1. Recent Progress in Nuclear Astrophysics at TRIUMF Using Indirect Techniques Barry Davids, TRIUMF 5 Mar 2009

2. Radiative Capture Reactions in the Sun Rates of radiative capture reactions needed for predictions of solar neutrino flux Rates of radiative capture reactions needed for predictions of solar neutrino flux 8 B solar  flux now measured to ± 8.6% by SNO, 7 Be flux measured to ± 10% by Borexino 8 B solar  flux now measured to ± 8.6% by SNO, 7 Be flux measured to ± 10% by Borexino S mn (0) is the astrophysical S factor for the radiative capture m + n  (m+n) +  at zero energy: S 17 is for 7 Be(p  ) 8 B and S 34 for 3 He(  ) 7 Be S mn (0) is the astrophysical S factor for the radiative capture m + n  (m+n) +  at zero energy: S 17 is for 7 Be(p  ) 8 B and S 34 for 3 He(  ) 7 Be 8 B flux  S 17 (0), S 34 (0) 0.81 8 B flux  S 17 (0), S 34 (0) 0.81 7 Be flux  S 34 (0) 0.86 7 Be flux  S 34 (0) 0.86

3. Radiative Captures in Big Bang Nucleosynthesis BBN a robust prediction of hot big bang cosmology for > 40 yr BBN a robust prediction of hot big bang cosmology for > 40 yr Explains origin of large universal He abundance, trace quantities of D, 3 He, & 7 Li Explains origin of large universal He abundance, trace quantities of D, 3 He, & 7 Li Given general relativity, cosmological principle, abundance predictions depend only on mean lifetime of neutron, number of active, light neutrino flavours, universal baryon density, and nuclear reaction rates Given general relativity, cosmological principle, abundance predictions depend only on mean lifetime of neutron, number of active, light neutrino flavours, universal baryon density, and nuclear reaction rates 7 Li produced via 3 He(  ) 7 Be 7 Li produced via 3 He(  ) 7 Be Primordial 7 Li abundance proportional to S 34 (300 keV) 0.96 Primordial 7 Li abundance proportional to S 34 (300 keV) 0.96

4. Theoretical S 34 Models Potential model and cluster model of Kajino [NPA 460, 559 (1986)] shapes agree below 500 keV, but is it fortuitous? Absolute values of calculations significantly underestimate data Potential model and cluster model of Kajino [NPA 460, 559 (1986)] shapes agree below 500 keV, but is it fortuitous? Absolute values of calculations significantly underestimate data Uncertainty in cluster model S 34 (E) derived from theoretical estimates of uncertainty in S 34 (0) and its logarithmic derivative, shown by dotted lines Uncertainty in cluster model S 34 (E) derived from theoretical estimates of uncertainty in S 34 (0) and its logarithmic derivative, shown by dotted lines Can we use data and well-known physics to determine S 34 (E) independent of structure model? Can we use data and well-known physics to determine S 34 (E) independent of structure model? We (Cyburt, BD) use a formalism capable of handling discrepant modern measurements dominated by systematic uncertainties We (Cyburt, BD) use a formalism capable of handling discrepant modern measurements dominated by systematic uncertainties

5. Modern S 34 Data Shape of cross section near threshold described by Mukhamedzhanov and Nunes, NPA 708, 437 (2002) We take account of fact that only l = 0 and l = 2 incoming partial waves can contribute to the E1 capture, finding

6. Modern Branching Ratio Data Precise data for the branching ratio between the ground and first excited state transitions permit simultaneous fit of both transitions using same form but different parameters Modern data allow simultaneous determination of 3 parameters, s 0, s 2, & a for each transition; 4 parameter fit was not higher quality, hence c  0

7. Partial Wave Contributions

8. Comparison with Cluster Model Significant differences with most commonly used cluster model found Significant differences with most commonly used cluster model found Data are able to determine shape without dependence on structure model Data are able to determine shape without dependence on structure model S 34 (0) = 0.580 ± 0.043 keV b at the 68.3% CL (± 7.4%) S 34 (0) = 0.580 ± 0.043 keV b at the 68.3% CL (± 7.4%) S 34 (0) = 0.580 ± 0.054 keV b at the 95.4% CL (± 9.3%) S 34 (0) = 0.580 ± 0.054 keV b at the 95.4% CL (± 9.3%) Size of latter smaller than 68.3% CL interval from 1998 RMP evaluation of solar nuclear fusion cross sections Size of latter smaller than 68.3% CL interval from 1998 RMP evaluation of solar nuclear fusion cross sections Cyburt and Davids, Phys. Rev. C 78, 064614 (2008) Cyburt and Davids, Phys. Rev. C 78, 064614 (2008)

9. Comparison of Observations with BBN Predictions Using this S 34 (E), the BBN prediction based on the WMAP5 universal mean baryon density (± 2.7%) differs from the primordial 7 Li abundances inferred from globular cluster stars and halo field stars by 4.2  and 5.3  respectively [Cyburt, Fields, & Olive, JCAP 11, 012 (2008)] Using this S 34 (E), the BBN prediction based on the WMAP5 universal mean baryon density (± 2.7%) differs from the primordial 7 Li abundances inferred from globular cluster stars and halo field stars by 4.2  and 5.3  respectively [Cyburt, Fields, & Olive, JCAP 11, 012 (2008)] Unresolved, this discrepancy shakes the foundations of “precision” cosmology (one of the pillars!) Unresolved, this discrepancy shakes the foundations of “precision” cosmology (one of the pillars!) Assumptions of  CDM cosmology must be questioned (effects of inhomogeneities, Copernican principle, alternative gravitational theories?) Assumptions of  CDM cosmology must be questioned (effects of inhomogeneities, Copernican principle, alternative gravitational theories?)

