Nuclear and Coulomb breakup of 6Li 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 9Be
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
n
p
after
measured
Courtesy of Luong
measured
before
calculated by p
conservation
known
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 σCF or σTF= 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
, para cada um destes físicos,
We did not include any resonance of the projectiles in CCC.
Suppression above the barrier- enhancement below the barrier
Same as before, but with new data (ANU) for
9Be + 209Bi
Systematics reached from investigation of the role of BU
dynamical effects on fusion of
neutron halo 6He, 11Be weakly bound systems
Suppression above the barrier- enhancement below the barrier
Fusion of
neutron halo 6,8He, 11Be 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
Di Pietro – PRC 87, 064614 (2013)
Sargsyan PRC 88, 044606 (2013)
Measurements of 6,7Li + 64Zn
E > VB
ToF
σTF = σCF + ICF
I. Padron et al; PRC66 (2002),044608
Analyses in the original papers
Beck et al. (2003)
Gomes, Padron (2004, 2005)
Controversy on 6He + 206Pb fusion
Lukyanov PLB 670, 321 (2009)
Wolski- EPJA 47, 111 (2011)
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, 115103(2012)
What about proton-halo systems?
Up to recently, there was only one system
measured
• Fusion of proton-halo 8B + 58Ni
(Aguilera PRL 107, 092701 (2011)
Fusion of proton-halo 8B + 58Ni
New dynamic effect for
proton-halo fusion?
Or
Something wrong with the
data?
Some details of Aguilera’s derivation of fusion cross section
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 TostevinNunes-Thompson.
However, see what happens for 6,7Li at sub-barrier energies
(measurements at ANU (Canberra). They measured NCBU by
detecting charged fragments at backward angles.
Other recent result: Fusion of 8B + 28Si
Pakou et al. PRC 87, 014619 (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, 024617 (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
Prediction for BU protons at
Elab = 25.8 MeV (Tostevin)
Experimental “evaporation” protons at
Elab = 22.4 MeV (Aguilera)
Rangel et al., EPJA 49, 57 (2013)
How can one separate experimentally protons from
fusion and breakup?
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 6Li BU on CF cross
sections
Kumawat – PRC 86, 024607 (2012) Pradhan – PRC 83, 064606 (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, 014615 (2013)
M.S. Hussein, P.R.S. Gomes, J. Lubian,
D.R. Otomar, L. F. Canto
PRC 88, 047601 (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
6Li
+ 59Co
6Li
+ 144Sm
6Li
+ 208Pb
A few words about the CDCC calculations
performed by Otomar and Lubian
-6Li breaks up into alpha + deuteron. We use the cluster
model.
- Calculations performed with FRESCO.
- Projectile-target interaction:
- Continuum states of 6Li are discretized.
- The interaction between deuteron and alpha cluster
within 6Li 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
For higher energies and light
targets, nuclear BU may
predominate
Small angles (large distances) – Coulomb BU always predominates
For larger angles, nuclear BU may predominate – crossing angle.
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 AT 1/3 for the
same E c.m./VB
The Coulomb BU increases
linearly with ZT for the same
Ec.m./VB
Suppression of the Coulomb-Nuclear BU
interference peak in the elastic scattering
Di Pietro
Keeley- PRC82,
034606 (2010)
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 ZT, which should lead to a ZT2
dependence, whereas the cross sections are
proportional to 1/E.
2- Since the collision energy corresponds to the same
E/VB ratio and VB is proportional to ZT, one gets a
1/ ZT factor.
3- From (1) and (2) we get a linear dependence on ZT.
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.
2 2
é
æ
G
Lc ö ù
2
s F = p R ln ê1+ exp ç
2 ÷ú
E
è 2mR G ø û
ë
where Γ = ћ ω/ 2π (width of the barrier) and
ΛC 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:
é
æ
G
2
s R = p R ln ê1+ exp ç
ê
E
çè
ë
2
(
)
Lc + D ö ù
ú
÷
2
2 m R G ÷ø ú
û
2
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
(
s Nbu
)
é
æ 2 L +D 2öù
c
ê1+ exp ç
÷ú
2
ê
çè 2 m R G ÷ø ú
G
ú
= s R - s F = p R 2 ln ê
2 2
E
æ Lc ö ú
ê
ê 1 + exp çè 2 m R 2 G ÷ø ú
ê
ú
ë
û
This expression can be simplified by expanding in
the lowest order of Δ / ΛC to give:
Why does the nuclear breakup behave like that? (4)
s
bu
N
p
é VB ù
= 2 2 L c D = 2p a ê1- ú Rp + RT
k
ë Eû
(
Where we have used
L = 2m
2
c
and
2
(R
p
+ RT
2
= P1 + P2 A T 1/3
) [ E - V ] = k [1- V E ]( R
2
2
B
D = k [1- VB E ] a
2
)
B
p
+ RT
2
With a being the diffuseness of the nuclear surface.
Clearly P1 = 2π a (1 – VB / E) RP and P2 = 2π a r0 (1 – VB / E)
)
2