Direct Reactions with Exotic Nuclei

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Direct Reactions with Exotic Nuclei
Angela Bonaccorso
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A.A. Ibraheem and A. Bonaccorso, Recoil
effects on the optical potentials of weakly
bound nuclei Nucl. Phys. A748 (2005) 414.
A. Bonaccorso and F. Carstoiu Optical potentials
of halo and weakly bound nuclei Nucl. Phys. A706
(2002) 322.
GANIL data 49 A.MeV, P. Roussel-Chomaz et al.,
private communication.
10Be
11Be
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Plan of the talk

• 1. Present and future most challenging
  problems
• Determination of dripline position
• Nuclear (both stripping and diffraction) and
  Coulomb breakup _at_ all energies.
• Two nucleon breakup (two-n halo proton
  radioactivity)
• Elastic scattering including above channels.
• Transfer Fusion _at_ barrier energies.
• 2. Illustration of reaction mechanisms

• 3. Review of numerical vs analytical models.
• Numerical
• CDCC (Sakuragi, Kamimura, I.Thompson),
• Full time dep. Schrödinger eq. with wave packet
  evolution (Yabana),
• With classical traject. (Bertulani,
• Capel Baye , Bertsch Esbensen).
• Analytical or semi-phenomenological
• Sudden (Hansen, Carstoiu).
• Eikonal (Yabana-Ogawa-Suzuki,
• Tostevin, Carstoiu).
• Transfer to the continuum, projectile
  fragmentation (G. Blanchon, D.M. Brink,
  A.Garcia-Camacho , N. Vinh Mau, A.B).

Observables measured calculated ---gt structure
information extracted.
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sudden vs final state interaction
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NN2006, Rio de Janeiro.
Reaction mechanism determination via n-core
coincidences
11Be 41 A.MeV
Barranco, Vigezzi, Broglia, PLB 1996
Coulomb breakup
Nuclear breakup
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11Be a test case for the projectile
fragmentation model
11Be12C _at_ 67A.MeV
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How to treat theoretically

• Nuclear breakup with final state interaction with
  target and core.
• Coulomb breakup (recoil effects).
• Both to all orders and full multipole expansion (
  for Coulomb potential) including coupling and
  interference effects.

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Seeking a clear physical interpretation of DWBA
(Brink et al. since 1978 H. Hasan). similar
to Alder Winther for Coulomb excitations.-
Transfer between bound states and spin coupling
(L. Lo Monaco, I. Stancu, H. Hashim , G.
Piccolo, 1985).- Transfer to the continuum
(1988). - Coulomb breakup to all orders and
coupled to nuclear breakup interference
effects. (J. Margueron, 2002). - Full multipole
expansion of Coulomb potential, proton breakup
(A. Garcia-Camacho, 2005/2006). - Projectile
fragmentation (G. Blanchon, 2005/06).
Analytical methods for transfer and breakup
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TRANSFER Stripping Diffraction Overlap of
momentum distribution (Fourier transforms)
INELASTIC Diffraction Fourier transform of the
overlap
Broglia and Winther book
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Projectile fragmentation a model for diffractive
breakup in which the observable studied is the
n-core relative energy spectrum and its resonances
Transf.
Inel.
cf.
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Differences

• Transfer to the continuum.
• Long range form factor.
• Overlap of momentum distributions
• On shell n-N S-Matrix

• Projectile fragmentation.
• Short range form factor.
• Momentum distribution of overlap
• Off-the-energy-shell n-N S-matrix

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Projectile fragmentation ---gt Dripline position
from bound nuclei to nuclei unstable by
neutron/proton decay.

• Neutron - core potential must be studied in order
  to understand borromean nuclei.
• 11Li , 14Be and 13Be
• From structure theory point of view
• S 1/2 g.s? relevant p and d components ? Core
  excitation effects?
• From reaction theory point of view
• i) Scattering with threshold resonances.
• ii) Sudden approximation and one- or two step
  processes.

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13Be an example of creation by the reaction
mechanism

• transfer to the continuum 12Be (d,p) RIKEN
• (Korsheninnikov) (1995).

• GSI (U. Datta Pramanik)( 2004).
• Unpublished

• 14B fragmentation GANIL (Lecouey, Orr) (2002).

14B (12C,X) 12Ben
H. Simon et al. N.P.A734 (2004) 323, and
private communication.
12Be (d,p)
G. Blanchon, A. Bonaccorso and N. Vinh
Mau Unbound exotic nuclei studied by transfer to
the continuum reactions Nucl. Phys. A739 (2004)
259.
14Be (12C,X) 12Ben
G. Blanchon, A. Bonaccorso, D. M. Brink,
A.Garcia-Camacho and N. Vinh Mau Unbound exotic
nuclei studied by projectile fragmentation
reactions. submitted to NPA
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Resumee13Be has been obtained from

• transfer to the continuum 12Be (d,p) RIKEN
  (Korsheninnikov) (1995).
• 14B fragmentation GANIL (Lecouey, Orr) (2002).
• GSI
  (U. Datta Pramanik)( 2004).
• 14Be nuclear breakup , GSI (Simon), 287AMeV,
  n-core angular correlations
• 14Be nuclear and Coulomb breakup GANIL
• (K. Jones thesis, 2000).
• 14C 11B multinucleon transfer (Berlin Group
  ,1998).
• 18O fragmentation MSU (Thoennessen, 2001) n-core
  relative velocity spectra.
• 14Be nuclear breakup RIKEN (Nakamura, Fukuda)
  (2004).