10. 7 Be(p,  ) 8 B Data 7 Be(p,  ) 8 B Data

11. Results of Analysis Model-dependent analysis of high precision Seattle data finds slight preference for 7 Li + n potential model over cluster model, but difference not significant Model-dependent analysis of high precision Seattle data finds slight preference for 7 Li + n potential model over cluster model, but difference not significant Using a minimally structure-dependent pole model taking account of rise at low energy, fit radiative capture data below 425 keV, allowing data to determine shape, consistent with cluster and potential models; 2 parameter fit, with a fixed at 45 keV Using a minimally structure-dependent pole model taking account of rise at low energy, fit radiative capture data below 425 keV, allowing data to determine shape, consistent with cluster and potential models; 2 parameter fit, with a fixed at 45 keV Junghans et al. result: 21.4 ± 0.7 eV b Junghans et al. result: 21.4 ± 0.7 eV b All other radiative capture: 16.3 ± 2.4 eV b All other radiative capture: 16.3 ± 2.4 eV b

12. TRIUMF Experiment Asymptotic normalization coefficients (ANC’s) derived from transfer reactions allow inference of S(0) directly Asymptotic normalization coefficients (ANC’s) derived from transfer reactions allow inference of S(0) directly Measure ANC of the valence neutron in 8 Li via the elastic scattering/transfer reaction 7 Li( 8 Li, 7 Li) 8 Li at 11 and 13 MeV Measure ANC of the valence neutron in 8 Li via the elastic scattering/transfer reaction 7 Li( 8 Li, 7 Li) 8 Li at 11 and 13 MeV Interference between elastic scattering and neutron transfer produces characteristic oscillations in differential cross section Interference between elastic scattering and neutron transfer produces characteristic oscillations in differential cross section Amplitudes of maxima and minima yield ANC Amplitudes of maxima and minima yield ANC Identical initial and final states => single vertex is involved Identical initial and final states => single vertex is involved Statistical precision greater (compared with distinct initial and final states) Statistical precision greater (compared with distinct initial and final states) Single optical model potential needed Single optical model potential needed Elastic scattering measured simultaneously Elastic scattering measured simultaneously More than one beam energy allows evaluation of remnant term in DWBA amplitude (in principle) More than one beam energy allows evaluation of remnant term in DWBA amplitude (in principle) Absolute normalization of cross section enters only as a higher-order effect in ANC determination Absolute normalization of cross section enters only as a higher-order effect in ANC determination

13. FRESCO DWBA Calculations by Sam Wright

14. Experimental Setup Two annular, segmented Si detectors Two annular, segmented Si detectors 25 µg -2 7 LiF target on 10 µg cm -2 C backing 25 µg cm -2 7 LiF target on 10 µg cm -2 C backing LEDA detector covers lab angles from 35-61° LEDA detector covers lab angles from 35-61° S2 detector covers 5-15° in the lab S2 detector covers 5-15° in the lab 7 Li cm angular coverage from 10-30° and 70-122° 7 Li cm angular coverage from 10-30° and 70-122° 8 Li beam intensities of 2-4  10 7 s -1 8 Li beam intensities of 2-4  10 7 s -1

15. 11 MeV Data

16. Coincidences: Energy-Angle Correlation

17. 11 MeV Data Revisited All S2 data, Elastics in LEDA

18. 14 N + p  15 O +  Ages of the Oldest Stars Old stars and massive stars fuse H into He via the CNO cycles Old stars and massive stars fuse H into He via the CNO cycles C, N, O are catalysts C, N, O are catalysts At low temperatures found in oldest globular cluster stars, energy release controlled by slowest reaction, 14 N(p,  ) 15 O At low temperatures found in oldest globular cluster stars, energy release controlled by slowest reaction, 14 N(p,  ) 15 O Reaction rate predominant nuclear uncertainty in age determination Reaction rate predominant nuclear uncertainty in age determination Stars can’t be older than universe! Stars can’t be older than universe!

