53 esimo Congresso della Societa Astronomica Italiana SAIt

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

Role of 17 O: astrophysical scenarios 1) It is one of the very few isotopes whose nucleosynthetic origin can be attributed to Novae, stellar explosion occurring in close binary system that contain White Dwarf (WD) as a compact object and a companion star. In novae, 17 O is produced in one of the two paths of CNO cycles leading to 18 F production which is of special interest for gamma ray astronomy. Nova Cygni 1992 γ-ray line fluxes measurement would shed light into the physical processes that occur in the early phases of the explosion. 2) The relative abundances of the oxygen isotopes have been observed at the surface of some Red Giant (RG) stars. The change in the surface composition offers an opportunity to probe the “history” of the stellar interior. Red Giant Mira

17 O production & destruction In nova 17 O is produced starting with the 16 O isotope found at the surface of the WD progenitor. 16 O nuclei can be processed in a two different competing cycles: CNO 2 cycle HCNO 2 cycle 16 O(p, )17 F( +)17 O(p, α)14 N(p, )15 O( +)15 N(p, )16 O 16 O(p, )17 F( +)17 O(p, )18 F(p, α)15 O( +)15 N(p, )16 O Production: 16 O(p, )17 F : reaction rate well known in literature (NACRE) Destruction: 17 O(p, )18 F: 17 O(p, )14 N important for 18 F production in novae : dominant channel for 17 O 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. )

Energetic Region of astrophysical interest for the 17 O(p, α)14 N reaction T=0. 01 -0. 4 GK: 17 O(p, α)14 N and 17 O(p, γ)18 F reaction cross section have to be precisely known in the center-of-mass energy range Ec. m. =0. 017 -0. 37 Me. V. In this energetic region, two resonant levels of 18 F are important for 17 O(p, α)14 N reaction: ü Ec. m. = 65. 0 ke. V Jπ = 1 - ü Ec. m. = 183. 3 ke. V Jπ = 2 - corresponding to Ex = 5. 673 Me. V and Ex = 5. 786 Me. V respectively. . Two sub-threshold levels at EX(Jπ)=5. 605 Me. V (1−) and EX(Jπ)=5. 603 Me. V (1+) could also play a significant role in the reaction rate through the high-energy tail of the levels. Possible interference effects between and 5. 605 Me. V level 5. 673 Me. V level

Status of the Art In the last years several efforts to measure the cross section for the 17 O(p, α)14 N at astrophysical energies were made in order to reduce the indetermination on reaction rate. J. C. Blackmon et al. , Phys. Rev. Lett. 74, 2642, (1995) The first direct measurement of the 17 O(p, α)14 N at low energy LARGE UNCERTAINTIES !! 183. 3 ke. V To reduce the uncertainties 65. 0 ke. V A. Chafa et al. , Phys. Rev. C 75, 035810, (2007) INDIRECT MEASUREMENT

Experimental Set-up 2 H break-up diretto n 17 O+d 14 N+ α +n 17 O+p 14 N+ α p 17 O 14 N Trojan Horse Method α Detectors Thickness [μm] θ [deg] r [mm] Δθ [deg] PSD 1 500 8. 0 ± 0. 1 470 5. 1 PSD 2 500 17. 4 ± 0. 1 372 7. 7 PSD 3 500 27. 8 ± 0. 1 392 6. 8 PSD 4 500 8. 0 ± 0. 1 470 5. 1 PSD 5 500 17. 4 ± 0. 1 372 7. 7 PSD 6 500 27. 8 ± 0. 1 392 6. 8 Two ionization chambers filled with 60 mbar of isobuthan gas as ΔE detector were in front of PSD 1 and PSD 4 detector CD 2 17 O L. N. S - Catania 3 2 1 5 4 6 Ebeam = 41 Me. V Target Thickness ~ 150 μg/cm 2

Selection of the 2 H(17 O, α 14 N)n reaction channel ü N particles were selected with the standard technique in both telescopes 1 and 4 ΔE-E ü The loci events in E 1 vs E 5 and E 4 vs E 2 for the 2 H(17 O, α 14 N)n reaction were deduced Good agreement with theoretical value 1. 033 Me. V ü Good detector calibration procedure!! ü Good reaction channel selection!!

Study of the presence of SD mechanism The 14 N+α+n exit channel can be fed through different reaction mechanism: Sequential Decay (SD) or Quasi-Free mechanism (QF). E 14 N-α (Me. V) Study of relative energy spectra: E 14 N-n (Me. V) E 14 N-n(Me. V) Eα-n(Me. V) The clear horizontal loci in E 14 N-α represent an evidence for the formation of the 18 F excited states.

