Unbound exotic nuclei studied via Unbound exotic nuclei studied via projectile fragmentationprojectile fragmentation

Guillaume BlanchonScuola di Dottorato G. Galilei, Pisa.

Universita` di Paris-Sud, Orsay.

A.A. Ibraheem and A. Bonaccorso, Recoil effects on the optical potentials of weakly bound nucleiNucl. Phys. A748 (2005) 414.

A. Bonaccorso and F. CarstoiuOptical potentials of halo andweakly bound nucleiNucl. Phys. A706 (2002) 322.

GANIL data 49 A.MeV, P. Roussel-Chomaz et al., private communication.GANIL data 49 A.MeV, P. Roussel-Chomaz et al., private communication.

10Be

11Be

Plan of the talkPlan of the talk 1. Illustration of reaction mechanisms

• Nuclear (both stripping and diffraction) and

Coulomb breakup.• Spectroscopy of unbound nuclei• Determination of dripline positionDetermination of dripline position

Observables measured & calculated, structure information Observables measured & calculated, structure information extractedextracted.

sudden vssudden vsfinal state interactionfinal state interaction

Nuclear breakup

Coulomb breakup

11Be 41 A.MeV

Barranco, Vigezzi, Broglia, PLB 1996

NN2006, Rio de Janeiro. NN2006, Rio de Janeiro.

Reaction mechanism determination via n-core coincidencesReaction mechanism determination via n-core coincidences

How to treat theoreticallyHow 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.

Seeking a clear physical interpretation of DWBA (BrinkBrink et al. since et al. since 19781978 H. Hasan).

similar to Alder& Winther for Coulomb excitationssimilar 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).

d2bc Pel (bc )Ptr(bc );

Ptr | A |2 A 1

i dt f (r, t)V2 i(r R(t), t)

Analytical methods for transfer and breakupAnalytical methods for transfer and breakup

INELASTICINELASTICDiffractionDiffractionFourier transform of the overlap

TRANSFERTRANSFERStripping & Stripping & DiffractionDiffractionOverlap of momentum distribution(Fourier transforms)

Broglia and Winther bookBroglia and Winther book

cf.

Transf.

Inel.

Projectile fragmentation: a model for diffractive breakup in which the Projectile fragmentation: a model for diffractive breakup in which the

observable studied is the n-core relative energy spectrum and its observable studied is the n-core relative energy spectrum and its

resonancesresonances

DifferencesDifferences

• Transfer to the Transfer to the continuum.continuum.

• Long range form factor.• Overlap of momentum

distributions• On shell n-N S-Matrix

• Projectile Projectile fragmentation.fragmentation.

• Short range form factor.• Momentum distribution

of overlap• Off-the-energy-shell n-N

S-matrix

11Be+12C @ 67A.MeV

G. Blanchon et al., to be published in NPA

11Be: a test case for the projectile fragmentation model

• 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.

Dripline positionDripline position: from bound nuclei to nuclei unstable : from bound nuclei to nuclei unstable by neutron/proton decay.by neutron/proton decay.

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

14B (12C,X) 12Be+n

14Be (12C,X) 12Be+n

H. Simon et al. N.P.A734 (2004) 323, and private communication.

G. Blanchon, A. Bonaccorso, D. M. Brink, A.Garcia-Camacho and N. Vinh MauUnbound exotic nuclei studied by projectile fragmentationprojectile fragmentation reactions.submitted to NPA

1313BeBe:: an example ofan example of creationcreation by the reaction mechanismby the reaction mechanism

G. Blanchon, A. Bonaccorso and N. Vinh MauUnbound exotic nuclei studied by transfer to the continuumtransfer to the continuum reactionsNucl. Phys. A739 (2004) 259.

12Be (d,p)

•1414BB fragmentation: GANIL (Lecouey, Orr) (2002).

•transfer to the continuumtransfer to the continuum: 12Be (d,p) RIKEN

(Korsheninnikov) (1995).

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

• 1414BB fragmentation: GANIL (Lecouey, Orr) (2002).

• GSI (U. Datta Pramanik)( 2004).

• 1414BeBe nuclear breakup , GSI (Simon), 287AMeV, n-core angular correlations

• 1414BeBe nuclear and Coulomb breakup: GANIL

(K. Jones thesis, 2000).

• 1414C+ C+ 1111BB multinucleon transfer: (Berlin Group ,1998).

• 1818O fragmentationO fragmentation MSU (Thoennessen, 2001) n-core relative velocity spectra.

• 1414BeBe nuclear breakup: RIKEN (Nakamura, Fukuda) (2004).

Resumee:Resumee:

1313Be Be has been obtained from:has been obtained from:

Transfer to the continuum and projectile fragmentationTransfer to the continuum and projectile fragmentation Do they convey the same information?…Do they convey the same information?… the same n-core phase shifts?the same n-core phase shifts? Is the overlap of resonances the same?Is the overlap of resonances the same?

2s

d5/2

p1/2

p3/2

1s1/2

2s

d5/2

p1/2

p3/2

1s1/2

d5/2

p1/2

2s

p3/2

1s1/2

.. ... .

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

It is not a GOOD CORE

12Be g.s. = 0+ 14Be g.s. = 0+ (?)

. ...

. . . .

d3/22sd5/2p1/2

p3/2

1s1/2

inve

rsio

n

threshold

.

