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 Santos, Brazil
th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

2. couplings 1)Nuclear Fusion : Barrier Penetration Model,
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
th 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. 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
Stokstad et al, PRL 41 (1978) 465
Leigh et al, PRC 52 (1995) 3151
M. Beckerman et al, PRL 45 (1980) 1472
Barrier Penetration model
without couplings

5. Surprises Nuclear chart and halo nuclei close to the drip-line19 C 18 5 10 15 20
Angle Neutron (deg.)
Section efficace (u.a.) n 25 30 35
“halo” nuclei Z
11Li
Number of neutrons

6. Halo nuclei
Borromean nature of 2n halo nuclei

7. Halo Nuclei 11Li core of 9Li 2 neutron halo 11Be10Be+n S2n = 0.33 MeV
 11Li9Li+2n
11Be10Be+n
4 fm
16 fm
11Li
core of 9Li
2 neutron halo
S2n = 0.33 MeV
T1/2= 8.5 ms
T. Nakamura etal. PRL 96, (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. Nuclear+Coulomb Potential
Density distribution
Nuclear+Coulomb Potential
S2n(6He) = 0.98 MeV T1/2 = 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
th 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
th 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. Continuum Discretized Coupled Channels Calculation (CDCC)
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.
th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

15. Schematic Schematic representation of bound and
continuum states and their couplings in
CDCC calculations
Schematic
th 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),
Complete fusion (solid)
only couplings to bound states
b) complete fusion
(solid)
also continuum –
continuum couplings
are included
th 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, (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 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 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-Neuve Beam 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 coverage about 70% of 4π)
Fission induced by transfer or inelastic excitation channels: a quasi-projectile particle is 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) = MeV
E*(240U) >20MeV  fissão
DWBA calculation with FRESCO including the continuum

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

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