The Breakup Threshold Anomaly in reactions with weakly bound projectiles

1
The Breakup Threshold Anomaly in reactions with
weakly bound projectiles
XXXI Symposium on Nuclear Physics, Cocoyoc,
Morelos, México, January 7-10, 2008
2
The Kramers-Krönig Dispersion Relations

• For a function ?(?) ?1(?) i ?2(?) analytic in
  the upper half
• plane such that ?(?) ?0 as ? ?8, the relations
  are given by,
• ?1(?) (1/p) P ? d? ?2(?) / (?- ?)
• and
• ?2(?) (1/p) P ? d? ?1(?) / (?- ?)

3
The Theshold Anomaly
16O208Pb
U ( r, E ) Vcoul ( r ) V0 ( r ) u( r, E )

?V(E)
u(r,E) ?V(r,E) i W(r,E)
Dispersion relation
W(E)
?V(r,E) (1/p) P ? dE W(r,E) / (E-E)
8
0
VB
M.A. Nagarajan et al., Phys. Rev. Lett. 54 1136
(1985)
4
The threshold Anomaly
16O60Ni
?V(E)
W(E)
VB?
B.R. Fulton et al., Phys. Lett. 162 B (1985) 55
5
Threshold Anomaly strongly bound nuclei

• ?V(E) sharply increases its strength and becomes
  attractive around the Coulomb barrier.

W(E) decreases as the energy is lowered around
the barrier which means that reaction channles
become closed.
Attractive ?V(E)
Enhances fusion
Reaction channels become closed
Decreasing W(E)
Direct reactions become suppressed
6
The threshold Anomaly
16O60Ni
? Total reaction ? Fusion
N. Keeley et al., Nucl. Phys. A582 (1995) 314
7
The Threshold Anomaly
16O64Zn
C. Tenreiro et al., Phys. Rev. C53 (1996) 2870
8
The Threshold Anomaly
C. Tenreiro et al., Phys. Rev. C53 (1996) 2870
9
Weakly Bound Projectiles
Low energy dipole modes
Small neutron and breakup threshold energies.
After the valence neutron(s) is knocked out, the
remaining nucleus is unstable (Borromean).
A strong coupling to the breakup channel is
present at low energies.
Halo structure ( small Sn ) ------ larger
nuclear radius ----- smaller Coulomb
barrier------ larger fusion cross section
Small Sn ---- larger breakup cross sections ----
smaller fusion cross section ---- larger
absorption cross sections
10
Weakly bound projectiles

• Recent experiments have been done for reactions
  involving weakly bound projectiles for such as,
  ?Be, 6Li, 7Li and 6He.
• ?Be ? 8Ben ? aan (Sn1.67 MeV)
• 6Li ? ad
  (Sa1.48 MeV),
• 7Li ? at
  (Sa2.47 MeV)
• 6He ? 4He2n (S2n0.98
  MeV)

208Pb,209Bi, 144Sm, 64Zn, 27Al
11
NUCLEAR REACTION MECHANISMS WEAKLY BOUND
PROJECTILES
DIRECT AND SEQUENTIAL COMPLETE FUSION
NON-CAPTURE BREAKUP
P
T
INCOMPLETE FUSION
NEUTRON TRANSFER
CF DCF SCF TF CF ICF
12
Reactions with weakly bound projectiles
VB
P.R.S. Gomes et al., Phys. Lett. B 601 , 20 (2004)
13
Reactions with weakly bound projectiles
P.R.S. Gomes et al., Phys. Rev. C73, 064606 (2006)
14
Objectives.

• A Distorted Wave Approximation model will be
  applied to
• simultaneously study elastic scattering, fusion
  and direct
• reactions involving weakly bound projectiles.

• An optical model polarization potential is used
  for which its
• imaginary absorption potential is decomposed into
  two parts
• a fusion (volume) WF and a direct reaction
  (surface) WDR, that is
• WWF WDR

• Within this Direct Reaction approach, a
  simultaneous decription of elastic scattering,
  fusion and direct reaction cross section is
  achieved. The variations with energy of WF , WDR
  and the real potentials VF and VDR explain why
  the usual TA does not appear in reactions with
  weakly bound proyectiles.

15
Objectives.
The effect of breakup reactions on fusion (strong
particularly at energies below the Coulomb
barrier) can be determined in terms of VDR( E )
and WDR( E )
Reduces the barrier
Attractive VDR
Fusion enhancement
Fusion suppression
Repulsive VDR
Increases the barrier
WDR suppresses fusion since absorbes incident
flow into direct reactions
These two competing physical effects on fusion
can be studied by means of, Ri sF ( i ) /
sF ( VDR WDR 0 ) , iVDR, WDR, VDRWDR
16
Basic formalism

• T U ?() E ?()
• U ( r, E ) Vcoul ( r ) V0 ( r ) u( r,
  E )
• where

Vcoul ( r ) Coulomb Potential V0 ( r
) Hartree-Fock Potential u (
r, E ) Polarization Potential
17
Polarization Potential

