Determining Two Reaction Rates in Novae using the ANCs Technique. Tariq Al-Abdullah Hashemite University, Jordan Russbach, March 2011

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1 Determining Two Reaction Rates in Novae using the ANCs Technique Tariq Al-Abdullah Hashemite University, Jordan Russbach, March 2011

2 Main Points Synthesis of 22Na and 18F in ONe novae. Asymptotic Normalization Coefficients. Reaction rates from Mirror Nuclear Systems. Results and Conclusions. M.S. Smith and K.E. Rehm, Ann. Rev. Nucl. Part. Sci, 51 (2001)

3 Motivations * Novae Produce a considerable amount of individual nuclei; events (30 yr-1). * Nucleosynthesis will occur via the HCNO, NeNa, MgAl cycles. * Long-Lived γ-ray emitters: 18F & 22Na, Observations direct test of TNR model. NeNe-Na cycle 18Ne 19Ne 17F 18F 21Ne 14O 13N 15O 16O 14N 19F 22Na 17O 25Mg 26Al 18O 21Na 22Ne 25Al 26Mg 20Ne 23Na 24Mg 27Al (p,γ) 13C 27Si 15N 19F 12C (p,γ) (p,α) (β+ ν) Ne-Na Cycle (p,α) (β+ ν) Mg-Al Cycle 28Si

4 Proton Capture Reaction Rate Direct Capture: * The cross section for a charged-particle is: 1 σ ( E) = exp( 2 πη) S( E) E * Nonresonant reaction rate per particle pair: Plane Wave Projectile X Target A γ Final Orbit Nucleus B Target A E b συ = S( E)exp de πµ KT E ( KT ) Resonant Capture: * The cross section (Breit-Wigner): λ 2 J + 1 Γ σ ( E ) = 4π 2 J J E E * The reaction rate: συ ω γ = π = µ KT ( )( ) ( ) ħ 2 J + 1 r ωγ exp ( 2 J p + 1)( 2 J t + 1) Γ Γ p Γ tot γ Er KT r p Γ 2 γ Γ + 2 Potential V(r) Coulomb Barrier Nuclear Radius R n Projectile Distance r

5 Experimental Difficulties FEATURES T ~ K PROBLEMS E 0 ~ 100 kev << E Coul. tunnelling effect Low cross section values average interaction time τ ~ <σv> -1 ~ 100s My Radioactive nuclei Low Cross Section detection efficiencies major experimental challenge extrapolation procedure required REQUIREMENTS Detection Efficiencies long measurements ultra pure targets high beam intensities high detection efficiency

6 Indirect Techniques 1. Coulomb Dissociation. (Baur G. et al, NPA 458 (1986) 188) 2. Trojan Horse. (Baur G, PLB 178 (1986) 135) 3. Asymptotic Normalization Coefficients. * Xu H. M. et al, PRL (1994) * A. M. Mukhamedzhanov et al., Phys. Rev. C 56, 1302 a) Transfer reaction. b) Break up reaction.

7 Asymptotic Normalization Coefficients (ANCs) Direct Capture Reactions for charges particles: The binding energy of the captured particle is low. The capture occurs through the tail of the overlap function. The Amplitude of the tail is given by the ANCs. E 0 γ p For a Transfer reaction (X+A Y+B): The DWBA amplitude: A B (A+p) M ( E) = χ I ( r ) V I ( r ) χ ( ) B X ( + ) f A, p A, p Y, p Y, p i The Asymptotic behavior of the radial overlap function: r > R N W ( ), 1 2 ( 2 B sp B η l ) B + κ B r I A, p ( r ) C A, p r The Asymptotic normalization of the bound-state wave function: r > R N W η, l 1 2 ( 2 ) B + κ B r ϕ n,, ( ) B lb j r b B l B, jb r For r > R N, the radial dependences are the same I ( r ) = S ϕ ( r ) B A, p A, p 2 2 C = Sb X (Y+P) rh, rφ (fm -1/2 ) Y r (fm) 12 C+n--> 13 C

