Fusion and break-up of weakly bound nuclei

Paulo Roberto S. GomesIF- Universidade Federal Fluminense, Niterói, R.J

VI SLAFNAP - Iguazu, Argentina, October, 2005

For a comprehensive review of thissubject, read Physics Report

(in press)

The break up of weakly bound nuclei

Suitable stable and unstableweakly bound nuclei

6Li → 4He + d Sα = 1.48 MeV7Li → 4He + t Sα = 2.45 MeV9Be → 8Be + n → 4He + 4He + n Sn = 1.67 MeV

11Li → 9Li + 2n S2n = 0.33 MeV

6He → 4He + 2n S2n = 0.98 MeV

11Be → 10Be + n Sn = 0.50 MeV

Halo Nuclei

The Fusion X Break-up problem

We are dealing with weakly bound nuclei:

Stables: 6Li, 7Li, 9BeRadioactives: 6He, 11Be, 11Li, 17F..

•The full understanding of the fusion and break-up processes induced by stable weakly boundnuclei is an important reference for theinvestigation of similar systems involvingradioactive beams.

Motivation for the investigation of thebreak-up effect on the fusion cross section

• Study of correlations and couplings between reaction

mechanisms in heavy ion collisions.

• Does the break-up coupling to fusion enhance its

cross section or does the BU compete with fusion and

suppress it?

• Important for astrophysical processes and

production of super-heavy elements.

Exotic (halo) nuclei near the drip-line and SuperHeavy Nuclei (SHE)

Reactions with radioactive beams

Fusion with tightly bound nucleiabove the Coulomb barrier

As the energy increases, other reaction mechanisms compete with the fusion, that becomes limited or saturated.

Fusion with tightly bound nucleibelow the Coulomb barrier

-Important nuclear structure effects.

-Usual enhancement of the cross section, when comparedwith predictions from one dimensional barrier penetrationmodels.

Role of coupled channels in the sub-barrierfusion cross section enhancement

Inelastic couplings Inelastic and transfer couplings

Is is well stablished that inelastic excited states and transferchannels enhance the sub-barrier fusion cross section.

Where is the fusion decided?

There is controversy whether the Coulomb barrier shouldbe transposed (rf = 1.2 fm) or if the fusion is decided evenbefore the barrier is reached (rf = 1.5 fm).

P. Gomes et al; JP G23 (1997), 1315

Threshold anomaly in the elastic scattering

• Optical Potencial : U(E) = V0 + ∆V(E) + W(E)where W(E) = WV (E) + WS (E)

Tenreiro et al – PRC 53 (1996), 2870

Processes to be considered in reactionswith weakly bound nuclei

CN

T1

2

DCF

T1CN2

2

ICF 1

T2

1CN

1ICF 2

T1

2T

12

CN

T1

2

ACN < AP+AT

ACN = AP+AT

B-Up

T1

2

Elastic Breakup

T1

2ACN = AP+AT

SCF

ICF

CF

DCF

Processes to be considered in reactionswith weakly bound nuclei

Theoretical aspects to be considered

• Static effects: longer tail of the opticalpotential arising from the weakly boundnucleons.

• Dynamical effects: strong coupling betweenthe elastic channel and the continuum states representing the break-up channel.

→ strong influence on reaction channels, particularly on fusion cross section.

• Relative motion of the fragments and their interactions. What are their trajectoriesfollowing the BU? EBU, ICF, CF?

Usual questions

-Does the BU channel enhance or suppressthe fusion cross section? Is the effect on σCF or σTF= CF + ICF?

-What are the effects on different energy regimes and on different target mass regions?

- Different BU threshold energies should affect σBU

elastic significantly. Is that true for σCF or σCF + ICF?

Theoretical methods• Schematic models: dynamical polarizatizion

potential; semiclassical trajectories, survivalprobabilities.

• More realistic calculations: CDCC (continuum discretized coupled channel) calculations: Bound-continuum states couplings, with or without resonance states, discretized continuum states, continuum-continuum couplings.