• u( r,E ) V( r, E ) i W( r, E )
• W( r , E )WF ( r , E )WDR ( r , E )
• V( r, E )VF ( r, E )VDR ( r, E )
• VF and VDR are related to WF and WDR by the
  dispersion relation

8
V ( Rsa , E ) ( 1/p ) P ? dE W ( Rsa , E )
/ ( E - E )
0
18
Fusion and direct reaction cross sections

• W WF WDR
• Fusion
• s F (2/hv) lt ?() ? WF ? ?() gt
• Direct reaction
• s DR (2/hv) lt ?() ? WDR ? ?() gt
• Total Reaction
• sR (2/hv) lt ?() ? W ? ?()gt
• 
  
• Where T U ?() E ?()

19
?2 -analysis of elastic scattering and fusion
experimental data
N

• ? 2 (1/N) S (si, theo-si, exp )2 / (?si, exp
  )2

i0
N Number of data points si, exp
i-th experimental data ?si, exp
i-th data error si, theo i-th
theoretical calculation
20
Optical Potentials
VF (r), WF (r)
VDR (r), WDR (r)
21
RESULTS
(MeV)
?V(E)
9Be209Bi
?V(E)
6Li208Pb
W(E)
9Be209Bi
W(E)
6Li208Pb
?
Ecm - VB (MeV)
C. Signorini et al., Phys. Rev. C61, 06603 (2000)
22
6He209Bi
VB
23
6He209Bi
VB
24
9Be64Zn
25
9Be64Zn
26
9Be64Zn
27
9Be144Sm
28
9Be144Sm
29
Breakup effects on fusion are related to the
Direct Reaction part of the optical potential,
VDR and WDR.
An attractive VDR lowers the Coulomb barrier
height and therefore enhances fusion. A
repulsive VDR suppresses fusion
The loss of flux from the elastic channel into
the breakup one suppresses fusion. This is
related with WDR
These two competing physical effects on fusion
can be studied by means of Ri sF ( i ) /
sF ( VDR WDR 0 ) , iVDR, WDR, VDRWDR
30
Effect of breakup on fusion
9Be64Zn
RVDR
RWDR
RVDR,WDR
VB 17 MeV
31
Effect of breakup on fusion
RVDRWDR
Enhancement Region
?
Suppression Region
32
Conclusions

• A distorted wave direct reaction model has been
  applied to reactions with weakly bound
  projectiles.

Optical potentials with volume (fusión) and
surface (direct reaction ) parts have been used
whose parameters are adjusted by a simultaneous
?2- analysis of elastic scattering and fusion
data.
It has been determined that these potentials
agree with the dispersion relation.
The energy dependence of these potentials at Rsa
show a very different behavior respect to
reactions involving tighly bound nuclei. TA vs BTA
The effect of breakup reactions induced by the
weakly bound projectile on fusion has been
studied in terms of the surface potentials VDR
and WDR and shows a strong suppression above and
around the Coulomb barrier.
33

• Collaborators
• E.F. Aguilera, ININ Mexico
• E.M. Quiroz, ININ, Mexico
• P.R.S. Gomes, J. Lubian, Universidade Federal
  Fluminense, Brazil
• I. Padron, Universidad de la Habana, Cuba

34

• THANK YOU

35
rF1.1 fm, rDR1.25 fm
rF1.1 fm, rDR1.4 fm
36
WDR
rF 1.1 fm rDR1.7 fm
WF
rF1.1 fm rDR1.9 fm
37
rF1.3 fm rDR1.9 fm
rF1.6 fm rDR1.9 fm
rF1.4 fm rDR1.9 fm
38
rF1.5 fm rDR1.9 fm
rF1.6 fm rDR1.9 fm
39
Elastic scattering cross section.
rF 1.58 fm, rDR 2 fm
rF 1.6 fm, rDR 1.92 fm
rF 1.6 fm, rDR 1.9 fm
rF 1.6 fm, rDR 1.9 fm
rF 1.57 fm, rDR 1.7 fm
rF 1.62 fm, rDR 1.76 fm
40
Complete fusion and total reaction cross sections
41
BreakupThreshold Anomaly. 9Be 64Zn
VF
WT
WF
WDR
VB17 MeV
VDR
42
Effect of breakup on fusion
9Be64Zn
R(VDR)
R(WDR)
R(VDR,WDR)
VB 17 MeV
Ri sF ( i ) / sF ( VDR WDR 0 ) ,
iVDR, WDR, VDRWDR
43
Conclusions

• In this model for the nuclear system under study,
  the absorptive potentials
• should extend to larger distances than usually
  assumed in order to
• simultaneously fit elastic scattering, fusion and
  total reaction cross sections.

The energy dependence of the fusion and direct
reaction potentials seem to show the presence
of the breakup threshold anomaly
The effect of breakup reactions induced by the
weakly bound projectile 9Be on fusion has been
studied in terms of the surface potentials VDR
and WDR and shows a strong suppression around
the Coulomb barrier.