8 Extracting the ANCs Peripheral Transfer Reaction (X+A Y+B): The reaction cross section: dσ = d Ω l j l j B B X X In terms of the ANCs: d σ = DWBA A al j y al j l j l j B B X X B B X X Procedure to extract the ANCs: S S B X ( C A al j ) ( C Y al j ) 2 2 B B X X 2 2 d Ω b A al B j b B Y al X j X Elastic Scattering σ σ DW B A A X (Y+a) C 2 (B) a C 2 (X) Transfer Reaction B(A+a) Y Experimental Angular Distribution DWBA calculation Experimental Angular Distribution Wood-Saxon Double Folding Comparison Spectroscopic factors OMPs A N C s

9 ANCs in Astrophysics Radiative Capture Reaction A + p B + γ at low Energy: The cross section: σ M The direct capture amplitude M is : 2 ^ ( ) B ( A, p, Ap ) ( Ap ) A ( A ) p ( p ) i ( Ap ) M = φ ζ ζ ζ O r φ ζ φ ζ ψ + r Integral over ζ : ^ DC B ( ) M = I Ap ( rap ) O( rap ) ψ + i ( rap ) For a Direct Capture Hence: DC B σ ( C Ap ) B M C Ap 2 A p B γ

10 Experiments using the ANCS 24 Si 25 Si 26 Si 23 Al 24 Al 25 Al 20 Mg 21 Mg 22 Mg 23 Mg 24 Mg 19 Na 20 Na 21 Na 22 Na 23 Na 17 Ne 18 Ne 19 Ne 20 Ne 21 Ne 22 Ne 15 F 16 F 17 F 18 F 19 F 13 O 14 O 15 O 16 O 17 O 18 O 11 N 12 N 13 N 14 N 15 N 9 C 10 C 11 C 12 C 13 C (p,γ) (p,α) (β + ν) 8 B 9 B 10 B 11 B = studied at TAMU 7 Be 8 Be 9 Be CNO, HCNO Ne-Na Na cycle

11 ANC s measured by stable beams 9 Be + p 10 B [ 9 Be( 3 He,d) 10 B; 9 Be( 10 B, 9 Be) 10 B] 7 Li + n 8 Li [ 12 C( 7 Li, 8 Li) 13 C] 13 C + p 14 N [ 13 C( 3 He,d) 14 N; 13 C( 14 N, 13 C) 14 N] 14 N + p 15 O [ 14 N( 3 He,d) 15 O] 16 O + p 17 F [ 16 O( 3 He,d) 17 F] 20 Ne + p 21 Na [ 20 Ne( 3 He,d) 21 Na] beams 10 MeV/u

12 ANC s measured by radioactive (rare isotope) beams 7 Be + p 8 B [ 10 B( 7 Be, 8 B) 9 Be] [ 14 N( 7 Be, 8 B) 13 C] 11 C + p 12 N [ 14 N( 11 C, 12 N) 13 C] 13 N + p 14 O [ 14 N( 13 N, 14 O) 13 C] 17 F + p 18 Ne [ 14 N( 17 F, 18 Ne) 13 C] beams MeV/u

13 ANC s measured by stable beams (mirror symmetry) 7 Be + p 8 B [ 13 C( 7 Li, 8 Li) 12 C] L. Trache, et al, PRC 81, (R) (2003) 22 Mg + p 23 Al [ 13 C( 22 Ne, 23 Ne) 12 C] T. Al-Abdullah, et al, PRC 81, (2010) 17 F + p 18 Ne [ 13 C( 17 O, 18 O) 12 C] T. Al-Abdullah, et al, to be submitted 26 Al + p 27 P [ 13 C( 26 Mg, 27 Mg) 12 C] M. McClesky, PhD Dissertation

