1. Indirect Techniques ( I) : Asymptotic Normalization Coefficients and the Trojan Horse Method NIC IX R.E. Tribble, Texas A&M University June, 2006

2. Why use Indirect Techniques? Reaction rates on radioactive nuclei Capture through subthreshold states Direct capture to add to resonant capture Screening and low-energy extrapolations Get cross sections difficult for direct studies! Including:

3. Some Indirect Techniques [focus on reaction rates] Widths (  and ‘p’) of resonance rates - populate resonance state and measure decay Resonance energies – determine E R Coulomb dissociation Trojan Horse Method - unique way to understand screening Asymptotic Normalization Coefficients - use with stable and radioactive beams  **  (T. Motobayashi) **Experts in audience for detailed questions! } resonant capture

4. Radiative [p(  )] Capture with resonant and subthreshold states: ANCs subthreshold state resonance Capture through resonance

5. Radiative [p(  )] Capture with resonant and subthreshold states: ANCs subthreshold state resonance Direct capture

6. Radiative [p(  )] Capture with resonant and subthreshold states: ANCs subthreshold state resonance Capture to ground state through subthreshold state

7. Measuring ANCs: Transfer Reactions Transition amplitude: Peripheral transfer: [S = C 2 /b 2 ]

8. ANC Examples: capture at stellar energies DC: 7 Be(p,  ) 8 B and 7 Be + p  8 B 22 Mg(p,  ) 23 Al and 22 Ne + n  23 Ne DC through subthreshold state: 14 N(p,  ) 15 O and 14 N + p  15 O 13 C( ,n) 16 O and 13 C +   17 O (2 posters) DC and resonance interference: 13 N(p,  ) 14 O and 13 N + p  14 O

9. S factor dominated by direct capture—our published value via ANCs from two ( 7 Be, 8 B) transfer reaction studies: S(0) = 18.0  1.9 eV  b  Result low by about 2  compared to most recent direct measurement (?)  Details about 7 Be(p,  ) 8 B from C.D. in later talk S factor for 7 Be(p,  ) 8 B

10. CNO Cycles 13 C 13 N 12 C 14 N 15 O 15 N 17 O 17 F 16 O 18 F 18 O 19 F 20 Ne (p,  ) (p, α) (p,  ) (e +,ν) (p,  ) (p, α) (p,  ) (e +,ν) ( p,  ) (e +,ν) (p,  ) (p,α) (e +,ν) (p,α) (p,  ) IIIIII IV

11. S factor for 14 N(p,  ) 15 O some preliminary results C 2 (E x  6.79 MeV)  fm -1 [non-resonant capture to this state dominates S factor] S(0)  1.41 ± 0.24 keV·b for E x  6.79 MeV S tot (0)  1.62 ± 0.25 keV·b Subthreshold state: slide from NIC VII

12. S factor dominated by direct capture to the subthreshold state—our published value S(0) = 1.62  0.25 keV  b reduces previous results by  2 New direct measurements from LUNA (1.7±0.2) and LENA (1.68±0.09±0.16) in excellent agreement with this Impacts stellar luminosity at transition period to red giants and ages of globular clusters by about 1 Gyr S factor for 14 N(p,  ) 15 O

13. Na Ne F O N C 345678910 CNO Hot CNO (T 9 =0.2) Hot CNO (T 9 =0.4) Breakout Reactions http://csep10.phys.utk.edu/guidry/NC-State-html/cno.html Hot CNO Cycle and 13 N(p,  ) 14 O

14. 14 N( 13 N, 14 O) 13 C DWBA by FRESCO (ANC for p)p) CN  1314 C 2 = 29.0 ± 4.3 fm -1

15. S Factor for 13 N(p,  ) 14 O DC/Decrock_dc = 1.4 Constructive/Decrock_tot =1.4 Constructive/Destructive =4.0 ( expected constructive interference for lower energy tail, useful to check) For Gamow peak at T 9 =0.1, Preliminary

16. Transition from CNO to HCNO 13 N(p,  ) 14 O vs  decay 14 N(p,  ) 15 O vs  decay Crossover at T 9   0.2 For novae find that 14 N(p,  ) 15 O slower than 13 N(p,  ) 14 O;  14 N(p,  ) 15 O dictates energy production X H =0.77

17. S factor dominated by subthreshold state ( E x =6.356 MeV) S factor for 13 C( ,n) 16 O and s-process neutrons ANC from 6 Li( 13 C,d) 17 O – sub Coulomb transfer (recent result from Florida State University and TAMU, earlier result - Kubono) ANC +  n gives S(0) = 2.36  0.52  10 6 Mev  b Factor of  10 below present NACRE value [posters on this topic!]

