Fusion of light halo nuclei

1. Fusion of light halo nuclei • Alinka Lépine-Szily • Instituto de Física-Universidade de São Paulo, São Paulo, Brazil 18th International Conference on Few-Body Problems in Physics, 21-25 august 2006 - Santos, Brazil 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

2. 1)Nuclear Fusion : Barrier Penetration Model, • couplings • 2) Halo nuclei: reduction of barrier, break-up • 3) Effect of halo on fusion and break-up • 4)Continuum Discretized Coupled Channels Calc. • 5)Comparison with experiments 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

3. Fusion of two atomic nuclei: quantum mechanical tunneling phenomenon. Barrier Penetration Model (BPM) works surprisingly well.

4. Stokstad et al, PRL 41 (1978) 465 • Leigh et al, PRC 52 (1995) 3151 • M. Beckerman et al, PRL 45 (1980) 1472 For energies below the Coulomb barrier: Increase in fusion cross section (F) over the BPM result. Decrease in the height of the barrier VN(R)+VC(R) -> coupling to deformations, vibrations, transfer channels or soft dipole resonances .......... Barrier Penetration model without couplings

5. “halo” nuclei 19 C n 18 C Section efficace (u.a.) 18 C 10 15 30 35 0 5 20 0 25 Angle Neutron (deg.) 11Li Nuclear chart and halo nuclei close to the drip-line Surprises Z Number of neutrons

6. Halo nuclei Borromean nature of 2n halo nuclei

7. core of 9Li 2 neutron halo 4 fm 11Li 16 fm Halo Nuclei 11Li9Li+2n 11Be10Be+n S2n = 0.33 MeV T1/2= 8.5 ms T. Nakamura etal. PRL 96, 252502 (2006) 11Li has strong E1 strength at 0.6 MeV, strong two-neutron correlation, <rc,2n2>1/2= 5.01(32)fm , <12> = 48(16)

8. Density distribution Nuclear+Coulomb Potential S2n(6He) = 0.98 MeV T1/2 = 806.7 ms S2n(8He) = 2.14 MeV T1/2 = 119 ms

9. Neutron halo Projectiles : 11Li, 11Be, 6He etc 6He ou Due to the neutron halo the strong force begins to act at larger distances the barrier is lower: an increase is predicted in the fusion probability V r

10. Fusion with “halo” nucleus

11. Fusion with “halo” nuclei couplings: additional degrees of freedom, that can increase the fusion - Strong low-lying E1 strength in halo projectiles (different spatial distribution of protons and neutrons) reduction in the height of the barrier: an increase is predicted in the fusion probability Break-up of the weakly bound halo projectile : CONFLICTING theoretical predictions about the effect of break-up on fusion: - break-up favours the fusion (treats break-up as an additional channel)Dasso, Vitturi Phys.Rev.C50(1994)R12 - break-up inhibits the fusion (incident flux is reduced) Hussein, Pato, Canto,Donangelo Phys. Rev. C46(1992)377

12. Fusion and Break-up of weakly bound halo nuclei 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs Break-up = coupling to the continuum, irreversible,

13. Comparison of break-up, fusion and total reaction cross section for 6Li + 64Zn (6Li stable weakly bound) Gomes PLB 601(2204)20 Comparison of break-up, fusion and total reaction cross section for 9Be + 144Sm (9Be stable weakly bound) R= CF + BU + ICF Gomes et al PLB 634(2006)356 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs Conclusion: for E<VCB break-up is much more probable than fusion. BU of halo nuclei > BU of stable nuclei for Coulomb break-up

14. ContinuumCContinuum • Continuum Discretized Coupled Channels • Calculation (CDCC) • Since the weakly bound nuclei break-up, it is necessary to include at least 3 body effects in the description of the collision. • The continuum must be considered. One has to truncate the number of states (CDCC). • CDCC calculations describing the break-up of the projectile P are performed replacing the continuum by a finite number of configurations of the P = F1 + F2 system. • CDCC calculations require the inclusion of both Coulomb and nuclear couplings, a large set of continuum states and multi-step processes. 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

15. Schematic representation of bound and continuum states and their couplings in CDCC calculations Schematic 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs Full lines: Hagino 2000. Dashed lines: additional couplings by Diaz-Torres and Thompson 2002

16. Full CDCC calculation for 11Be + 208Pb Diaz-Torres, Thompson- PRC65 (2002), 024606 • Complete fusion (solid) • only couplings to bound states b) complete fusion (solid) also continuum – continuum couplings are included 1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

17. Comparison of CDCC calculations for 6He+12C at 18MeV using 3 body nuclear break-up process (4He+dineutron+12C) with 4 body description (4He+n+n+12C) . The 4-body CDCC calculation takes the Borromean nature of 6He explicitly into account. The 4-body calculation reproduces well the total reaction cross section. Conclusion: 4-body CDCC calculation yields higher reaction cross section by 8%, than the 3-body calculation for light targets. Matsumoto and Kamimura et al Phys. Rev. C 70, 061601(R) (2004) PhysIcs

18. Experimental results on fusion of neutron halo projectiles with heavy targets --M. Trotta et al PRL 84 (2000) 2342 compared 4,6He + 238U fusion cross sections and found enhancement --J.J.Kolata et al P. R. L. 81 (1998) 4580 compared 4,6 He + 209 Bi fusion cross sections and found enhancement for the 6He halo nucleus --C.Signorini et al Nucl. Phys. A735 (2004)329 compared 9,10,11 Be + 209 Bi fusion cross sections and found no enhancement for the 11Be halo nucleus

19. 6He + 238U experiment in Louvain-la Neuve Fission as signature • Experiments in Louvain-la-NeuveBeam intensity of 6He 106 – 107 pps • 238U target 500 μg/cm2 • Detection of back-to-back fission fragments in an array of Si detectors (angular coverageabout 70% of 4π) • Fission induced by transfer or inelasticexcitation channels: a quasi-projectile particleis detected in coincidence

20. 6He + 238U in Louvain-la-Neuve Transfer and fusion 2 fission fragments and a 3rd particle in coincidence. Angular distribution and energy spectrum indicates the direct transfer of 2n. 238U(6He,4He)240U Q (transferencia) = +9.76 MeV E*(240U) >20MeV  fissão DWBA calculation with FRESCO including the continuum

21. No enhancementof the fusion cross section R. Raabe et al, Nature, 431 (2004) 823

22. Conclusions • The additional degrees of freedom in the halo nuclei 6He and 11Be enhance the break-up and reaction cross section on heavy and medium mass targets at energies around and below the potential barrier. • The results on Fusion are still controversial: The additional degrees of freedom in the halo nuclei do not enhance the fusion cross section for 6He + 238U and 11Be + 209Bi , while the 6He + 209Bi seems to exhibit some enhancement at energies around and below the potential barrier.

23. Outlook : more experimental data on fusion and break-up of halo nuclei is needed theory has to take into account Coulomb and nuclear interaction, Borromean nature (3-4 body problem),coupling to and into the continuum RIBRAS (Radioactive Ion Beams Brasil) installed in the Pelletron Laboratory of IF - USP allows the study of this kind of experiments