14 Applying the ANC method to estimate 22 Mg(p,γ) 23 Al reaction rate

15 22 Na? * Nova is an important source of 22 Na. * It is synthesized in Ne-Na cycle: 1- Cold cycle 2- Hot Cycle * For a typical ONe nova: - Ejected mass ~ M - Ejected 22 Na ~ /nova - Detected flux ~ 10-4 cm 2 s -1 * However?!? - Observation of five ONe novae using CGRO. - Neither nova is a promising object for γ-ray flux. 23 Al 470 ms 22 Mg s 21 Na s 20 Ne 23 Mg s 22 Na y 21 Ne 23 Na 22 Ne 22 Na 3 + β γ (1.275 MeV) Ne 22 Na(p,γ) 23 Mg F. Stegmüller et al, NPA 601 (1996) Na(p,γ) 22 Mg S. Bishop et al, PRL 90 (2003) Nova Distance [kpc] Observation Her prediction Cyg Κ prediction Pup No Sgr 1991 > 10 No Sct 1991 > 10 No * A. F. Iyudin et al, Astron. Astrophys. 300 (1995) 422

16 22 Mg(p,γ) 23 Al * The depletion of 22 Mg compensates the loss in 22 Na * 22 Na production is bypassed by 22 Mg(p,γ) 23 Al. * The reaction rate is due to proton capture to d 5/2 or s 1/2 states. g.s Al 383 kev 22 Mg + p 145 kev * The reaction rate is still uncertain: Low Q-value (145 kev). Mass of 23 Al (±25 kev). V. Jacob, PRC 74, (2006), A. Saastamonien PRC 80, , (2009) M. Wiescher et al, NPA 484 (1988) 90 Measured the location of the 1 st resonance. predictions J. A. Caggiano et al, PRC 64 (2001) Indirect estimation: 24 Mg( 7 Li, 8 He) 23 Al.

17 Mirror Nuclei 23 Al& 23 Ne 23 Al is now known!, Instead! Studying the mirror nucleus 23 Ne. The wave functions for mirror nuclei are the same C ( Ne) C ( Al ) is independent of NN-force. Timofeyuk * indicates that S-factor are equivalent ( 5 2 ) ( 0 ) δ ( 5 2 ) ( 0 ) Ne Ne Al Mg Al 22 Mg+p is replaced by 23 Ne 22 Ne+n. Stable beam 22 Ne and target 13 C. V. Jacob, PRC 74, (2006), A. Banu et al, Sumitted to PRC Extracting the ANCs of 23 Ne in 13 C( 22 Ne, 23 Ne) 12 C, φ r [fm] 23 Ne 23 Al ( Al) 2 23 d / 2 Cd ( Al) = C 5 / 2 d ( Ne) 5 / 2 b 2 23 d5 / 2 Ne b ( ) V (r) Ne 23 Al * N. Timofeyuk, P. Descouvemont, Phys. Rev. C 71, (2005). r [fm]

18 Experiments MDM Spectrometer MDM & Oxford Detector Reactions: 1-13C(22Ne,23Ne)12C 2- Elastic Scatterings. 3- Energy beam: 12 MeV/u Oxford Detector

19 Raw Data (Elastic) 22 Ne + 13 C ( 5 o E (channel) 22 Ne gs E (channel) gs 1st Angle (Deg) 2nd gs Pos (cm) 1st Pos (cm) [ ~E ] Energy Resolution ~ 320 KeV Angle (channel)

20 13 C( 22 Ne, 23 Ne) 12 C 22 Ne E CM =12 MeV/A V [MeV] r V [fm] a V [fm] W [MeV] r W [fm] a W [fm] χ2 V [MeV] r V [fm] a V [fm] W [MeV] r W [fm] a W [fm] χ o