CDCC• Since the weakly bound nuclei break-up, it is

necessary to include at least 3 body effects in thedescription of the collision.

• The continuum must be considered. One has to truncate the number of states (CDCC).

• CDCC calculations describing the break-up of theprojectile P are performed replacing the continuum by a finite number of configutrations of the P = F1 + F2 system.

• CDCC calculations require the inclusion of bothCoulomb and nuclear couplings, a large set ofcontinuum states and multi-step processes.

Schematic models• Takigawa 91: BU corresponds to a soft giant

resonance with infinite lifetime: coupling to this resonance leads to sub-barrier fusionenhancement.

• Hussein 92: take into account the decay of theresonance, coupling with elastic and BU channels. Nuclear BU only. CF

• Takigawa 93: take into account the real partof the DPP. TF

• Canto 95: take into account the Coulomb BU. The irreversibility of the BU process leads to suppression of CF. Survival probabilityconcept.

Different theoretical predictionsearly 90´s – 11Li + 208Pb

Hussein et al – PRC46 (1992), 377

Takigawa et al- PRC47 (1993),R2470

L.F. Canto et al; PRC52 (1995), R2848

Different theoretical predictionsearly 90´s – 11Li + 208Pb

Dasso and Vitturiconsidered elastic, soft mode and break-up channels andperformed usual CCC. The continuum is represented by a single channel. Theresults lead to fusionenhancement aboveand below thebarrier.

C. Dasso, A Vitturi –PRC50 (1994), R12

CDCC predictions – 11Be + 208Pb

•Continuum up to 2 MeV.

•Continuum-continuum couplings were neglected.

•Halo effect neglected.

The sub-barrier fusionenhancement is predominantly nuclear.

K. Hagino et al; PRC61 (2000), 037602

Full CDCC calculations – 11Be + 208Pb

The continuum-continuum coupling makesmore difficult for the projectilefragments to reunite andreconstruct boundstates (irreversibility) –see lower panel.

Diaz-Torres, Thompson- PRC65 (2002), 024606

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

Full lines: Hagino 2000. Dashed lines: additional couplingsby Diaz-Torres and Thompsom 2002

Difficulties with CDCC

• It does not calculate sequential CF.• Limited to 3 body (two fragments)• What are the bare potentials and form

factors to be used?• Very long computing time.

Experimental aspects to be considered

• What is it measured? σCF or σTF= CF + ICF?

• Can ICF be separated from transfer channels leading to the same compound nucleus?

• When one talks about enhancement or suppression, is that in relation to what?

Measurements of 6,7Li + 209Bi and 9Be + 208Pb

ANU 0.9VB ≤ E ≤ 1.7 VB

Yields of α particles (on-line and off-line)σCF, σ ICF and barrier distributions

M. Dasgupta et al; PRL82 (1999),1395 PRC66 (2002),041602R

Measurements of 6,7Li, 9Be + 64Zn, 27Al TANDAR

E > VBToF and E- ∆E σTF = σCF + ICF

I. Padron et al; PRC66 (2002),044608 R.M. Anjos et al; PLB534 (2002),45

Measurement of the inverse reaction 12C + 7LiANU E > VB

E-∆E multi-anodeσTF

A Mukherjee et al; PLB526 (2002), 295

Measurements of 9Be + 64Zn

USP E ≥ VB

Gamma rays (on-line and off-line)σCF σ ICF was found to be negligible.

