Nuclear and Coulomb breakup of 6 Li at near barrier energies, their interferences and their effect on fusion Paulo R. S. Gomes Univ. Fed. Fluminense (UFF), Niteroi, Brazil

Reactions with weakly bound nuclei – example with 9 Be

Things are much more complicated than that. Sequential BU. Nanda’s talk.

However, nature is more complicated than that simple picture: Breakup following transfer RESULTS measured calculated by p conservation known before after n p Courtesy of Luong

Breakup time scale Only prompt breakup may affect fusion

Questions that we investigate and try to answer -Does the BU channel enhance or suppress the fusion cross section? Is the effect on σ CF or σ TF= CF + ICF ? -What are the effects on different energy regimes and on different target mass regions? -What is the relative importance between nuclear and Coulomb breakups? Do they interfer ? -How large is the  NCBU compared with  CF ? How does it depend on the energy region and target mass?

Different answers, depending on several things

Example of Model Dependent Conclusions Kolata et al., PRL 81, 4580 (1998) Gomes et al., PLB 695, 320 (2011)

Old controversy between Kolata`s and Raabe`s data (6He + 209Bi and 238U) Important: Bare Potential deduced from double-folding procedure

Systematics reached from the investigation of he role of BU dynamical effects on the complete and total 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, para cada um destes físicos,

Same as before, but with new data (ANU) for 9 Be Bi

Systematics reached from investigation of the role of BU dynamical effects on fusion of neutron halo 6 He, 11 Be weakly bound systems Suppression above the barrier- enhancement below the barrier

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

Do all the systems follow the systematics? If not, either a) There is something very special with those systems. b) There is something wrong with the data. c) Wrong CC calculations

Examples

Indeed, there are some new data (di Pietro et al) for this system Sargsyan PRC 88, (2013) Di Pietro – PRC 87, (2013)

Measurements of 6,7 Li + 64 Zn E > V B ToF σ TF = σ CF + ICF I. Padron et al; PRC66 (2002),044608

Analyses in the original papers Beck et al. (2003) Gomes, Padron (2004, 2005)

Lukyanov PLB 670, 321 (2009)Wolski- EPJA 47, 111 (2011) Controversy on 6He + 206Pb fusion How are the fusion functions?

Transfer effect on sub-barrier fusion fucntion Shorto PRC (2010)

Conclusion from the systematics (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? Possible answer: read P.R.S. Gomes et al., J. Phys. G 39, (2012)

What about proton-halo systems? Up to recently, there was only one system measured Fusion of proton-halo 8 B + 58 Ni (Aguilera PRL 107, (2011)

Fusion of proton-halo 8 B + 58 Ni New dynamic effect for proton-halo fusion? Or Something wrong with the data?

Fusion cross section was obtained by measuring proton multiplicities. It was assumed that all protons detected at backward angles come from fusion evaporation, and no protons from breakup reach the detectors, based on CDCC calculations by Tostevin- Nunes-Thompson. However, see what happens for 6,7 Li at sub-barrier energies (measurements at ANU (Canberra). They measured NCBU by detecting charged fragments at backward angles. Some details of Aguilera’s derivation of fusion cross section

Other recent result: Fusion of 8 B + 28 Si Pakou et al. PRC 87, (2013) Measurements at Legnaro. Fusion cross sections derived from alpha measurements (there is no alpha from BU) Normal behavior, within our systematic!!!

Calculations by Tostevin, Nunes and Thompson used by Aguilera to say that no breakup protons reach the detectors placed at backward angles (PRC 63, (2001)) Does it go to zero at backward angles?

Tostevin extended the calculations up to 180 degrees (for us) It does not vanish at large angles!!!!