Transfer to the continuum and projectile
fragmentation Do they convey the same
information? the same n-core phase shifts?
Is the overlap of resonances the same?
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.
.
Breakdown of shell closure
.
.
.
.
d5/2
.
.
d5/2
d5/2
.
.
. .
.
.
.
p1/2
p1/2
p1/2
a1
a2
a3
2s
2s
2s
p3/2
p3/2
p3/2
1s1/2
1s1/2
1s1/2
.7
.6
12Be g.s. ( 0) is not a GOOD CORE
14Be g.s. 0 (?)
14B g.s. 2- p p3/2n 2s
.
inversion
threshold
A.Navin et al, PRL85,266 (2000)
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Potential corrections due to the
particle-vibration coupling (N. Vinh Mau and J.
C. Pacheco, NPA607 (1996) 163.
also T. Tarutina, I.J. Thompson, J.A.
Tostevin NPA733 (2004) 53 ) can be modeled as
U( r ) VWS Vso dV
dV ( r ) 16 a e(r-R)/a / (1e(r-R)/a)4
n12Be
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Bound to unbound transitions
Results
sudden q0
sudden
Einc independent ?if important
check of sudden approximation
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Final s-state continuum vs bound
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Peak positions of possible continuum s-states in
13Be are not close enough to thereshold to make
accurate predictions by the
effective range theory to 10 order higher
orders needed
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Nucl. Phys. A (2007)
Core excitation via imaginary potential wash out
d-resonance effect
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10Li 1) virtual state sudden approach OK 2)
evidence for a d5/2 resonance
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Consistent results only if

• All bound to continuum transitions are considered
  (final state effects vs. sudden).
• Correct form factor.
• Optical model phase shifts.
• Final state interaction effect seems MORE
  important than sudden effect for not very
  developed haloes

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Motivation
A. Gade et al.
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Proton breakup to all orders and all multipoles
in the Coulomb potential
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CDCC Y. Sakuragi, Ph.D thesis, Kyushu
Univ.1985.M. Yahiro, Ph.D thesis, Kyushu Univ.
1985.M. Kamimura, M. Kawai I.Thompson, F. Nunes
et al.
Calculates elastic breakup only, BUT both nuclear
and Coulomb consistently. Includes core
deformations. Most often used in proj. reference
frame. Can use only REAL, non energy dependent
BUT l -dependent n-C interactions, while n-T and
C-T can be complex. Observables obtained n-C
relative energy spectra, core angular
distributions, sometimes core momentum
distributions, total cross sections. Neutron-angul
ar distributions ? Numerical accuracy? Predictive
power?
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Time dependent Schrödinger eq.for the nucleon
(Yabana Co., Baye Co see Capel
talk.Bertulani, Bertsch Esbensen, Scarpaci
Chomaz et al.).
(with classical C-T trajectory).
Valid at high incident energies use classical
trajectory. Calculates similar observables as
CDCC (core angular distributions, n-core energy
distributions) in CB version (mainly Coulomb
breakup). In BE version core momentum
distributions are also obtained. Stripping?
Eikonal (Yabana, Ogawa, Suzuki, Bertsch
Esbensen, Carstoiu, Tostevin) elastic and
inelastic (absorptive) nuclear breakup provided
no-bound excited states. Total breakup cross
sections. In BBr, BBe neutron energy
conservation is included.
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Full time dependent Schrödinger eq. with wave
packet evolution (Yabana et al.).
Best hope method for future applications clear
physical interpretation. So far used to estimate
transfer and fusion at barrier energies. Shows
breakup presence. Uses real potentials. Needs
supercomputers for high energy/large impact
parameter calculations.
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Brasilian School
German School
C. Bertulani, G.Baur, S. Typel Coulomb
dissociation G.Baur et al. Stripping to the
continuum
M. Hussein, A. Kerman, Mc Voy direct
reactions F. Canto, R. Donangelo et al breakup
fusion, semiclassical models.
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Polish School
Unify structure and reaction models
..via shell model in the continuum
..

• Three body specialists

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EURISOL User Group http//www.eurisol.org/site01
/indice.php?pag1s
CONCLUSIONS
Our field is exciting and expanding RIA(?),
EURISOL, SPIRAL2, FAIR, MAFF, RIKEN, HIE-ISOLDE,
SPES, EXCYT, etc. will provide more and more
data which will make all of us (experimentalists
and theoreticians) happily working hard for many
years to come.
Coordinator A.B. bonac_at_df.unipi.it
Many theoreticians are involved and more are
invited to join.
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Fourier transform of the overlap
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s-state potentiallong range added
p-state potentiallong range subtracted
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REACTION MECHANISMS

• Transfer to the continuum dynamics (knockout)

x
.
P
before collision
Vi(r)
k1
z
vz
bc
Vf(r)
T
k
.
P-1
k2
after
k2 -k1k ? f-?imv2/2 ?fopt gt0 for halo
T1
diffraction and stripping
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2. Projectile fragmentation
n-core final state interaction
x
14Be 14B
.
.
before
Vi(r)
z
vz
bc
.
Vf(r)
T
13Be
.
Core
after
T
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3. Coulomb Breakup core recoil
x
P
.
before collision
Vi(r)
z
vz
bc
Vf(r)
T
.
P-1
proton halo feels an effective Coulomb barrier
T
after