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Unbound exotic nuclei studied via projectile fragmentation

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Scuola di Dottorato G. Galilei, Pisa.

Universita` di Paris-Sud, Orsay.

Unbound exotic nuclei studied via projectile fragmentationOptical 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

1. Illustration of reaction mechanisms

Nuclear (both stripping and diffraction) and Coulomb breakup.

Spectroscopy of unbound nuclei

Determination of dripline position

Plan of the talkObservables measured & calculated, structure information extracted.

final state interaction

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 1978H. 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).

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.

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

Differences11Be: 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 ofcreationby 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) 12Be+n

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) 12Be+n

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

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+ 11Bmultinucleon transfer: (Berlin Group ,1998).
- 18O fragmentationMSU (Thoennessen, 2001) n-core relative velocity spectra.
- 14Benuclear 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?

.

Breakdown of shell closure*

.

.

.

.

d3/2

2s

d5/2

p1/2

p3/2

1s1/2

.

.

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

It is not a GOOD CORE

12Be g.s. = 0+

14Be g.s. = 0+ (?)

14B g.s. = 2- =p p3/2+n 2s

.

inversion

threshold

*A.Navin et al, PRL85,266 (2000)

2s

d5/2

p1/2

inversion

threshold

p3/2

1s1/2

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 ) = 16a e(r-R)/a / (1+e(r-R)/a)4

n+12Be:

Results

sudden q=0

sudden

Einc: independent

if : important

check of sudden approximation

1

2

+

ro k

k cotan = -

as

2

Peak positions of continuum states are not low enough

to make accurate predictions by the

effective range theory (10 order)

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

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.

Brasilian 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…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

EURISOL, task 10: Physics & Instrumentations

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.

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]

From the book of Daniel in the Bible (reported by Goldstein: Classical Mechanics)

THANKS TO ALL OF YOU FOR YOUR WORK WITHOUT

WHICH THIS TALK WOULD NOT HAVE BEEN POSSIBLE,

AND FOR YOUR ATTENTION.

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.

s-state potential:long range added

p-state potential:long range subtracted

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 -k1=k

f-i=mv2/2 fopt>0 for halo

T+1

diffraction and stripping

2. Projectile fragmentation

n-core final state interaction

x

14Be

14B

.

.

before

Vi(r)

z

vz

bc

.

Vf(r)

T

13Be

.

Core

after

T

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

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