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 Ec. m. =183± 50 ke. V In a energy windows of 100 ke. V d /d const. dividing the resulting three-body coincidence yield by the kinematic factor, the p-n momentum distribution in arbitrary units is obtained The extracted experimental momentum distribution is compared with theoretical one, given by the Hulthén wave function in momentum space: N: normalization parameter a=0. 2317 fm-1 b=1. 202 fm-1 | (ks)|2 = |Pn| < 30 Me. V/c

17 O(p, α)14 N cross section & angular distributions Extraction of nuclear part of the two body cross section by using the PWIA approach dσN dΩ ∝ d 3σ dΩα dΩ 14 Nd. Ecm KF · |Φ(Ps)|2 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. )=a 1+a 2 P 2(cosθc. m. )

Trojan Horse Cross section σNTHM (arb. un. ) The extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution. Trojan Horse cross section: horizontal error bar refers to the integration bin while the vertical one arise for the statistics ( 25%) In order to separate the different contributions on this cross section, a fit of the nuclear cross section has been performed. Extraction of: ü Resonance energies: ER 1=65± 5 ke. V and ER 2=183± 5 ke. V. Ec. m. (Me. V) ü Peak value of the two resonances: N 1=0. 170± 0. 025 and N 2=0. 220± 0. 031, used to derive the resonance strengths ωγ (case of narrow resonances).

Reaction rate determination KEY PARAMETER: STRENGTH OF THE RESONANCE: The strength of the resonance at 65 ke. V is given from the ratio between the peak value N 1 and N 2 through the relation: ch a ro p ap ew N La Cognata et al. , PRL 101, 152501, (2008) where Mi(E) is the direct transfer reaction amplitude for the binary reaction 17 O+d->18 F*+s populating the resonant state 18 F* with the resonance energy ERi; σNTHM (arb. un. ) We focussed on the 0 -0. 3 Me. V energy region and in particular on both Ec. m. =65 ke. V and Ec. m. =183 ke. V, obtaining the strength of the resonance at Ec. m. =65 ke. V by using the available information in literature on the well measured Ec. m. =183 ke. V resonance. 1 2 Ec. m. (Me. V)

Reaction rate determination II ωγ RESULTS: This two values are in agreement ü each other; ü with the value 5. 5+1. 8 -1. 0 · 10 -9 e. V adopted in NACRE; 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: ü with the (4. 7± 0. 8)· 10 -9 e. V calculated by using the value of Γα and Γp reported in Chafa’ 07. Ratio of the THM reaction rate to the NACRE one (blu line). The THM reaction rate was calculated by considering the value of ωγ=(4. 4± 1. 1)x 10 -9 e. V for the 65 ke. V resonance. Ratio between the reaction rate evaluated by Chafa’ 07 and NACRE adopted reaction rate.

Reaction rate determination II ωγ RESULTS: This two values are in agreement ü each other; ü with the value 5. 5+1. 8 -1. 0 · 10 -9 e. V adopted in NACRE; 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: ü with the (4. 7± 0. 8)· 10 -9 e. V calculated by using the value of Γα and Γp reported in Chafa’ 07. T=0. 02 -0. 1 GK: the difference between the rate adopted in literature and the total rate calculated, if one considers the NA<σv>65 THM extracted as explained before, are smaller than 10%. Agreement between the two sets of data

Main results: Conclusions 1. A clear evidence of both levels at Ec. m. =65 and 183 ke. V is present in the excitation function. 2. Extraction of angular distributions for both levels at Ec. m. =65 (for the first time!!) and 183 ke. V and comparison with theoretical calculation and direct measurement (only for Ec. m. =183 ke. V). 3. The 17 O(p, α)14 N reaction rate was extracted and compared with that one reported in Chafa’ 07, giving a difference of less than 10%. … in progress: ü A deeper analysis of contribution of sub-threshold level is needed üOur 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.

ALTRE DIAPOSITIVE

Roche Model Solution of restricted three body problem Assumptions: 1. the third mass must be infinitesimal mass; 2. The two large masses must be in circular orbit. L 1, L 2… L 5 Lagrange points: points where there was not net force exerted on the third mass. Roche surface: equipotential surface where the sum of the rotational and gravitational potential energy is constant. Roche surface through L 1: consists of two Roche lobes and form the inner critical potential. If one star completely fills its Roche lobe then it may loss matter to its companion star through L 1. Roche surface through L 2: it defines the outer critical potential. If a star has a potential greater than the outer critical potential mass may be transferred out of the system

Kopal Classification Comparison between the star potential and the inner critical potential. Detached system: neither star completely fill the Roche lobe. evolve separately. The stars Semi-detached system: only one of the two stars completely fills its Roche lobe. Mass transfer (NOVA EXPLOSION). Contact system: both stars have the potentials greater than the inner critical potential but less than the outer critical potential. Both componetes of the binary fill their Roche lobe and a common envolope surrounds both stars.

