Transcript Status of art of direct reaction calculations for

Guillaume Blanchon
Scuola di Dottorato G. Galilei, Pisa.
Universita` di Paris-Sud, Orsay.
Unbound exotic nuclei studied via
projectile fragmentation
A. Bonaccorso and F. Carstoiu
Optical potentials of halo and
weakly bound nuclei
Nucl. Phys. A706 (2002) 322.
A.A. Ibraheem and A. Bonaccorso,
Recoil effects on the optical
potentials of weakly bound nuclei
Nucl. Phys. A748 (2005) 414.
GANIL data 49 A.MeV, P. Roussel-Chomaz et al., private communication.
10Be
11Be
Plan of the talk
1. Illustration of reaction mechanisms
• Nuclear (both stripping and diffraction) and
Coulomb breakup.
• Spectroscopy of unbound nuclei
• Determination of dripline position
Observables measured & calculated, structure information
extracted.
sudden vs
final state interaction
NN2006, Rio de Janeiro.
Reaction mechanism determination via n-core coincidences
11Be
41 A.MeV
Barranco, Vigezzi, Broglia, PLB 1996
Coulomb breakup
Nuclear breakup
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.
Analytical methods for transfer and breakup
Seeking a clear physical interpretation of DWBA (Brink et al. since
1978 H. Hasan).
1
   d 2bc Pel (bc )Ptr (bc ); Ptr | A |2 
 A   dt  f (r,t) V2 i (r  R(t),t)
i
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).
TRANSFER
Stripping &
Diffraction
Overlap of
momentum
distribution
(Fourier
transforms)
INELASTIC
Diffraction
Fourier transform
of the overlap
Broglia and Winther book
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.
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
11Be:
a test case for the projectile fragmentation model
11Be+12C
@ 67A.MeV
G. Blanchon et al., to be published in NPA
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.
13Be:
an example of creation by the reaction mechanism
•transfer to the continuum: 12Be (d,p) RIKEN
(Korsheninnikov) (1995).
•14B
fragmentation: GANIL (Lecouey, Orr) (2002).
•GSI (U. Datta Pramanik)( 2004).
•Unpublished
14B (12C,X) 12Be+n
12Be
H. Simon et al. N.P.A734 (2004) 323,
and private communication.
(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.
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
14Be (12C,X) 12Be+n
Resumee:
13Be
•
•
•
•
•
•
•
•
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?
a1
.... .
.7
d5/2
p1/2
2s
p3/2
Breakdown of shell closure*
+a2
. .. .
1s1/2
..
d5/2
p1/2
2s
p3/2
1s1/2
+a3
. .
..
d5/2
p1/2
2s
p3/2
1s1/2
.6
It is not a GOOD CORE
- =pp3/2+n 2s
=
2
g.s.
.
12Be
g.s.
= 0+
14Be
+ (?)
=
0
g.s.
d3/2
2s
d5/2
p1/2
threshold
*A.Navin et al, PRL85,266 (2000)
p3/2
1s1/2
inversion
14B
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 / (1+e(r-R)/a)4
n+12Be:
d3/2
2s
d5/2
p1/2
threshold
p3/2
1s1/2
Results
sudden
q=0
check of sudden approximation
sudden
Einc:
independent
 : important
Final s-state: continuum vs bound
Peak positions of continuum states are not low enough
to make accurate predictions by the
effective range theory (10 order)
k cotan d = -
1 +
as
1 r k2
o
2
in preparation, private communication.
Core excitation via imaginary potential wash
out d-resonance effect
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
All orders breakup of heavy exotic nuclei
Motivation
A. Gade et al.
Proton breakup to all orders and all
multipoles in the Coulomb potential
to be submitted
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-angular distributions ?
Numerical accuracy? Predictive power?
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 C&B version (mainly Coulomb breakup).
In B&E 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 B&Br, B&Be neutron energy
conservation is included.
Full time dependent Schrödinger eq. with wave
packet evolution (Yabana…see his talk).
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.
German School
C. Bertulani, G.Baur, S. Typel: Coulomb dissociation
G.Baur et al. : Stripping to the continuum
Brasilian School
M. Hussein, A. Kerman, Mc Voy: direct reactions
F. Canto, R. Donangelo et al: breakup & fusion,
semiclassical models…see talks.
Unify structure and reaction models
• Polish School
…..via shell model in the continuum…see Ploszajczak talk
…..
• Three body specialists
...see talks by Jensen and Garrido
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.
EURISOL, task 10:
Physics & Instrumentations
www.lnl.infn.it/eurisol/
Many theoreticians are involved and more
are invited to join.
Task leader: Robert Page [email protected]
or
Nigel Orr
[email protected]
or
A.B. [email protected]
THANKS TO ALL OF YOU FOR YOUR WORK WITHOUT
WHICH THIS TALK WOULD NOT HAVE BEEN POSSIBLE,
AND FOR YOUR ATTENTION.
From the book of Daniel in the Bible (reported by Goldstein: Classical
Mechanics)
I wish to thank You, Good of my ancestors,
because you have given me wisdom
and capacity of understanding.
You have revealed to me the mysteries
for which I have begged You.
Fourier transform of the overlap
s-state potential:long range added
p-state potential:long range subtracted
REACTION MECHANISMS
1. Transfer to the continuum dynamics (knockout)
x
before collision
Vi(r)
.
P
k1
vz
bc
Vf(r)
T
after
k2 -k1=k
 - =mv2/2
 opt >0 for halo
.
z
k
k2
T+1
P-1
diffraction and stripping
NN2006, Rio de Janeiro.
2. Projectile fragmentation
n-core final state interaction
.
x
14Be
.
before
Vi(r)
14B
vz
bc
Vf(r)
T
.
after
T
.
Core
z
13Be
NN2006, Rio de Janeiro.
3. Coulomb Breakup : core recoil
x
P
.
before collision
Vi(r)
vz
bc
Vf(r)
T
proton halo feels an effective
Coulomb barrier
after
T
.
z
P-1
208Pb
target
energy spectra n-core and n-target
12C
target
Fukuda, Nakamura et al.
Capel & Baye et al.