19. 14 N + p  15 O +  Solar Neutrinos and Core Composition Temperature of solar core implies 99% of energy released through pp chains, ~ 1% via CN cycle Temperature of solar core implies 99% of energy released through pp chains, ~ 1% via CN cycle Predicted solar neutrino fluxes due to 13 N, 15 O exceed 10 8 cm -2 s -1 on Earth Predicted solar neutrino fluxes due to 13 N, 15 O exceed 10 8 cm -2 s -1 on Earth Measurements reveal primordial composition of solar core Measurements reveal primordial composition of solar core Flux predictions depend on 14 N(p,  ) 15 O rate at very low energy, require ± 3.5% error Flux predictions depend on 14 N(p,  ) 15 O rate at very low energy, require ± 3.5% error Reaction rate depends on lifetime of subthreshold 6.79 MeV state in 15 O Reaction rate depends on lifetime of subthreshold 6.79 MeV state in 15 O

20. Lifetime Measurements Lifetimes measured via Doppler shift of emitted  rays as nucleus slows down in foil Lifetimes measured via Doppler shift of emitted  rays as nucleus slows down in foil Short lifetime  large Doppler shift, long lifetime  small Doppler shift Short lifetime  large Doppler shift, long lifetime  small Doppler shift Shapes of detected  ray lines yield lifetime; sensitive to fs lifetimes Shapes of detected  ray lines yield lifetime; sensitive to fs lifetimes Previous measurements of 6.79 MeV state lifetime marginally inconsistent, not generally accepted; TUNL reported  = 1.60 (+ 0.75, -0.72) fs, Bochum finds  < 0.77 fs, both @ 90% CL Previous measurements of 6.79 MeV state lifetime marginally inconsistent, not generally accepted; TUNL reported  = 1.60 (+ 0.75, -0.72) fs, Bochum finds  < 0.77 fs, both @ 90% CL

21. Doppler Shift Lifetimes (DSL) Chamber Collimator 16 O beam E Si detector (500 μm) TIGRESS detector at 0 °  E Si detector (100 μm) Implanted 3 He (6 × 10 17 cm -2 ) Au foil Vacuum chamber 16 O 15 O  

22. Experimental Setup DSL chamber TIGRESS Detector

23. Si Telescope Particle Identification  E (MeV) E (MeV) 15 O GS  ( 15 O GS )  ( 15 O Ex ) Elastic 3 He p ( 18 F) d ( 17 F)

24. Gamma Ray Energy Spectrum

25. Future Work 3 He(  ) 7 Be measurement at large relative energy using DRAGON 3 He(  ) 7 Be measurement at large relative energy using DRAGON Measurement of 12 C( 8 Li, 7 Li) 13 C for valence neutron ANC in 8 Li Measurement of 12 C( 8 Li, 7 Li) 13 C for valence neutron ANC in 8 Li Collect additional 15 O lifetime data using 3 He- implanted Zr target foil Collect additional 15 O lifetime data using 3 He- implanted Zr target foil Figure credit: F. Strieder

26. Summary Improvements in precision of solar neutrino flux measurements and observations of cosmic microwave background radiation require continued attention to nuclear reaction rate uncertainties, namely radiative capture rates Improvements in precision of solar neutrino flux measurements and observations of cosmic microwave background radiation require continued attention to nuclear reaction rate uncertainties, namely radiative capture rates 7 Be(p  ) 8 B has been measured very precisely once, and this measurement dominates other radiative capture measurements and ANC determinations which are 1- 2  lower; TRIUMF ANC determination via 7 Li( 8 Li, 7 Li) 8 Li and 12 C( 8 Li, 7 Li) 13 C still under analysis 7 Be(p  ) 8 B has been measured very precisely once, and this measurement dominates other radiative capture measurements and ANC determinations which are 1- 2  lower; TRIUMF ANC determination via 7 Li( 8 Li, 7 Li) 8 Li and 12 C( 8 Li, 7 Li) 13 C still under analysis 3 He(  ) 7 Be measured precisely several times since turn of century; quality of data permit determination of reliable, structure model-independent best value and confidence intervals using MCMC method 3 He(  ) 7 Be measured precisely several times since turn of century; quality of data permit determination of reliable, structure model-independent best value and confidence intervals using MCMC method 5  disagreement of primordial Li abundances inferred from observations of field halo stars with precise BBN predictions made possible by new 3 He(  ) 7 Be and CMB measurements raises serious doubts about the assumptions of the standard cosmological model 5  disagreement of primordial Li abundances inferred from observations of field halo stars with precise BBN predictions made possible by new 3 He(  ) 7 Be and CMB measurements raises serious doubts about the assumptions of the standard cosmological model Precision of 14 N(p,  ) 15 O reaction rate determination at low energy limited by knowledge of lifetime of 6.79 MeV subthreshold state in 15 O; Ongoing TRIUMF measurement promises to be best yet Precision of 14 N(p,  ) 15 O reaction rate determination at low energy limited by knowledge of lifetime of 6.79 MeV subthreshold state in 15 O; Ongoing TRIUMF measurement promises to be best yet

27. Derek Howell & Naomi Galinski, Simon Fraser University Sky Sjue, TRIUMF Richard Cyburt, Joint Institute for Nuclear Astrophysics & National Superconducting Cyclotron Laboratory, Michigan State University CANADA ’ S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada LABORATOIRE NATIONAL CANADIEN POUR LA RECHERCHE EN PHYSIQUE NUCLÉAIRE ET EN PHYSIQUE DES PARTICULES Propriété d ’ un consortium d ’ universités canadiennes, géré en co-entreprise à partir d ’ une contribution administrée par le Conseil national de recherches Canada