. The appearenceof the transfer reactionamplitude Mi(E) insteadof the entry channelpartialresonancewidthΓ(Ax)i(E) is the maindifferencebetween the THM cross section and the cross sectionfor the resonantbinarysub-reaction A+x->C+c

  34. New approach to extract the ωγ parameter for a resonance II σ(E) The peak TH cross sectiontaken at the resonanceERienergyfor the (p,α) reaction A+x->C+cisgivenby Ni ERi Γi/2 -Γi/2 In our case, wehavetworesonances: 2 1 Strengthofresonance 2 (Ec.m.=183 keV) wellmeasured in tworecentworks !!

  35. Г1=Гris IfГ1<<ГrisandГ2<<Гris Г2=Гris But 2 1 Г1 ~ 130 eV Г2 ~ 7 eV Гris ~ 20 keV The strengthof the resonance at 65 keVisgivenfrom the ratiobetween the peakvalue N1 and N2 through the relation:

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