fusion, transfer and breakup of light weakly-bound and halo nuclei at near barrier energies. j....
TRANSCRIPT
Fusion, transfer and breakup of light weakly-bound and halo nuclei at near
barrier energies.
J. LubianUniversidade Federal Fluminense (UFF), Niteroi, Brazil
ISPUN-2014, Ho Chi Minh, Nov. 3- 8 (2014)
Why the complete fusion of light weakly bound nuclei is enhanced at sub-barrier energies and suppressed above the barrier?
Outline:
1- Systematic for CF comparing reduced data with a benchmark (UFF);
2- Same conclusion by studing the energy dependence of the optical potential, obtained by fitting the elastic scattering angular distributions;
3- Explanation of the hindrance above the Coulomb barrier.
4- Explanation of the enhancement below the Coulomb barrier
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
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
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- 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 CC calc.
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?
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 NCBU at 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
7Li + 144Sm
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
P.R.S. Gomes, D. R. Otomar (UFF),
L. F. Canto (UFRJ), M.S. Hussein (USP),
M. Dasgupta, D. J. Hinde, D.H. Luong (ANU)
Thank you for your attention!