21 13 C( 22 Ne, 23 Ne) 12 C * OMPs from the entrance/exit channels DWBA. * The Angular distribution for: 1- Transfer Reaction p 1/2 d 5/2 (Q=0.254 MeV) 2- Inelastic Transfer Reaction p 1/2 s 1/2 (E=1.02 MeV) * The reaction is Peripheral ( ) * The ANC in the other vertex: C C = 2.24 ± 0.01 fm S & C p 1/ b ( 23 Ne) [fm -1/2 ] p 1/2 d 5/ Cd ( Ne ) = 0.86 ± 0.08 ± 0.12 fm S ( ) 5 / 2 C Ne = ± 1.8 ± 3.8 fm / 2 p 1/ 2 d 1/ 2 1/ 2 5/ 2 p s

22 * The ANC in 23 Al: S 5 / 2 5 / 2 22 Mg(p,γ) 23 Al, S-factor 5 / 2 ( ) ( Al) = S ( Ne) ( Al) = 4.63 ± 0.77 * 10 fm d d C d * T. Al-Abdullah, et al, PRC 81, (2010) * This value agrees well with the results from 23 Al 22 Mg + p breakup 5 / 2 ( ) C d ( Al) = ± *10 fm A. Banu et al, Submitted to PRC Config. mixing of 23 Al ground state

23 Reaction Rate 22 Mg(p,γ) 23 Al * The Direct Capture Reaction Rate: 3 2 cm N A σ v = τ S ( E ) exp ( ) eff o τ mole.s * The Resonant Capture Reaction Rate: [46] T. Gomi, T. Motobayashiet al, JPG 31 (2005) * R dc & R res are competitive for T 9 = * The total reaction rate is compared with previous rates. * The loss in 22 Na is slightly compensated by the production of 22 Mg and 23 Al * The reaction is significant for T and ρ>10 4 gm/cm 3,

24 Applying the ANC method to estimate 17 F(p,γ) 18 Ne reaction rate

25 * Major sources of γ-ray lines: 1- Following β-decays 2- electron-positron annihilation. Why 18 F? 511 kev * 18 F emits positron (T 1/2 = 158 min). * The detection of 511 kev will measure the nova rate and add constraints. * 18 F is synthesized in HCNO cycle 1) 16 O(p,γ) 17 F(p,γ) 18 Ne(βν) 18 F 2) 16 O(p,γ) 17 F(βν) 17 O(p,γ) 18 F 3) 14 O(p,α) 17 F(p,γ) 18 Ne(βν) 18 F * 18 F production may be influenced by: 17 F(p,γ) 18 Ne? * 18 F is destroyed via 1) 18 F(p,α) 15 O 2) 18 F(p,γ) 19 Ne * The importance of the reaction: 1- Influences the abundances of 15 O, 17 F, 18 F, 18 Ne. 2- Determines the 17 O/ 18 O ratio. 3- Provides a transition sequence from HCNO into rp-process. 14 O 15 O 18 Ne 17 F 16 O 19 Ne 18 F 17 O

26 17 F(p,γ) 18 Ne * The reaction rate will be dominated by: 1- Resonant capture to first 3 + state, (T 9 >0.5). 2- Direct capture to the proton bound states, (T 9 <0.46). Reference Ex [MeV] Γ p [kev] Wiescher Garcia Sherr Bardayan Y. Parpottas D. W. Bardayan et al, PRC 62 (2000) * M. Dufour, P. Descouvemont, NPA 730 (2004) 316

27 Mirror Nuclei 18 Ne & 18 O The nuclear structure for 18 O & 18 Ne are similar. The ANCs for 18 O will be obtained from 13 C( 17 O, 18 O) 12 C reaction. Stable beam 17 O enables the ability to separate between interesting levels in 18 O.