S.B. Moraes et al; PRC61 (2000),064608

Measurements of 9Be + 144SmTandar

0.8VB ≤ E ≤ 1.4 VB Detection of X-K rays (off-line)

σCF, σICF

Gomes et al – BJP 35 (2005)

Measurements of elastic scattering of6,7Li, 9Be + 27Al, 64Zn, 138Ba

USP E ≥ VB

system of 9 SSB detectorsσR

Maciel et al; PRC 59 (1999), 2103

New radioactive beam facility at São Paulo: RIBRAS

Double solenoid NbTi, 6 TeslaReactions9Be (7Li, 6He) 20 < θ< 60 -105 p/s9Be (7Li, 8Li) 20 < θ< 60 -106 p/s3He (6Li, 7Be) ; 3He (6Li, 8B)

With LINAC (future): 10Be, 11C, 17F

Detector used at Louvain la Neuve for fusion-fission andtransfer-fission of the 6He + 238U system

(40 Si SBD – 70% of 4π – triple coincidences)

Raabe et al – Nature 431 (2004), 823 Trotta et al – PRL 84 (2000), 2342

Heavy Targets9Be + 208Pb

complete fusion cross section

M. Dasgupta et al – PRL 82 (1999), 1395

6,7Li + 209Bi, 9Be + 208Pb Complete fusion cross section suppression factor

as a function of the energy

M. Dasgupta et al – PRC 70 (2004), 024606

6,7Li + 209Bi and 9Be + 208Pbtotal fusion

(eventual transfer channels are included)(for 6,7Li + 209Bi , the data are lower limits at the highest energies)

Gomes et al;

BJP 34 (2004)

Those results agree with CCC and SBPM predictions

9Be + 144Sm : CF and ICFSuppression factor: 0.90

Gomes et al – subm to PLB

Conclusions for Heavy Targets

• The BU inhibits σCF at E > VB

• There is a suppression factor for CF at this regime, but the BU threshold energy differences are notvery much reflected in σCF

• σTF is not affected by the BU at E > VB

• σICF is important in the whole energy range.• At E ≤ VB, the situation is not so clear, as there is

competition between enhancement of CF due to couplings and suppression due to the BU.

Systems involving radioactive nuclei: 6He + 238U

Raabe et al- Nature 431 (2004), 823Trotta et al– PRL 84 (2000), 342

Recent speculation: (Hinde et al – Nature 431 (2004), 748) –neutron halo move to the target and then the core fuses).

Systems involving radioactive nuclei: 6He + 209Bi

Kolata et al – PRL 81 (1998), 4580

Systems involving radioactiveproton rich nuclei:

17F + 208Pb

Rehm et al – PRL 81 (1998), 3341

No systematic behavior

Alamanos et al – PRC 65 (2002), 054606

Care should be taken when comparingdifferent systems.How to “reduce”?

Gomes et al – PRC 71 (2005), 017601

Care should be takenHow to “reduce”?

What is the potential to be used?How to perform CC calculations?

Signorini et al – NPA735 (2004), 329

Reliable potential: the double folding São Paulo potential

• It reproduces, without any free parameter, calculationsobtained with potentials which match derived barrierdistributions. (Crema et al – PRC72 (2005) – in press)

• What about elastic break-up cross sections?

• What about reaction cross sections?

• What about elastic scattering?

Measurements of elastic breakup cross sections

6He +209 Bi

E.F. Aguilera et al; PRC63 (2001), 061603R C. Signorini; NPA693 (2001), 190

D.J. Hinde et al; PRL 89 (2002), 272701C. Signorini; NPA693 (2001), 190

9Be + 144Sm : reaction, inelastic, CF and ICF

9Be + 144Sm : relative importance ofdifferent reaction mechanisms

What about σReaction ?

• σReaction have the same qualitative behaviour as σBU

Elastic, that is, quite different for differentprojectiles.

•σelastic also have different behaviours for thedifferent projectiles

Reaction Cross Sectionsfor 6, 7Li + 138Ba

20 24 28 32ELab(MeV)

10

100

1000

σ R(m

b)

A M.M. Maciel et al –PRC59 (1999), 2103

Elastic Scattering for 6Li + 138Ba

A M.M. Maciel et al –PRC59 (1999), 2103

Elastic and Inelastic Scattering for 7Li + 138Ba

J. Lubian et al - PRC64 (2001), 027601

A new type of threshold anomaly: break-up thereshold anomaly (BTA)

Gomes et al –

J Phys G 31 (2005), S1669

The large BUelastic at low energies produces a repulsive polarization potential and supress at E < VB .

