Recent Results for proton capture S-factors from measurements of Asymptotic Normalization Coefficients R. Tribble Texas A&M University OMEG03 November, 2003

Nuclear Astrophysics Issues CNO cycle - energy producing cycle following p-p chain - important in wide range of stellar environments, including our Sun

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

Nuclear Astrophysics Issues CNO cycle reaction - 14 N(p,  ) 15 O (ANCs from ( 3 He,d) reaction) HCNO cycle - turns on as temperature and/or density increase - yields higher energy release, precursor to runaway

Na Ne F O N C CNO Hot CNO (T 9 =0.2) Hot CNO (T 9 =0.4) Breakout Reactions Hot CNO Cycle and 13 N(p,  ) 14 O

Nuclear Astrophysics Issues CNO cycle reaction - 14 N(p,  ) 15 O (ANCs from ( 3 He,d) reaction) HCNO cycle reaction - 13 N(p,  ) 14 O (ANCs from ( 13 N, 14 O) reaction) Ne-Na cycle reaction - next cycle, 21 Ne likely source of neutrons

Important in second generation stars Ne – Na Cycle

Nuclear Astrophysics Issues CNO cycle reaction - 14 N(p,  ) 15 O (ANCs from ( 3 He,d) reaction) HCNO cycle reaction - 13 N(p,  ) 14 O (ANCs from ( 13 N, 14 O) reaction) Ne-Na cycle reaction - 20 Ne(p,  ) 21 Na (ANCs from ( 3 He,d) reaction) S 17 – yet a different measurement!

Direct Radiative proton capture M is: Integrate over ξ: Low B.E.: Find:

Radiative Capture of Charged Particle Real, ?Complex, ANC observed r>R N r<R N

Capture through subthreshold states well known problem for many years Subthreshold state resonance Examples: 12 C( ,  ) 16 O 13 C( ,n) 16 O 14 N(p,  ) 15 O 20 Ne(p,  ) 21 Na

Let us consider the radiative capture For near-threshold level, bound or resonance, assuming Coulomb plus nuclear potential Subthreshold bound state contribution behaves like resonance

Subthreshold Capture p radiative capture: near threshold – S matrix is: where:

Transfer Reaction Transition amplitude: Peripheral transfer:

ANC’s measured by our group 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

S factor for 14 N(p,  ) 15 O ANC’s  14 N( 3 He,d) 15 O (d)  Rez/TAMU (27 MeV) (e)  TUNL (20 MeV) NRC to subthreshold state at E x = 6.79 MeV Subthreshold resonance width from Bertone, et al. R-Matrix fits to data from Schr ö der, et al.

S factor for 14 N(p,  ) 15 O C 2 (E x  6.79 MeV)  fm -1 [non-resonant capture to this state dominates S factor] S(0) = 1.40 ± 0.20 keV·b for E x  6.79 MeV S tot (0)  1.70 ± 0.22 keV·b

S factor dominated by direct capture to the subthreshold state Contribution from the tail of the subthreshold resonance: is negligible New reaction rate at.007 < T 9 < 0.1 lower (up to 2) than NACRE. (Impacts stellar luminosity at transition period to red giants and ages of globular clusters.) S factor for 14 N(p,  ) 15 O  width is small 

S factor for 20 Ne(p,  ) 21 Na Ne - Na cycle reaction Subthreshold state dominates rate 2s 1/2 at E x = MeV,  =7.1± 0.6 keV

Experimental results and DWBA analysis 20 Ne( 3 He,d) 21 Na

present work C. Rolfs and W. S. Rodney, NPA 241, 460 (1975) Higher reaction rate for increases the abundance of and, correspondingly, the number of neutrons from    fitting parameter; new measurement would help! For subthreshold resonance (dashed line)

ANC’s measured by our group 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] {ORNL (TAMU collaborator)} beams  MeV/u