28 13 C( 17 O, 18 O) 12 C Elastic Scattering Extracting the Optical Model Parameters

29 ( ) J π = 0 +, 2 +, 4 +, C( 17 O, 18 O) 12 C 2 + states is a combination of (d 5/2 ) 2 & (d 5/2 s 1/2 ), T. Dehnhard, et al, PRC 13 (1976) and 0 + have pure (d 5/2 ) 2 configuration O 0 +

30 13 C( 17 O, 18 O) 12 C * Comparison ANC vs S: The reaction is peripheral * The ANCs are obtained using: C 1 2 d σ = + d Ω b b b C D W D W 1 2 σ σ C, , 1 8, 2 O 2 2 O 2 2 C 5 C 1 O, O, C, O, O, lj 18 lj 18 * Charge Symmetry implies: 2 ( O) = 2 ( Ne) C b lj C b lj 15 S J π Proton Orbital B.E. [MeV] 18 O 2 C l j [fm -1 ] B.E. [MeV] 18 Ne 2 C l j [fm -1 ] d 5/ ± ± d 5/ ± ± 0.24 s 1/ ± ± d 5/ ± ± d 5/ ± ± 0.32 s 1/ ± ± 17

31 17 F(p,γ) 18 Ne * The Astrophysical S-factor for the transitions: ( 0 ) 1, 21, 41, 2 2 J π = * S(E) for & are the sum of (dd) & (ds) components * & dominate the DC over & * 2 + is the major E<400 kev 2 * At E=0, S-factor: ( ) S = 2.5 ± 0.4 kev b Determined < S1 17 ( 0) = 2.9 ± 0.4 kev b ( ) S = 3.5 kev b Calculated * Garcia,PRC 43, 2012(1991) * Dufour, NPA 730 (2004) 316

32 17 F(p,γ) 18 Ne * Direct Capture Reaction Rate: 3 2 cm N A σ v 51 τ S eff ( T9 ) e τ = m ole.s * Resonant Capture reaction rate: ( γ ) π + J = 3 E r = 600 kev, Γ = 56 ± 38 mev K. A. Chipps, PRL 102, (2009) * DC >> RS for T DC dominates in ONe novae * The uncertainty of DC rate is ±20% * Astrophysical Implications: Our rate is nearly 30 times smaller than the upper limit found in K. A. Chipps, PRL 2009 ( It is Considered SLOW) S. Parete-Koon AJ 598, 1239 (2003)

33 17 F(p,γ) 18 Ne What does slow mean? If nova M = 1.25 M, more 18 F & 18 O. If M 1.35 M, less 18 F but more 17 F & 17 O. S. Parete-Koon AJ 598, 1239 (2003) SLOW FAST

34 Conclusion The elastic & inelastic angular distributions have been measured to obtain the OMPs that are used in DWBA calculations for: 22 Ne+ 13 C & 22 Ne+ 12 C 12 C+ 13 C 17 O+ 13 C & 18 O+ 12 C The reaction rate for 22 Mg(p,γ) 23 Al has been determined through the measurements of the ANCs in 13 C( 22 Ne, 23 Ne) 12 C. This reaction is not important to understand the destruction of 22 Na in ONe novae. The ANCs from 13 C( 17 O, 18 O) 12 C have been used to evaluate the reaction rate at stellar energies for 17 F(p,γ) 18 Ne. More 18 F is synthesized in Novae.

35 Thank You Collaborators: C. A. Gagliardi, R. E. Tribble, L. Trache, G. Tabacaru, X. Chen, H. Clark, Y.-W. Lui, Y. Tokimoto, C. Fu, Y. Zhai, A. M. Mukhamedzhanov Cyclotron Institute, Texas A&M University F. Carstoiu. Institute of Nuclear Physics and Engineering, Romania

36 13 C( 12 C, 13 C) 12 C & ANC Contribution only from p 1/2 p 1/2 For identical entrance/exit channels: dσ/ σ/dω [mb/sr] Data DWBA dσ C p C d b C 13 ( ) 1 / 2 = 13 Ω p ( ) 1 / 2 The reaction is peripheral 4 σ DW BA S or C b( 13 C) [fm -1/2 ] θ CM [Deg] This work: C 2 = 2.24±0.10 fm -1 Literature: C 2 = 2.39±0.12 fm -1 A. M. Mukhamedzhanov, Sov. J. Nucl. 51, 431 (1990) Adopted: C 2 = 2.31±0.08 fm -1