Why the complete fusion of weakly bound nuclei is enhanced at sub-barrier energies and suppressed

above the barrier.

Paulo R. S. GomesUniv. Fed. Fluminense (UFF), Niteroi, Brazil

NN2012- San Antonio, May 27th-June 1st (2012)

Reactions with weakly bound nuclei

However, nature is more complicated than that simple picture: Breakup following transfer

RESULTS

measured measured calculated by p conservation

known

beforeafter

np

Courtesy of Luong

See talk by Nanda Dasgupta next Friday

Frequently used procedures to answer “Enhancement or

suppression in relation to what?

a) Comparison of data with theoretical predictions.

b) Comparison of data for weakly and tightly bound systems.

Effects to be considered

• Static effects: longer tail of the optical potential arising from the weakly bound nucleons.

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

1.   Experiment vs. theory F    

F

exp - F

theo   'ingredients' missing in the theory

a) Single channel - standard densities

F  arises from all static and dynamic effects

b) Single channel - realistic densities

F  arises from couplings to all channels

c) CC calculation with all relevant bound channels

F  arises from continuum couplings

d) CDCC

no deviation expected

Theoretical possibilities:

Example: 6He + 209BiSingle channel - no halo

Single channel – with halo

CC with bound channels(schematic calculation)

Shortcomings of the procedure:

• Choice of interaction plays fundamental role• Does not allow comparisons of different systems• Difficult to include continuum – no separate CF and ICF

Conclusions about static effects of halo nuclei.

• Fusion enhancement when compared with what it should be without halo properties.

• There is no more discussion left about that.

Differences due to static effects:

2.   Compare with F of a similar tightly bound system

1. Gross dependence on size and charge:

ZP , ZT, AP , AT affects VB and RB

 VB : ZPZTe2 / RB;    geo : RB2 ,   RB A

P

1/3 AT

1/3)

2. Different barrier parameters due to diffuse densities

(lower and thicker barriers)

Fusion data reduction required !

Fusion functions F(x) (our reduction method)

E x

E VB

hand F

exp Fexp (x) 2E

hRB2

  Fexp

Inspired in Wong’s approximation

F

W RB2 h

2Eln 1 exp

2 E VB h

If Fexp F

W    F(x) F0(x) ln 1 exp 2 x

F0(x) = Universal Fusion Function (UFF)

system independent !

Direct use of the reduction method

Compare Fexp

(x) with UFF for x values where Fopt

FW

Deviations are due to couplings with bound channels and breakup

Refining the method

Eliminate influence of couplings with bound channels

Renormalized fusion function

Fexp

(x) Fexp

(x) F

exp(x)

R(x), with R(x)

FCC

FW

FCC

Fopt

If CC calculation describes data F

expUFF

Eliminate the failure of the Wong model for light systems at sub-barrier energies

Applications with weakly bound systems

1. Canto, Gomes, Lubian, Chamon, Crema, J.Phys. G36 (2009) 015109; NPA 821(2009)51

2. Gomes, , Lubian, Canto, PRC 79 (2009) 027606

2. Gomes, Canto, Lubian, Hussein, PLB 695 (2011), 320

Use of UFF for investigating the role of BU dynamical effects on the total fusion of heavy

weakly bound systems

No effect above the barrier- large enhancement below the barrier

Use of UFF for investigating the role of BU dynamical effects on the total fusion of very light

weakly bound systems

No effect above the barrier- almost no data below the barrier

Use of UFF for investigating the role of BU dynamical effects on the total fusion of light

weakly bound systems

No effect above the barrier- no data below the barrier

Use of UFF for investigating the role of BU dynamical effects on the complete fusion of

stable weakly bound heavy systems

We did not include any resonance of the projectiles in CCC.

Suppression above the barrier- enhancement below the barrier

Fusion of neutron halo 6,8He, 11Be weakly bound systems

Conclusion from the systematic (several systems) : CF enhancement at sub-barrier energies and suppression above the barrier, when compared with what it should be without any dynamical effect due to breakup and transfer channels.

Question: Why?

Example for Complete fusion of 6,7Li + 209Bi

Effects of suppression and enhancement are more important for 6Li than for 7Li. (6Li has smaller BU threshold energy and no bound state)

Approaches which might be used

- Coupled channel calculations (CDCC calculations including transfer channels and sequential breakup) – not available so far

- Dynamic polarization potential (substitutes many channels by one single channel – energy dependent optical potential.

