Fusion, break-up and scattering of stable weakly bound nuclei

Paulo Roberto S. GomesInstituto de Fisica

Universidade Federal Fluminense Niterói, R.J, Brazil

For a comprehensive review of this subject:Phys. Rep. 424 (2006), 1-111

The break up of stable weakly bound nuclei

Suitable stable weakly bound nuclei

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

The Fusion X Break-up problem

•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.

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

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

Inelastic couplings Inelastic and transfer couplings

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

T1

CN22

ICF 1

T2

1CN

1ICF 2

T1

2T

1

2CN

T1

2

ACN < AP+AT

ACN = AP+AT

B-Up

T1

2

Elastic Breakup

T1

2ACN = AP+AT

SCF

ICF

CF DCF

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 s CF or s TF= 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.

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

Experimental aspects to be considered

• What is it measured? s CF or s TF= 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)s CF, s 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

s TF = s CF + 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-anodes TF

A Mukherjee et al; PLB526 (2002), 295

Measurements of 9Be + 64Zn

USP E ≥ VB

Gamma rays (on-line and off-line)s CF s 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)

s CF, s ICF

Gomes et al – BJP 35 (2005), 902

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)

Those results agree with CCC and SBPM predictions

Gomes et al;

BJP 34 (2004), 737

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

Gomes et al –PLB 634(2006), 356

Conclusions for Heavy Targets

• The BU inhibits s CF at E > VB

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

• s TF is not affected by the BU at E > VB

• s ICF 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.

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

Gomes et al – PRC 71 (2005), 017601

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

Gomes et al – PRC 71 (2005), 017601

64Zn target

Different conclusions depending on

What is the potential to be used

How to perform CC calculations

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) – 034610)

2 24v /( ) ( ) cFoldV R V R e−=

finite-range approachnucleon distributions for ρ

→ M3Y – Reid or Paris( )rνr

1/31.31 0.84oR A fm= −0.50 fm a =

{

v = relative velocity between the nuclei

[ ])()(222 RVRVEE LECkinetic −−==µµ

v

ρ {

VFold(R) = ρ1(r1)ρ(r2) ν(R-r1+r2)dr1dr2? ? ? ? ? ? ??

Analysis of the 4,6He + 238U fusionby the São Paulo Potential

Crema et al, subm. PRL SF = 0.84

Analysis of the 6He + 209Bi fusionby the São Paulo Potential

SF = 0.81

There is no sub-barrierfusion enhancement!!

Crema et al - subm to PRL

• What about elastic break-up cross sections?

• What about reaction cross sections?

• What about elastic scattering?

Measurements of elastic breakup cross sections

D.J. Hinde et al; PRL 89 (2002), 272701

C. Signorini; NPA693 (2001), 190

C. Signorini; NPA693 (2001), 190

E.F. Aguilera et al; PRC63 (2001), 061603R

6He +209 Bi

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

Gomes et al – PLB 634(2006), 356

9Be + 144Sm : relative importance ofdifferent reaction mechanisms

Gomes et al –PLB 634(2006), 356

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

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

Gomes et al –

J Phys G 31 (2005), S1669

BTA

Hussein et al – PRC (RC) – in press

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

Gomes et al, PLB 601 (2004), 20

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

PRC69 (2004), 044613

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

Benjamin et al – subm PRL

Light target – there were controverses12C + 7Li

Total Fusion

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

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

Gomes – J Phys G 31 (2005) S1669Figueira et al – unpubl.

Conclusions for light and medium mass targets

•No s CF 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, A. Lepine, R. Lichtenhaler

• 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

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