1. α - capture reactions using the 4π γ-summing technique Α. Lagoyannis Institute of Nuclear Physics, N.C.S.R. “Demokritos”

2. 1.The problem 2.Ways of coping with the problem 3.The 4π γ - summing technique 4.Results 5.Conclusions Outline

3. - + Pathways for heavy-element nucleosynthesis   100 yr   10 8 n/cm 3   1 sec   10 20 n/cm 3

4. S. Galanopoulos et al., Phys. Rev. C 67, 015801 (2003) Woosley and Howard, Ap. J. Suppl. 36, 285 (1978) S. Goriely et al., A&A 375, 35 (2001) abundances p nuclei and p-nuclei abundances

5. Initial “stellar” conditions Key reactions 22 Ne( ,n) 25 Mg 12 C( ,  ) 16 O ………… seed abundances s process Reaction network p-nuclei abundances p process Almost 2000 nuclei are involved in this network powered by more than 20000 reactions ( ,n), ( ,p), ( ,  ), n-, p-,  -captures,  -decays, e-captures  a huge number of cross sections have to be known HAUSER-FESHBACH THEORY is required ! Reaction network HAUSER-FESHBACH THEORY Optical Model Potentials - Nuclear Level Densities γ-ray strength functions - Masses (32≤Z≤83, 36≤N≤131) NEED FOR GLOBAL MODELS OF OMP, NLD, …

6. CN reaction: a + A  C *  B * + b entrance channel α exit channel β TRANSMISSION COEFFICIENTS When CN is excited to “continuum”then Ts have to be averaged Nuclear Level Density (NLD) γ Emission is described by the Giant Dipole Resonance γ-ray strength functions Ts are calculated by γ-ray strength functions Optical Model Potentials (OMP) Particle emission Ts are calculated by Optical Model Potentials (OMP) Cross section calculations using the HF theory

7. Input parameters in HF calculations up to 2 orders of magnitude up to 40%3-5 %

8. r:= max. / min. M. Arnould and S. Goriely, Phys. Rep. 384, 1 (2003) n captures p captures α captures A≈100 A≈180 obtained with 14 different sets of nuclear ingredients (OMP, NLD, …) in HF calculations. Demetriou, Grama, Goriely, Nucl. Phys. A 707, 253 (2002) Impact of nuclear physics uncertainties on p-nuclei abundances

9. charged-particle induced reactions reaction barrier (MeV) E 0 (keV) T (K) p + p (sun) 0.555.91.5×10 7  + 12 C (red giants) 300561.5×10 8 12 C + 12 C (massive stars) 10.441500≈ 1×10 9 p + 74 Se (p process) 7.92800≈ 3×10 9 (p,γ) reactions: E CM = 1 – 5 MeV (α,γ) reactions: E CM = 6–12 MeV Gamow peaks and windows: the astrophysically relevant energies OUR GOAL To measure the cross section σ at these energy regions

10. Direct experimental techniques ActivationAngular Distribution 4π γ – summing method

11. MINIBALL @ IKP/Cologne γ angular distribution measurements: the (α,γ) problem (p,γ) reactions: E CM = 1 – 5 MeV, σ = 1 μb ÷ 1 mb (α,γ) reactions: E CM = 6–12 MeV, σ = 0.1 ÷100 μb (p,γ) reactions: NO PROBLEM TO MEASURE (α,γ) reactions: MAJOR PROBLEMS WITH BEAM-INDUCED BACKGROUND

12. The 4π γ-summing method: The principle

13. The 4π γ-summing method: The setup @ DTL-Bochum@ INP-Demokritos

14. 12 C(α,α) 12 C NaI + n 27 Αl(n,γ) 28 Al α + 92 Μο beam-induced bgd sum peak sum peaks 10.6 E α =11 MeV 10.2 9.8 92 Mo(α,γ) 96 Ru Ε α = 6 – 12 MeV ξ=398 μgr/cm 2 Solutions (up to now): Theoretical calculations Simulation No “real” experimental solution The 4π γ-summing method: The 92 Mo(α,γ) 96 Ru example   =(Y/  )*(1/  )*(A/N A ) BUT  =ƒ(E,M)

15. pos. a pos. b pos. c The 4π γ-summing method: Efficiency calculation I in/out ratios: M=1  R = 2 M=2  R = 2 × 2 = 4 M=3  R = 2 × 2 × 2 = 8 M=4  R = 2 × 2 × 2 × 2 = 16

16. The 4π γ-summing method: Efficiency calculation II ε 0, α and b vary for even-even, odd-even and odd-odd compound nucleus 12 odd-odd compound nucleus even-even compound nucleus odd-even compound nucleus

17. The 4π γ-summing method: Efficiency check with known reactions

18. (α,γ) results: Comparison with theory Proposed reactions: 68 Zn(α,γ) 72 Ge 86 Sr(α,γ) 90 Zr 90 Zr(α,γ) 94 Mo 94 Mo(α,γ) 98 Ru 116 Sn(α,γ) 120 Te

19. Imag. part W : Woods-Saxon type Volume + Surface Volume + Surface (ratio, damping C) geometry: r W, a W Fermi-type energy dependence of imaginary potential depth fitted to el. scattering + reaction data at E< 20 MeV U = V c + V + iW + ΔV Real part V : double-folding method effective NN interaction: M3Y -density dependent (Kobos et al, 1984) projectile density: n/p densities from elastic scattering data target density: Hartree-Fock theory Correction ∆V : dispersive relations Nucl. Phys. A. 707, 253 (2002) DG 2 : a global α – optical model potential

20. Alpha-particle capture reaction cross-section systematics (α,γ) cross section data: 10 isotopes Summary The global  -potential of Demetriou, Grama, Goriely seems to be working well in mass region A ≤ 100. However very few data exist in higher mass regions where uncertainties are large. But from experimental point of view such measurements are very challenging: need high current α beams + target development + efficient γ - arrays. Perspectives: Explore the unstable mass regions using RIB’s