Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil

1. Why the complete fusion of weakly bound nuclei is enhanced at sub-barrier energies and suppressed above the barrier. Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil NN2012- San Antonio, May 27th-June 1st (2012)

2. Reactions with weakly bound nuclei

3. However, nature is more complicated than that simple picture: Breakup following transfer n p RESULTS after before measured measured known calculated by p conservation Courtesy of Luong

4. See talk by Nanda Dasgupta next Friday

5. Frequently used procedures to answer “Enhancement or suppression in relation to what? • Comparison of data with theoretical predictions. b) Comparison of data for weakly and tightly bound systems.

6. Effects to be considered • Static effects: longer tail of the optical potential arising from the weakly bound nucleons. • Dynamical effects: strong coupling between the elastic channel and the continuum states representing the break-up channel.

8. Example: 6He + 209Bi Single channel - no halo Single channel – with halo CC with bound channels (schematic calculation) • Shortcomings of the procedure: • Choice of interaction plays fundamental role • Does not allow comparisons of different systems • Difficult to include continuum – no separate CF and ICF

9. Conclusions about static effects of halo nuclei. • Fusion enhancement when compared with what it should be without halo properties. • There is no more discussion left about that.

10. Differences due to static effects:

11. Fusion functions F(x) (our reduction method) Inspired in Wong’s approximation F0(x) = Universal Fusion Function (UFF) system independent !

12. Direct use of the reduction method Refining the method Eliminate the failure of the Wong model for light systems at sub-barrier energies

13. Applications with weakly bound systems Canto, Gomes, Lubian, Chamon, Crema, J.Phys. G36 (2009) 015109; NPA 821(2009)51 Gomes, , Lubian, Canto, PRC 79 (2009) 027606 Gomes, Canto, Lubian, Hussein, PLB 695 (2011), 320

14. Use of UFF for investigating the role of BU dynamical effects on the total fusion of heavy weakly bound systems No effect above the barrier- large enhancement below the barrier

15. Use of UFF for investigating the role of BU dynamical effects on the total fusion of very light weakly bound systems No effect above the barrier- almost no data below the barrier

16. Use of UFF for investigating the role of BU dynamical effects on the total fusion of light weakly bound systems No effect above the barrier- no data below the barrier

17. Use of UFF for investigating the role of BU dynamical effects on the complete fusion of stable weakly bound heavy systems We did not include any resonance of the projectiles in CCC. Suppression above the barrier- enhancement below the barrier

18. Fusion of neutron halo 6,8He, 11Be weakly bound systems

19. Conclusion from the systematic (several systems) : CF enhancement at sub-barrier energies and suppression above the barrier, when compared with what it should be without any dynamical effect due to breakup and transfer channels. Question: Why?

20. Example for Complete fusion of 6,7Li + 209Bi Effects of suppression and enhancement are more important for 6Li than for 7Li. (6Li has smaller BU threshold energy and no bound state)

21. Approaches which might be used • Coupled channel calculations (CDCC calculations including transfer channels and sequential breakup) – not available so far • Dynamic polarization potential (substitutes many channels by one single channel – energy dependent optical potential.

22. Suppression of fusion above the barrier

23. Threshold anomaly in the elastic scattering of tightly bound systems • Optical Potencial : U(E) = V0 + ∆V(E) + W(E) where W(E) = WV (E) + WS (E) Tenreiro et al – PRC 53 (1996), 2870

24. The Threshold Anomaly for “normal systems “ • As the energy decreases towards the barrier, reaction channels close and the imaginary potential decreases and vanishes. • Due to the dispersion relation, the real potential increases when the imaginary potential decreases. The attraction increases (attractive polarization potential) and consequently there is sub-barrier fusion enhancement. • Polarization potentials associated with couplings to transfer and inelastic channels were shown to be attractive

25. A new type of threshold anomaly: break-up thereshold anomaly (BTA) Gomes et al – J Phys G 31 (2005), S1669 The large NCBUat low energies produces a repulsive polarization potential and suppress fusion.