Suppression of fusion above the barrier

Threshold anomaly in the elastic scattering of tightly bound systems

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

where W(E) = WV (E) + WS (E)

Tenreiro et al – PRC 53 (1996), 2870

The Threshold Anomaly for “normal systems “

• As the energy decreases towards the barrier, reaction channels close and the imaginary potential decreases and vanishes.

• Due to the dispersion relation, the real potential increases when the imaginary potential decreases. The attraction increases (attractive polarization potential) and consequently there is sub-barrier fusion enhancement.

• Polarization potentials associated with couplings to transfer and inelastic channels were shown to be attractive

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

The large NCBUat low energies produces a repulsive polarization potential and suppress fusion.

Gomes et al –

J Phys G 31 (2005), S1669

The behavior for weakly bound systems

• The breakup is important even below the barrier. So, the imaginary potential does not decrease at the barrier energy. Indeed, it can increase.

• Consequently, the real potential decreases at this energy region. Fusion is suppressed.

• This behavior is called ‘breakup threshold anomaly’ (BTA).

• Of course, the imaginary potential must decrease and vanish at lower energies (we will discuss this point later).

BTA

M.S. Hussein, P.R.S. Gomes, J. Lubian, L.C. Chamon – PRC 73 (2006) 044610

Systems with 6Li

Figueira et al. – PRC 75 (2007), 017602

A. Gomez-Camacho et al., NPA 833 (2010), 156Figueira et al. – PRC 81 (2010), 024603

Hussein et al., PRC 73 (2006) 044610

Keeley et al., NPA571 (1994) 326

Gomes et al JPG 31 (2005) S1669

6Li + 144Sm

Deshmukh et al. PRC 83, 024607 (2011)

6Li + 116Sn

More Systems with 6Li

Souza – PRC75, 044601 (2007)

Zadro, di Pietro- PRC 80, 064610 (2009)

6Li + 64Zn

Kunawat – PRC 78, 044617 (2008)

6Li + 90Zr

Biswas- NPA 802, 67 (2008) Biswas- NPA 802, 67 (2008)

Santra – PRC83, 034616 (2011)

6Li + 209Bi

Systems with 7Li

Souza – PRC75, 044601 (2007)Pakou PRC 69, 054602 (2004)

Lubian- PRC 64, 027601 (2001)

Gomes JPG 31 (2005) S1669

Figueira – PRC 73, 054603 (2006)

7Li + 27Al

Deshmukh et al, accepted EPJA

7Li + 116Sn

Systems with 9Be

Signorini –PRC 61, 061603R (2000)

Woolliscroft – PRC 69, 044612 (2003)

9be + 208Pb

Gomes JPG 31 (2005) S1669

Gomes- PRC70, 054605 (2004)

Gomes – NPA 828, 233 (2009)

9Be + 144Sm

Systems with radioactive nuclei

A. Gomez-Camacho et al., NPA 833 (2010), 156

A. Gomez-Camacho et al., NPA 833 (2010), 156

Garcia, Lubian – PRC 76, 067603 (2007)

6He + 209Bi

Calculations of DPP considering direct breakup : repulsive DPP

8B + 58Ni – Lubian6Li + 209Bi - Santra

7LI + 27Al - Lubian

QE barrier distributions

BU enhances the Coulomb barrier

J. Lubian, T. Correa, P.R.S. Gomes, L. F. Canto – PRC 78 (2008) 064615

Conclusions

• The effect of the coupling to BU was shown to come from the repulsive DPP they provoke. It hinders the CF cross sections.

• The BU channel increases the barrier as shown in the QE barrier distributions. This leads to the hindrance of the fusion cross section

What about the enhancement of CF at sub-barrier energies?

• We have to look at the low energies for the elastic scattering:

The DPP becomes attractive at low energies (below the barrier)

Why?

• At sub-barrier energies, the breakup following transfer predominates over the direct breakup. Each one of them has different DPP: direct BU produces repulsive DPP. BU after transfer produces attractive DPP. The total DPP is attractive

Direct BU Sequential BU

7Li + 144Sm

Otomar 2012

Conclusions

• Direct breakup produces repulsive polarization potential which suppress fusion at energies above the barrier.

• At sub-barrier energies, the breakup following transfer predominates and produces attractive polarization potential which enhances fusion.

• More quantitative calculations are required (CDCC calculations including transfer and BU following transfer)

Collaborators

J. Lubian. R. Linares (UFF),

L. F. Canto (UFRJ), M.S. Hussein (USP),

M. Dasgupta, D. J. Hinde, D.H. Luong (ANU)