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

Nuclear and Coulomb breakup of 6 Li at near barrier energies, their interferences and their effect on fusion. Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil. Reactions with weakly bound nuclei – example with 9 Be. Things are much more complicated than that. Sequential BU.

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

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  1. Nuclear and Coulomb breakup of 6Li at near barrier energies, their interferences and their effect on fusion Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil

  2. Reactions with weakly bound nuclei – example with 9Be

  3. Things are much more complicated than that. Sequential BU. Nanda’s talk.

  4. 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

  5. Breakup time scale Only prompt breakup may affect fusion

  6. Questions that we investigate and try to answer -Does the BU channel enhance orsuppress the fusion cross section? Is the effect on σCForσTF= CF + ICF? -What are the effects on different energy regimes and on different target mass regions? • Whatistherelativeimportancebetween nuclear and Coulomb breakups? Do theyinterfer ? • HowlargeistheNCBU compared with CF ? How does it depend on the energy region and target mass?

  7. Different answers, depending on several things

  8. Kolata et al., PRL 81, 4580 (1998) Gomes et al., PLB 695, 320 (2011) Example of Model Dependent Conclusions

  9. Old controversy between Kolata`s and Raabe`s data (6He + 209Bi and 238U) Important:Bare Potential deduced from double-folding procedure

  10. Systematics reached from the investigation of he role of BU dynamical effects on the complete and total fusion of stable weakly bound heavy systems , para cada um destes físicos, , para cada um destes físicos, We did not include any resonance of the projectiles in CCC. Suppression above the barrier- enhancement below the barrier

  11. Same as before, but with new data (ANU) for 9Be + 209Bi

  12. Systematics reached from investigation of the role of BU dynamical effects on fusion of neutron halo 6He, 11Be weakly bound systems Suppression above the barrier- enhancement below the barrier

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

  14. Do all the systems follow the systematics? If not, either a) There is something very special with those systems. b) There is something wrong with the data. c) Wrong CC calculations

  15. Examples

  16. Indeed, there are some new data (di Pietro et al) for this system Di Pietro – PRC 87, 064614 (2013) Sargsyan PRC 88, 044606 (2013)

  17. Measurements of 6,7Li + 64Zn E > VB ToF σTF = σCF + ICF I. Padron et al; PRC66 (2002),044608

  18. Analyses in the original papers Beck et al. (2003) Gomes, Padron (2004, 2005)

  19. Controversy on 6He + 206Pb fusion Lukyanov PLB 670, 321 (2009) Wolski- EPJA 47, 111 (2011) How are the fusion functions?

  20. Transfer effect on sub-barrier fusion fucntion Shorto PRC (2010)

  21. Conclusion from the systematics (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? Possible answer: read P.R.S. Gomes et al., J. Phys. G 39, 115103(2012)

  22. What about proton-halo systems?Up to recently, there was only one system measured • Fusion of proton-halo 8B + 58Ni (Aguilera PRL 107, 092701 (2011)

  23. Fusion of proton-halo 8B + 58Ni New dynamic effect for proton-halo fusion? Or Something wrong with the data?

  24. Some details of Aguilera’s derivation of fusion cross section Fusion cross section was obtained by measuring proton multiplicities. It was assumed that all protons detected at backward angles come from fusion evaporation, and no protons from breakup reach the detectors, based on CDCC calculations by Tostevin-Nunes-Thompson. However, see what happens for 6,7Li at sub-barrier energies (measurements at ANU (Canberra). They measured NCBU by detecting charged fragments at backward angles.

  25. Other recent result: Fusion of 8B + 28Si Pakou et al. PRC 87, 014619 (2013) Measurements at Legnaro. Fusion cross sections derived from alpha measurements (there is no alpha from BU) Normal behavior, within our systematic!!!

  26. Calculations by Tostevin, Nunes and Thompson used by Aguilera to say that no breakup protons reach the detectors placed at backward angles (PRC 63, 024617 (2001)) Does it go to zero at backward angles?

  27. Tostevin extended the calculations up to 180 degrees (for us) It does not vanish at large angles!!!!

  28. Furthermore, see the proton spectra and Tostevin calculations Prediction for BU protons at Elab = 25.8 MeV (Tostevin) Experimental “evaporation” protons at Elab = 22.4 MeV (Aguilera) Rangel et al., EPJA 49, 57 (2013) How can one separate experimentally protons from fusion and breakup?