26. The behavior for weakly bound systems • The breakup is important even below the barrier. So, the imaginary potential does not decrease at the barrier energy. Indeed, it can increase. • Consequently, the real potential decreases at this energy region. Fusion is suppressed. • This behavior is called ‘breakup threshold anomaly’ (BTA). • Of course, the imaginary potential must decrease and vanish at lower energies (we will discuss this point later).

27. BTA M.S. Hussein, P.R.S. Gomes, J. Lubian, L.C. Chamon – PRC 73 (2006) 044610

28. Systems with 6Li Gomes et al JPG 31 (2005) S1669 Hussein et al., PRC 73 (2006) 044610 Keeley et al., NPA571 (1994) 326 Figueira et al. – PRC 75 (2007), 017602 6Li + 116Sn 6Li + 144Sm Figueira et al. – PRC 81 (2010), 024603 Deshmukh et al. PRC 83, 024607 (2011) A. Gomez-Camacho et al., NPA 833 (2010), 156

29. More Systems with 6Li Souza – PRC75, 044601 (2007) Biswas- NPA 802, 67 (2008) Biswas- NPA 802, 67 (2008) 6Li + 209Bi 6Li + 90Zr 6Li + 64Zn Zadro, di Pietro- PRC 80, 064610 (2009) Santra – PRC83, 034616 (2011) Kunawat – PRC 78, 044617 (2008)

30. Systems with 7Li Pakou PRC 69, 054602 (2004) Souza – PRC75, 044601 (2007) Gomes JPG 31 (2005) S1669 7Li + 27Al 7Li + 116Sn Deshmukh et al, accepted EPJA Lubian- PRC 64, 027601 (2001) Figueira – PRC 73, 054603 (2006)

31. Systems with 9Be 9be + 208Pb Gomes JPG 31 (2005) S1669 Woolliscroft – PRC 69, 044612 (2003) 9Be + 144Sm Signorini –PRC 61, 061603R (2000) Gomes – NPA 828, 233 (2009) Gomes- PRC70, 054605 (2004)

32. Systems with radioactive nuclei 6He + 209Bi A. Gomez-Camacho et al., NPA 833 (2010), 156 Garcia, Lubian – PRC 76, 067603 (2007) A. Gomez-Camacho et al., NPA 833 (2010), 156

33. Calculations of DPP considering direct breakup : repulsive DPP 8B + 58Ni – Lubian 6Li + 209Bi - Santra 7LI + 27Al - Lubian

34. QE barrier distributions BU enhances the Coulomb barrier J. Lubian, T. Correa, P.R.S. Gomes, L. F. Canto – PRC 78 (2008) 064615

35. Conclusions • The effect of the coupling to BU was shown to come from the repulsive DPP they provoke. It hinders the CF cross sections. • The BU channel increases the barrier as shown in the QE barrier distributions. This leads to the hindrance of the fusion cross section

36. What about the enhancement of CF at sub-barrier energies? • We have to look at the low energies for the elastic scattering: The DPP becomes attractive at low energies (below the barrier) Why?

37. At sub-barrier energies, the breakup following transfer predominates over the direct breakup. Each one of them has different DPP: direct BU produces repulsive DPP. BU after transfer produces attractive DPP. The total DPP is attractive 7Li + 144Sm Otomar 2012 Sequential BU Direct BU

38. Conclusions • Direct breakup produces repulsive polarization potential which suppress fusion at energies above the barrier. • At sub-barrier energies, the breakup following transfer predominates and produces attractive polarization potential which enhances fusion. • More quantitative calculations are required (CDCC calculations including transfer and BU following transfer)

39. Collaborators J. Lubian. R. Linares (UFF), L. F. Canto (UFRJ), M.S. Hussein (USP), M. Dasgupta, D. J. Hinde, D.H. Luong (ANU)