.

Breakdown of shell closureBreakdown of shell closure**

*A.Navin et al, PRL*A.Navin et al, PRL8585,266 (2000),266 (2000)

Potential corrections due to the particle-vibrationcoupling (N. Vinh Mau and J. C. Pacheco, NPA607 (1996) 163.

also T. Tarutina, I.J. Thompson, J.A. Tostevin NPA733 (2004) 53 )…can be can be modeled modeled as: as:

n+12Be: d3/22sd5/2p1/2

p3/2

1s1/2

inve

rsio

n

threshold

U( r ) = VWS + Vso + V

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

Bound to unbound transitions

Einc: independent

if : important

check of sudden approximationcheck of sudden approximation

Results

sudden q=0 sudden

Final s-state: continuum vs bound

effective range theory (10 order)

k cotan = - 1as

+ 12

ro k2

Peak positions of continuum states are not low enough Peak positions of continuum states are not low enough to make accurate predictions by theto make accurate predictions by the

in preparation, private communicationin preparation, private communication.

Core excitation via imaginary potential wash out d-resonance effect

Consistent results only if: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 nucleiAll orders breakup of heavy exotic nuclei

MotivationMotivation

A. Gade et al.

Proton breakup to all orders and all Proton breakup to all orders and all multipoles in the Coulomb potentialmultipoles in the Coulomb potential

to be submitted

CDCC 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,only, BUT both nuclear and Coulomb consistently. Includes core deformations.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 Time dependent Schrödinger eq.for the nucleon (Yabana & Co., Baye & Co {see Capel talk}.Bertulani, Bertsch &

Esbensen, Scarpaci & Chomaz et al.).

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??

EikonalEikonal :(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.

((with classical C-T trajectorywith classical C-T trajectory).).

Full time dependent Schrödinger eq. with wave Full time dependent Schrödinger eq. with wave

packet evolutionpacket evolution (Yabana…see his talk).

Best hope method for future applications: clear physicalBest hope method for future applications: clear physicalinterpretation.interpretation.

So far used to estimate transfer and fusion at barrier energies.So far used to estimate transfer and fusion at barrier energies.Shows breakup presence. Uses real potentials.Shows breakup presence. Uses real potentials.

Needs supercomputers for high energy/large impact parameterNeeds supercomputers for high energy/large impact parametercalculations.calculations.

Brasilian SchoolBrasilian SchoolM. Hussein, A. Kerman, Mc Voy: direct reactionsdirect reactionsF. Canto, R. Donangelo et al: breakup & fusion,semiclassical semiclassical models…see talks.

C. Bertulani, G.Baur, S. Typel: Coulomb dissociationG.Baur et al. : Stripping to the continuum

German SchoolGerman School

• Polish SchoolPolish School…..via shell model in the continuum…see Ploszajczak talk

• Three body specialistsThree body specialists

Unify structure and reaction modelsUnify structure and reaction models

…..

...see talks by Jensen and Garrido

EURISOL, task 10: Physics & Instrumentations

Task leader: Robert Page rdp@ns.ph.liv.ac.uk

or Nigel Orr orr@lpccaen.in2p3.fror A.B. angela.bonaccorso@pi.infn.it

Many theoreticians are involved and more are invited to join.

www.lnl.infn.it/eurisol/

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)happilyhappily working hard for many years to come.

CONCLUSIONSCONCLUSIONS

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

I wish to thank You, Good of my ancestors,I wish to thank You, Good of my ancestors,because you have given me wisdombecause you have given me wisdomand capacity of understanding.and capacity of understanding.You have revealed to me the mysteriesYou have revealed to me the mysteriesfor which I have begged You.for which I have begged You.

THANKS TO ALL OF YOU FOR YOUR WORK WITHOUTTHANKS TO ALL OF YOU FOR YOUR WORK WITHOUTWHICH THIS TALK WOULD NOT HAVE BEEN POSSIBLE,WHICH THIS TALK WOULD NOT HAVE BEEN POSSIBLE,AND FOR YOUR ATTENTION.AND FOR YOUR ATTENTION.

Fourier transform of the overlap

p-state potential:long range subtracted

s-state potential:long range added

bc

x

z

P

T

vz

Vi(r)

Vf(r)

.before collision

after

T+1

. P-1

1.1. Transfer to the continuum dynamicsTransfer to the continuum dynamics (knockout)

k1

k2

k2 -k1=k

f-i=mv2/2 fopt

>0 for halo

k

REACTION MECHANISMSREACTION MECHANISMS

diffraction and stripping

bc

x

z

14Be14B

T

vz

Vi(r)

Vf(r)

n-core final state interaction

.before

afterT

.Core

.

13Be

.

NN2006, Rio de Janeiro. NN2006, Rio de Janeiro. 2. Projectile fragmentation2. Projectile fragmentation

bc

x

z

P

T

vz

Vi(r)

Vf(r)

.before collision

after T

P-1

3. Coulomb Breakup : core recoil3. Coulomb Breakup : core recoil

.

proton halo feels an effective Coulomb barrier

NN2006, Rio de Janeiro. NN2006, Rio de Janeiro.

energy spectra n-core and n-target

Fukuda, Nakamura et al.Capel & Baye et al.

208Pb target

12C target