18. S factor dominated by direct capture up to T 9  0.2 S factor for 22 Mg(p,  ) 23 Al 22 Mg produced in ONe novae in Ne-Na cycle  source of 22 Na  decay or p capture dominate? Use charge symmetry for ANC:  -decay of 23 Al  gnd. state is 5/2 +

19. 22 Mg (p,  ) 23 Al Reaction Rate E C.M [MeV] S -factor [KeV b] T 9 (10 9 K) S(E) – Direct Capture reaction rate ρ=10 6 gm/cm 3, T 9 =0.4 22 Mg(p,  ) 23 Al competes with β + rate but photodisintegration is issue Reaction Rate (cm 3 /mole/s)

20. Charged Particle Capture: the Trojan Horse Method I Many charged-particle reaction rates important in stellar evolution Laboratory measurements  Coulomb barrier issues (e.g. electron screening) making extrapolation difficult THM (Baur – 1986) uses surrogate to remove Coulomb effects

21. THM - Example Consider a reaction 6 Li(d,  ) 4 He THM  use 6 Li( 6 Li,  ) 4 He d spectator 6 Li( 6 Li,  ) 4 He for 6 Li(d,  ) 4 He THM - Spitaleri et al. Direct data Englster et al. 6 Li   

22. Charged Particle Capture: the Trojan Horse Method II Issues: – transferred particle is off energy shell – initial and final state effects important – no absolute normalization – must have quasi-free kinematics – analysis with PWIA and MPWIA

23. Some Reaction Mechanism Issues Coulomb effects included [Mukhamedzhanov et al., nucl/th-0602001] Three calculations (spectator  ignored) as a function of  =(p  d ) 2 /(   d ) 2 ‘on shell’ transfer   =0 (black) ‘half off shell’ with QF kinematics  =m  +m d -m Li = BE (red) ‘half off shell’ with  = 1.5  BE (blue) 6 Li + 6 Li  +  +   for Final state effects also not important!

24. THM Applications Direct Capture: – extrapolation to S(0) without e-screening – extraction of screening potential Resonant capture: – extrapolation to S(0) with small uncertainty Subthreshold Capture: – observe effects at very low relative energy

25. U e (ad) U e (Dir) 6 Li+d 186 eV330 ± 120 eV U e (ad) U e (Dir) 6 Li+p 186 eV440 ± 80 eV U e (ad) U e (Dir) 7 Li+p 186 eV300 ± 160 eV 7 Li + p   +  S 0 =55  3 keV b 6 Li + d   +  S 0 = 16.9 MeV b 6 Li+p  + 3 He So = 3  0.9 MeVb 6 Li+d   +  7 Li+p   +  6 Li+p   + 3 He R-matrix calculation direct data From C.S. Direct Capture

26. 9 Be(p,  ) 6 Li reaction 2 H( 9 Be,  6 Li)n The 9 Be(p,  ) 6 Li reaction via 2 H( 9 Be,  6 Li)n Laboratory: Tandem: LNS INFN-Catania Energy: E 9Be = 22 MeV 2H2H p 9 Be n 6 Li α I II THM Direct data Reaction important for depletion of light nuclei From C.S. Resonant Capture

27. The 15 N(p,  ) 12 C reaction via d( 15 N,  12 C )n 2H2H p n α I II 15 N 12 C Destroys 15 N  reduces 19 F production in AGB stars From C.S. Laboratory: TAMU (K500 cyclotron) 2 H( 15 N,  12 C)n E beam = 60 MeV S(0)  37 MeVb [about 1/2 NACRE value] Preliminary

28. Summary Indirect techniques  valuable tools in N.A. Useful for range of reaction types S(0) with different extrapolation systematics Can provide auxiliary information Yield cross sections difficult to get otherwise! Challenge for the future: find new techniques to understand (n,  ) rates

29. Collaborators ANCs: T. Al-Abdullah, A. Azhari, A. Banu, P. Bem, V. Burjan, F. Carstoiu, C. Fu, C. Gagliardi, V. Kroha, J. Piskor, A. Sattarov, E. Simeckova, G. Tabacaru, X. Tang, L. Trache, J. Vincour, Y. Zhai, A. Mukhamedzhanov THM (TAMU experiment) : C. Spitaleri,S. Cherubini, V. Crucilla, M. La Cognata, L. Lamia, R.G. Pizzone, S. Romano, A. Tumino