Dipole polarizability of 6He(the long range dipole Coulomb excitation ofthe 6He strongly reduces the scattering cross

section at forward angles)

Rusek et al – PRC 67 (2003), 041604R

Simple picture

[1]- BUelhigh l partial waves [2]- BUel

low l partial waves

[3] – ICF [4] – CFBU [5]- CFn

- [1] does not affect [5], since they are concerned withdifferent partial waves.

- [1] afects σReaction significantly, mainly at low energies, and it is the main responsible for the experimental σBU

Elastic

- it depends strongly on the BU threshold energy.

- [2] does not affect [5] significantly, at high energies, sinceICF + CFBU + CFn cross sections agree with SBPC.

- [3] suppress [5] in the whole energy range.

- [4] can not be measured separated from [5]. It may beimportant at low energies.

Is the effect the same for medium and lightmass targets?

Reaction, TF, CF, ICF and estimate of BUelastic cross sections for 9Be + 64Zn

Gomes et al, PLB 601 (2004), 20

Reaction, TF and estimate of BUelastic crosssections for 6,7Li + 64Zn

Gomes et al, PLB 601 (2004), 20

Reaction and TF cross sections for 16O , 6He + 64Zn

Gomes et al, PLB 601 (2004), 20

Di Pietro et al, EPL 64 (2003), 309;

PRC69 (2004), 044613

Gomes et al, PLB 601(2004), 20

6He, 6,7Li, 9Be, 16O + 64Zn Reduced reaction cross sections

Gomes et al, PLB 601 (2004), 20

Reaction, TF and estimate of BUelastic

cross sections for 9Be + 27Al

Marti et al – PRC 71 (2005), 027602

Reduced reaction cross sections for 27Al target: here are the first experiments in theSouth Hemisphere with radioactive beams

Light target – there were controverses12C + 7Li

Total Fusion

A. Mukherjee et al - PLB 526 (2002), 295

Is there threshold anomaly for elasticscattering of light weakly bound

nuclei?9Be + 64Zn 9Be + 27Al

Moraes, Gomes et al – PRC 61 (2000), 064608

Gomes et al – PRC 70 (2004) 054605

Similar results were observed for 6Li + 28Si (Pakou et al – PRL 90 (2003), 202701 ; PLB 556 (2003), 21)

Is there break-up thereshold anomaly (BTA) for light targets?

Gomes – J Phys G 31 (2005), Hussein – AIP 791 (2005), 140

Conclusions for light and medium mass targets

•No σCF suppression was measured, at highenergies.•The incomplete fusion is much less important thanfor heavy targets.•Elastic break-up is still important, even with a weak Coulomb field.•Reaction cross sections are increased by the break-up process.•The break-up threshold anomaly is still present.

Perspectives

- Need of additional data at the sub-barrierenergy regime.

- Need of more exclusive experiments on elasticbreak-up, elastic scattering, complete fusionand incomplete fusion, in order to obtainprecise information for the calculations.

- Need of more data with radioactive beams.

- Need of development of theoretical models andcalculations which take into account all relevantaspects.

Main Collaborators

• USP (São Paulo): L.C. Chamon, D. Pereira, E. Crema, M.S. Hussein

• CEADEN (Havana): I. Padrón• Tandar (Buenos Aires): G.V. Marti, J.O. Fernandez

Niello, A.J. Pacheco, O.A. Capurro, J.E. Testoni, A. Arazi

• UFF (Niterói): J. Lubian, R.M. Anjos• UFRJ (Rio de Janeiro): L.F. Canto, R. Donangelo• ANU (Canberra): M. Dasgupta, D. Hinde• Tohoku (Sendai): K. Hagino• INFN (Napoli): M. Trotta