Fusion, transfer and breakup of light weakly bound nuclei at near barrier

energies.

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

Eurisol Week

Lisbon, Portugal – October 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

Breakup mechanism: Q-valuesRESULTS

n

d

Usual questions

-Does the BU channel enhance or suppress the 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 NCBU significantly. Is that true for CF or CF + ICF? And for TR ?

- May prompt and delayed BU affect fusion?

Usual questions• How large is the NCBU compared with CF or CF + ICF ?

How does it depend on the energy region and target mass?

• Is transfer important for every weakly bound projectiles?

• Does direct BU and BU following transfer produce repulsive polarization potentials?

• Is there BTA for the elastic scattering of any weakly bound projectile?

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? So, instead of TF, one measures TF + transfer?

• How to distinguish NCBU from transfer and ICF by measuring single fragments?

Importance of transfer for fusion of 6He. Is it also important for other weakly bound nuclei? If yes,

how to separate it from total fusion?

Raabe – Nature 431, 823(2004) X Trotta – PRL 84, 2342(2000) - same authors

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

Example of Model Dependent Conclusions

Kolata et al., PRL 81, 4580 (1998) Gomes et al., PLB 695, 320 (2011)

Raabe et al: Nature 431 (2004) 823

If one uses folding potentials, the halo density is taken into account. So, one does not observe halo effects!!!

Important: Bare Potential deduced from double-folding procedure

Gomes et al, PLB 695, 320 (2011)

Conclusions about static effects of halo nuclei.

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

• We believe that 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

Is TF really total fusion or total fusion + transfer?

Fang – submitted to publication

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

6He + 206PB (Dubna data) ????

New 6He + 206Pb data (Wolski – EPJA 47, 111 (2011))

Application : transfer coupling effects on medium-heavy systems

Shorto – PRC 81, 044601 (2010)

Zhang – PRC 82, 054609 (2010)

Only inelastic channels were considered

What about proton-halo systems?

So far, there is only one system measured

• Fusion of proton-halo 8B + 58Ni

(Aguilera PRL 107, 092701 (2011))

Fusion of proton-halo 8B + 58Ni (Aguilera PRL 107, 092701 (2011))

New dynamic effect for proton-halo fusion?

New measurements are required

Rangel – submitted to publication

Two independent calculations without any fit parameter

(Rangel et al., submitted to publication)

CCC with SPPCDCC calculations

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?

What has to be done?

- Need of additional data at the sub-barrier energy regime. We still do not fully understand this important energy regime, very important for nucleosynthesis and production of SHE.

-Need of more data with radioactive beams. We need better data, with smaller error bars.

-More fusion cross section measurements for proton-halo nuclei.

- Sub-barrier total fusion for light targets. Is there enhancement?- CF and ICF for light systems, below and above the barrier. Is ICF negligible? - CF and ICF for medium mass targets. How does the suppression vary with mass?

- More separated CF and ICF data, specially for light and medium mass systems. Can we separate transfer?

Final Message

• Although we have learned a lot in the last years, we still have many things to learn.

• We need more good data and more calculations and theoretical developments.

Collaborators

J. Lubian, D. R. Otomar, R. Linares (UFF),

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

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