  29. We believe that there is nothing special with fusion of proton-halo nuclei

  30. So, the next question is: How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups: Is there interference between them? One believes that the BU depends on the target mass (charge).

  31. Effect of the 6Li BU on CF cross sections Pradhan – PRC 83, 064606 (2011) Kumawat – PRC 86, 024607 (2012) The BU effect on fusion does not seem to depend on the target charge!!!!

  32. References: D. R. Otomar, P.R.S. Gomes, J. Lubian, L.F. Canto, M. S. Hussein PRC 87, 014615 (2013) M.S. Hussein, P.R.S. Gomes, J. Lubian, D.R. Otomar, L. F. Canto PRC 88, 047601 (2013)

  33. Ourfirsttheoreticalstepwastoperformreliable CDCC calculations.What do wemeanbyreliable? No freeparameters, onlypredictions. The predictionshavetoagreewith some data.Which data are available? Elasticscattering angular distributions.

  34. Examplesofcalculations for elasticscattering 6Li + 59Co 6Li + 144Sm 6Li + 208Pb

  35. A few words about the CDCC calculations performed by Otomar and Lubian • -6Li breaks upinto alpha + deuteron. We use the cluster model. • Calculationsperformedwith FRESCO. • Projectile-targetinteraction: • Continuumstatesof6Li are discretized. • The interactionbetweendeuteronand alpha cluster within6Li isgivenby a Woods-Saxonpotential. • The real partsofinteractions are givenbythe São Paulo potential. • The imaginarypartsoftheinteractions are representedby a short range fusionabsorption (IWBC). • The CDCC calculations include inelasticchannels.

  36. Relativeimportancebetween Coulomb and nuclear breakups Total BU – black Coulomb BU – red Nuclear BU - blue For higher energies and light targets, nuclear BU may predominate Small angles (large distances) – Coulomb BU always predominates For larger angles, nuclear BU may predominate – crossing angle.

  37. Interferencebetween Coulomb and nuclear breakups If there were were no interference, the last column should be unity.

  38. What is the relative importance between breakup and fusion cross sections?

  39. How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups? The nuclear BU increases linearly with AT 1/3 for the same E c.m./VB The Coulomb BU increases linearly with ZT for the same Ec.m./VB

  40. Suppression of the Coulomb-Nuclear BU interference peak in the elastic scattering Di Pietro Keeley- PRC82, 034606 (2010)

  41. See Alexis`s talk

  42. Conclusions The relative importance between nuclear and Coulomb breakups is not so simple as it is usually thought. There is a strong destructive interference between nuclear and Coulomb breakup. When one calculates BU cross sections with CDCC, one does not distinguish prompt and delayed BU. Most of the BU seems to be delayed and only the prompt BU affects fusion.

  43. Why does the Coulomb breakupbehavelikethat? 1- The electromagnetic coupling matrix-elements are proportional to ZT, which should lead to a ZT2 dependence, whereas the cross sections are proportional to 1/E. 2- Since the collision energy corresponds to the same E/VB ratio and VB is proportional to ZT, one gets a 1/ ZT factor. 3- From (1) and (2) we get a linear dependence on ZT.

  44. Why does the nuclear breakup behave like that? (1) Wong formula for fusion X-section taken to be the total nuclear reaction X- section without BU. where Γ = ћ ω/ 2π (width of the barrier) and ΛC is the critical angular momentum for fusion.

  45. Why does the nuclear breakup behave like that? (2) The reaction X-section including nuclear BU but not Coulomb BU may be written as: The Coulomb BU is of long range and can not be described by the Wong formula.

  46. Why does the nuclear breakup behave like that? (3) The nuclear BU X- section is taken to be the difference This expression can be simplified by expanding in the lowest order of Δ / ΛC to give:

  47. Why does the nuclear breakup behave like that? (4) = P1 + P2 A T1/3 Where we have used and With a being the diffuseness of the nuclear surface. Clearly P1 = 2π a (1 – VB / E) RP and P2 = 2π a r0 (1 – VB / E)

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