13 N(p,  ) 14 O D.Decrock et al., PRC48, 2057(1993)

ANC’s for 13 N + p  14 O reaction: 14 N( 13 N, 14 O) 13 C K500: 13 C beam  195 MeV MARS: 13 N beam  153 MeV

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

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,

Transition from CNO to HCNO 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

ANC’s measured by our group stable beams (mirror symmetry) 7 Be + p  8 B [ 13 C( 7 Li, 8 Li) 12 C] 22 Mg + p  23 Al [ 13 C( 22 Ne, 23 Ne) 12 C] [underway now]

ANC’s for 7 Be + p  8 B from mirror reaction 13 C( 7 Li, 8 Li) 12 C separate p 1/2 and p 3/2 Fits  ANC’s 7 Li + n   Li: C 2 (p 3/2 ) =.384±.038 fm -1 C 2 (p 1/2 ) =.048±.006 fm -1  7 Be + p   B: C 2 (p 3/2 ) =.405±.041 fm -1 C 2 (p 1/2 ) =.050±.006 fm -1 p 1/2 p 3/2 S 17 (0) = 17.6±1.7 eVb

Collaborators TAMU: A. Azhari, H. Clark, C. Gagliardi, Y.-W. Lui, A. Sattarov, X. Tang, L. Trache, A. Zhanov INP (Czech Republic): V. Burjan, J. Cepjek, V. Kroha, J. Piskor, J. Vincour IAP (Romania): F. Carstoiu

TAMU Upgrade Plans Further develop RIB capability Produce accelerated RIB’s at intermediate energies [white paper at

TAMU Upgrade Plans Stage I - commission K150(88”) cyclotron - ECR source injection - commission beam lines to existing apparatus Stage II - isotope production stations completed - production of rare isotopes Stage III - K500 acceleration of rare isotope beams

Proposed Layout

TAMU Upgrade Stage I – Performance K150 beams IsotopeEI EI MeV/upApA pApA p Ne263 d Ne He S He Ar Li Ca Li Co B Kr B Kr O Xe (Simultaneous operation of K150 and K500 into different experimental areas.)

TAMU Upgrade Stage II and III Couple IG (light ion beams) and HI target stations to K150 Complete 1 +  n + ECR source Begin Rare Ion production

TAMU Upgrade Stage III Performance Ion Guide (heavy ions) into K500 Isotope Max. EnergyIntensity Mev/upps 9 Li453 x Be455 x S365 x S262 x Ar397 x Fe384 x B8B702 x O631 x Mg576 x P622 x Ga474 x Ga452 x 10 4 neutron-rich isotopes proton-rich isotopes

TAMU Upgrade Plans Cost  $4 M Proposal submitted - 12/1/03 Time line  2 years for stage I - II  2 more years for completion and first experiment

Check for Peripheral Transfer d  /d  as function of radial cutoff localization of angular momentum transfer vary r and a in Wood-Saxon well i.e.  vary b

30  cm (deg) d  /d  ( mb/sr ) 3/2 -, 6.18 MeV 30  cm (deg) d  /d  ( mb/sr ) /2 -, 0.0 MeV 14 N( 3 He,d) 15 O

Fates of Massive Pop III Stars G 33 H G pp-I,II,III H G CNO, rp Collapse Black Hole Explode Metallicity=(X A /X H )/(X A /X H ) sun 3   sufficient 12 C for M < 5x10 5 M sun metallicity(Z)  5x10 -5 to explode

Updated Reaction Sequences in Pop III Stars Rap-I,II and III, substitution for 3  and CNO! (Wiescher et al., 1989)

Asymptotic Normalization Constant Both tails dominated by Coulomb interaction->same solution ANC describes the absolute magnitude of the tail of the overlap function and is determined by the complicated internal n-n interaction b lj, obtained with potential model, strongly depends on geometric parameters

Recent Results for proton capture S-factors from measurements of Asymptotic Normalization Coefficients R. Tribble Texas A&M University OMEG03 November, 2003