Furthermore, see the proton spectra and Tostevin calculations Experimental “evaporation” protons at E lab = 22.4 MeV (Aguilera) Prediction for BU protons at E lab = 25.8 MeV (Tostevin) How can one separate experimentally protons from fusion and breakup? Rangel et al., EPJA 49, 57 (2013)

We believe that there is nothing special with fusion of proton-halo nuclei

So, the next question is: How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups: Is there interference between them? One believes that the BU depends on the target mass (charge).

Effect of the 6 Li BU on CF cross sections Kumawat – PRC 86, (2012) Pradhan – PRC 83, (2011) The BU effect on fusion does not seem to depend on the target charge!!!!

References: D. R. Otomar, P.R.S. Gomes, J. Lubian, L.F. Canto, M. S. Hussein PRC 87, (2013) M.S. Hussein, P.R.S. Gomes, J. Lubian, D.R. Otomar, L. F. Canto PRC 88, (2013)

Our first theoretical step was to perform reliable CDCC calculations. What do we mean by reliable? No free parameters, only predictions. The predictions have to agree with some data. Which data are available? Elastic scattering angular distributions.

Examples of calculations for elastic scattering 6 Li + 59 Co 6 Li Sm 6 Li Pb

A few words about the CDCC calculations performed by Otomar and Lubian - 6 Li breaks up into alpha + deuteron. We use the cluster model. -Calculations performed with FRESCO. -Projectile-target interaction: -Continuum states of 6 Li are discretized. -The interaction between deuteron and alpha cluster within 6 Li is given by a Woods-Saxon potential. -The real parts of interactions are given by the São Paulo potential. -The imaginary parts of the interactions are represented by a short range fusion absorption (IWBC). -The CDCC calculations include inelastic channels.

Relative importance between Coulomb and nuclear breakups Total BU – black Coulomb BU – red Nuclear BU - blue Small angles (large distances) – Coulomb BU always predominates For larger angles, nuclear BU may predominate – crossing angle. For higher energies and light targets, nuclear BU may predominate

Interference between Coulomb and nuclear breakups If there were were no interference, the last column should be unity.

What is the relative importance between breakup and fusion cross sections?

How does the BU vary with target mass (or charge)? Coulomb and nuclear breakups? The nuclear BU increases linearly with A T 1/3 for the same E c.m. /V B The Coulomb BU increases linearly with Z T for the same E c.m. /V B

Suppression of the Coulomb-Nuclear BU interference peak in the elastic scattering Keeley- PRC82, (2010) Di Pietro

See Alexis`s talk

Conclusions The relative importance between nuclear and Coulomb breakups is not so simple as it is usually thought. There is a strong destructive interference between nuclear and Coulomb breakup. When one calculates BU cross sections with CDCC, one does not distinguish prompt and delayed BU. Most of the BU seems to be delayed and only the prompt BU affects fusion.

Why does the Coulomb breakup behave like that? 1- The electromagnetic coupling matrix-elements are proportional to Z T, which should lead to a Z T 2 dependence, whereas the cross sections are proportional to 1/E. 2- Since the collision energy corresponds to the same E/V B ratio and V B is proportional to Z T, one gets a 1/ Z T factor. 3- From (1) and (2) we get a linear dependence on Z T.

Why does the nuclear breakup behave like that? (1) Wong formula for fusion X-section taken to be the total nuclear reaction X- section without BU. where Γ = ћ ω/ 2π (width of the barrier) and Λ C is the critical angular momentum for fusion.

Why does the nuclear breakup behave like that? (2) The reaction X-section including nuclear BU but not Coulomb BU may be written as: The Coulomb BU is of long range and can not be described by the Wong formula.

Why does the nuclear breakup behave like that? (3) The nuclear BU X- section is taken to be the difference This expression can be simplified by expanding in the lowest order of Δ / Λ C to give:

Where we have used Why does the nuclear breakup behave like that? (4) and With a being the diffuseness of the nuclear surface. Clearly P 1 = 2π a (1 – V B / E) R P and P 2 = 2π a r 0 (1 – V B / E) = P 1 + P 2 A T 1/3