Fusion, transfer and breakup of light
weakly bound nuclei at near barrier
energies.
Paulo R. S. Gomes
Univ. 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
n
p
after
measured
Courtesy of Luong
measured
before
calculated by p
conservation
known
Breakup mechanism: Q-values
RESULTS
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
theo
 F   exp

 'ingredients' missing in the theory
F
F
Theoretical possibilities:
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
Example: 6He + 209Bi
Single 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
Important: Bare Potential deduced from double-folding procedure
Gomes et al, PLB 695, 320 (2011)
If one uses folding potentials, the halo density is taken into
account. So, one does not observe halo effects!!!
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.
2. Compare with  F of a similar tightly bound system
Differences due to static effects:
1. Gross dependence on size and charge:
ZP , Z T , AP , AT  affects VB and RB
VB : ZP Z Te2 / RB;  geo :  RB2 , RB  A1/P 3  A1/T 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  VB
Ex
h
and

exp
F
2E
exp
 Fexp (x) 

F
h RB2
Inspired in Wong’s approximation

W
F

 2 E  VB  
h
R
ln 1  exp 


2E
h


 

2
B
If  Fexp   FW
 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 the failure of the Wong model for light
systems at sub-barrier energies
Eliminate influence of couplings with bound channels
Renormalized fusion function
Fexp (x)
 FCC  FCC
Fexp (x)  Fexp (x) 
, with R(x)  W  opt
R(x)
F
F
If CC calculation describes data  Fexp  UFF
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)
Only inelastic channels
were considered
Zhang – PRC 82,
054609 (2010)
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 SPP
CDCC 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.
- More separated CF and ICF data, specially for light and medium
mass systems. Can we separate transfer?
- 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?
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)