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− 9 M⊙ 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 [Iliadis 07]. 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.

σ(E)THM (arb. un. ) 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 Si. Mi 2(ERi): M. La Cognata at al. PRL, in press ar. Xiv: 0806. 1274 con Si fattore spettroscopico dell’iesimo stato dell’ 18 F • Strength della resonanza: Ec. m. (Me. V) Sostituendo: con “single particle width” ottenuta con calcoli di ANC

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

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’

If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J 0 and parity Π 0, the cross section for the α->α’ reaction is given by where

If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J 0 and parity Π 0, the cross section for the α->α’ reaction is given by where PL are the Legendre polynomials

NOTATION where W is the Racah coefficients defined in Racah 1942

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

NOTATION , where Γαsl is the partial widths of the resonant level. ξl is the phase shifts for the potential scattering, in the hard sphere approximation, defined by equation 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)

First consideration PSD 1 -PSD 6 and PSD 4 -PSD 3 coincidences: PSD 3 and PSD 6 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. PSD 1 The same for PSD 4 Ec. m. >500 ke. V ps> 30 Me. V/c Not possible to use coincidence 1 -4 !! E 1 and E 4 calculation! obtained by kinematical Run 86 E (Me. V) Run 79 Run 56

Reaction Rate Cross section is necessary input to know the stellar reaction rate: where σBW is the Breit-Wigner cross section Statistical factor depending by nuclear spin of compound nucleus JC*, target JX and projectile Ja For an isolated and narrow resonance: The product of the statistical factor ω and the width ratio γ=Γ 1Γ 2/Γ is referred as the strength of the resonance: Г 1 and Г 2 represent the partial widths describing the formation and the decay of the compound nucleus. Г= Г 1+Г 2 is the total width

Reaction Rate Cross section is necessary input to know the stellar reaction rate: where σBW is the Breit-Wigner cross section Statistical factor depending by nuclear spin of compound nucleus JC*, target JX and projectile Ja For an isolated and narrow resonance: The product of the statistical factor ω and the width ratio γ=Γ 1Γ 2/Γ is referred as the strength of the resonance: KEY PARAMETER FOR NUCLEAR RATE DETERMINATION!!

Consideration on the extraction of the ωγ parameter for the 65 ke. V resonant level The first step of the reaction rate calculation is to evaluate the strengths of the resonances We focussed on the 0 -0. 3 Me. V energy region and in particular on both Ec. m. =65 ke. V and Ec. m. =183 ke. V, obtaining the strength of the resonance at Ec. m. =65 Ke. V by using the available information in literature on the well measured Ec. m. =183 ke. V resonance. To this aim, the extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution.

Reaction Rate calculation I In the narrow resonance approximation, the reaction rate is deduced by relation where NA<σv>R is expressed in cm 3 mol-1 sec-1, ER and ωγ in Me. V and S(O) in Me. V b. Z 1 and Z 2 are the projectile and the target atomic number respectively. In the calculation of the 17 O(p, α)14 N reaction rate, we followed the same procedure adopted in Chafa’ 07 by using for the resonance at Ec. m. =65 ke. V the two value of ωγ extracted as explained before.

New approach to extract the ωγ parameter for a resonance I The THM cross section for the A+a(x+s)->c+C+s reaction proceeding through a resonance Fi in the subsystem F=A+x=C+c is: where A. M. Mukhamedzhanov et al. , J. Phys. G: Nucl. Part. Phys. 35 (2008) 014016 ü Mi(E) is the direct transfer reaction amplitude for the binary reaction A+a->Fi+s populating the resonant state Fi with the resonance energy ERi; ü Γcci(E) is the partial resonance width for the decay Fi -> C+c; ü Γi is the total resonance width of Fi. The appearence of the transfer reaction amplitude Mi(E) instead of the entry channel partial resonance width Γ(Ax)i(E) is the main difference between the THM cross section and the cross section for the resonant binary sub-reaction A+x->C+c

New approach to extract the ωγ parameter for a resonance II The peak TH cross section taken at the resonance ERi energy for the (p, α) reaction A+x->C+c is given by σ(E) Ni -Γi/2 ERi In our case, resonances: Γi/2 we have two 1 Strength of resonance 2 (Ec. m. =183 ke. V) well measured in two recent works !! 2

If Г 1<<Гris and Г 2<<Гris Г 1=Гris Г 2=Гris But 1 2 Г 1 ~ 130 e. V Г 2 ~ 7 e. V Гris ~ 20 ke. V The strength of the resonance at 65 ke. V is given from the ratio between the peak value N 1 and N 2 through the relation: