Fusion of light halo nuclei

Alinka Lépine-Szily

Instituto de Física-Universidade de São Paulo, São Paulo, Brazil

1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs 18th International Conference on Few-Body Problems in Physics, 21-25 august 2006 - Santos, Brazil

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

Fusion of two atomic nuclei: quantum mechanical tunneling phenomenon.

Barrier Penetration Model (BPM) works surprisingly well.

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

Surprises

1111LiLi1111LiLi

19C

18C

0 5 10 15 20 Angle Neutron (deg.)

Secti

on

eff

icace (u

.a.)

n 18C

0 25 30 35

“ “halo” nucleihalo” nuclei “ “halo” nucleihalo” nuclei

Number of neutronsNumber of neutrons

Nuclear chart and halo nuclei close to the drip-line

Z

Halo nuclei

Borromean nature of 2n halo nuclei

 11Li9Li+2n 

11Be10Be+n

Halo Nuclei

4 fm

16 fm

11Li

core of 9Li2 neutron halo

T. Nakamura etal. PRL 96, 252502 (2006) 11Li has strong E1 strength at 0.6 MeV, strong two-neutron correlation, <rc,2n

2>1/2 = 5.01(32)fm , <12> = 48(16)

S2n = 0.33 MeVT1/2= 8.5 ms

Density distribution Nuclear+Coulomb Potential

S2n(6He) = 0.98 MeV T1/2 = 806.7 msS2n(8He) = 2.14 MeV T1/2 = 119 ms

Neutron halo Projectiles : 11Li, 11Be, 6He etc

ou 6He

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

r

V

Fusion with “halo” nucleus

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

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

C N

T1

2

D C F

T1

C N22

IC F 1

T2

1C N

1IC F 2

T1

2T

1

2C N

T1

2

A C N < A P+ A T

A C N = A P + A T

B -U p

T1

2

E la stic B reak u p

T1

2A C N = A P+ A T

S C F

IC F

C F

D C F

Break-up = coupling to the continuum, irreversible,

1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

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

Conclusion: for E<VCB break-up is much more probable than fusion.BU of halo nuclei > BU of stable nucleifor Coulomb break-up

1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

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

Schematic representation of bound and continuum states and their couplings in CDCC calculations

Full lines: Hagino 2000.

Dashed lines: additional couplings by Diaz-Torres and Thompson 2002

1111118th 118th Intn Few-Body Problems in PhysIcs 8th International IUPAP Conference on Few-Body Problems in PhysIcs

Full CDCC calculation for 11Be + 208Pb Diaz-Torres, Thompson- PRC65 (2002), 024606

a) Complete fusion (solid)

only couplings to bound states

b) complete fusion (solid)also continuum –continuum couplings are included

PhysIcs

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 alPhys. Rev. C 70, 061601(R) (2004)

Experimental results on fusion of neutron halo projectiles with heavy targets

--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

--M. Trotta et al PRL 84 (2000) 2342 compared 4,6He + 238U fusion cross sections and found enhancement

Fission as signature

6He + 238U experiment in Louvain-la Neuve

• 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 coverage about 70% of 4π)

• Fission induced by transfer or inelasticexcitation channels: a quasi-projectile particle is detected in coincidence

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)240UQ (transferencia) = +9.76 MeVE*(240U) >20MeV fissão

DWBA calculation with FRESCO including the continuum

R. Raabe et al, Nature, 431 (2004) 823

No enhancementof the fusion cross section

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.

RIBRAS (Radioactive Ion Beams Brasil) installed in the Pelletron Laboratory of IF - USP allows the study of this kind of experiments

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