Nuclear structure

Test the models at their limits

High spin nuclei: to explore the nuclei at the limits of the angular momentum.

Heavy and super heavy nuclei: to explore the nuclei at the limits in charge.

Exotic nuclei: to explore the nuclei at the limits in isospin.

Why ?To identify the different phenomena at the origin of the nuclear propertiesTo develop models able to describe these phenomena

Development of exotic beams since 25 years

Development of new experimental devices+

How ?

Tin Isotopes

measured masses

com

paris

onw

ithth

em

odel

ofM

olle

rand

Nix

(M

eV)

http://www-csnsm.in2p3.fr/

measured masses

com

paris

onw

ithth

em

odel

ofM

olle

rand

Nix

(M

eV)

Tin Isotopes

http://www-csnsm.in2p3.fr/

S. Pieper et al., Phys. Rev. C64, (2001), 014001

2 body interaction

3 body interaction

Exp

Ener

gy(M

eV)

Binding energies of ground states and of the first excited states

S. Pieper

Predictions for a 4-neutron system

" I show that it does not seem possible to change modern nuclearHamiltonians to bind tetraneutron without destroying many othersuccessful predictions of those Hamiltonians.

This means that, should a recent experimental claim of a boundtetraneutron be confirmed, our understanding of nuclear forces will have to be significantly changed. "

S. C. Pieper, PRL 90, 252501, June 2003

a lot of experiments since the 60's try to probe or notthe existence of a tetraneutron .

4n ?

Si

CsI

DEMON

12C

The 14Be break-up experiment

F. M. Marques et al., PRC 65, 044006 (2002)

14Be 10Be + 4 n

10Be

4n ?

14Be 12Be + n

4n = The quest of the holy Graal for physicistsin structure !

Tools for structure studies

- Tools depends on the beam energy and intensity

- Different ways to study the same problem !

ex: shell closures with mass measurements, inelastic scattering, coulex, transfer reactions etc....

- Different ways to confirm a new feature !

one information --> one piece of the puzzle in structure ....+ complementary informations

BUT

Tools for structure studies

Existence one (preferably 2)

Mass measurements > a few per day

β decay > a few per min E(2+)

Inelastic scattering > 10 pps Collectivity 2+, 3- states

Breakup or knockout > 102 pps Single particles properties

Transfer Reactions >104 pps Single particles properties, clustering

Coulomb excitation > 102 pps B(E2)

Com

plex

ity

Energy regimes

< 5 MeV/nucleon

5-70 MeV/nucleon

100-1000 MeV/nucleon

REX-ISOLDE

GANIL SISSI-SPIRAL

GSI-FRS

Transfer

knockout

Nuclear structure at the driplines

stable nuclei

known nuclei

skinshalos

superheavys

super novae

the magic numbersevolution of

Halo nuclei

Rutherford's experimentRutherford's experiment

Measurement of reaction cross sectionsI. Tanihata et al., Phys. Rev. Lett. 55 (1985) 2676

Size of nucleiSize of nuclei

22

22

88

88

Neutrons number

Pro

trons

num

ber

σR = π (Rproj + Rtarget)2

Halo nucleiExotic nucleianormally big 1.18 A1/36He

Halo nucleiHalo nuclei11Li

9Lin

n

6Heαn

n

17B, 19C, 8B one neutron, one proton halo

22C, 17Ne borromean

Borromean

6He 8He

12C

14Be12Be

n n

Heisenberg's principle

∆x ∆p ≥ h

Ground state wave function of 6He

6He binding energy well reproduced with a t+t configuration

A. Csoto, PRC 48 (1993) 165

M. Zhukov et al. Phys. Rep. 231 (1993) 151

<6He|4He + n + n > 1.10 to 1.56

6Li(p,3He)αAnalogy with 6Li

clusters α+d and 3He+tsame importance !!

t tα

n

n

Microscopic calculations

K. Arai et al., PRC 59 (1999) 1432

Yu. F. Smirnov, PRC 15 (1977) 84<6He|t + t > 0.44 to 1.77

????

(4He + 2n) + p α + t

( t + t ) + p t + α

6He + p α + t

t t

αn

n

θθcmcm degdeg

2n

dd σσ/d/dΩΩ

mb

mb //

srsr

t

Search for t+t clustering in 6He L.G et al., NPA, 378 (2004) 426c

Investigation of 6He cluster structures L.G et al., accepted in PRC

dσ/dΩ

(mb/

sr)

θcm (deg)

transfert 2n

transfert t

6He(p,t)4He 150 MeV

transfert 2n+t

Ground state wave function of 6He

t+t exist but very small !!

α + t

6He + p

2n

t 5He + d

n

n

2n2+

états du continuum6He* + p

Coupled channels calculations

Ground state wave function of 8He

♦ 6He(2+) is predominant

in the 8Heg.s wave function

A. Korsheninnikov, PRL 90 (2003) 082501

Active Target Maya

lower energy higher cross sections

but optical potentials ?

compound nuclei ?

6He(2+): 66% 6Heg.s: 33%

8He(p,t)6Heg.s , 8He(p,t)6He2+@ 60 MeV, Riken

@ 3.9 MeV, Ganil/SPIRAL with MAYA

6He(2+), 6Heg.s same weight than Riken

8He(p,t)6Heg.s 3.9 MeV

dσ/dΩ

(mb/

sr)

θcm (deg)

W. Mittig, Ch. E Demonchy thesis

W. Mittig, C.E. Demonchy et al., GANIL

Active Target

MAYA

- detection gazalso used as a target

very efficient

Low detection threshold for particles

used as a thick target

Large angular acceptance

Important reaction energy range

Experiment- elastic resonance scattering

IAS of 9He8He+p- 26F(d,3He)25O

Actar Project: GSI involved

Molecular states

Ne

9 31

Wolfram von Oertzen, private comm.K. Ikeda, Suppl. Prog. Theor. Phys. 464, 1968

Be8

C

C12

7.27

C

16O

O

7.16

14.44

C

Ne20

O

Ne

11.89

19.17

4.73

C

Mg24

O

CC

Ne

Mg

28.48

21.21

14.05

13.93

9.31

C

Si28

O

CC

Ne

C O

Mg

Si

31.19

38.46

24.03

23.91

19.29

16.75

9.98

Exci

tatio

n En

ergy

Mass Number

IkedaDiagramIkeda's diagramN=Z nuclei

12Be

n

n

α

n

n

α

Liaison π

New Structures New Structures

M. Freer et al., PRL 82, 7 (1999)

6He 6He

12Be

Exc

itatio

n E

nerg

y(M

eV)

J(J+1)

• Inelastic Experiments

AMD calculations Kanada-Enyo, Horiuchi et al.

Density

Molecular states in 10,12Be

Inelastic scattering

M. Freer et al., PRL 82, 1383 (1999)

Knockout

6He 6He

12Be

Exc

itatio

n en

ergy

(MeV

)

J(J+1)

Clustering

Test of a new method

10Be 12Be

6He 4He 8He 4He6He 6He

Collaboration CHARISSA:

N. Orr, M. Marques, LPC Caen M. Freer, Univ. de Birmingham

F. Carstoiu, Univ. de Buccarest

in the ground state

Clustering of excited states

Molecular states of 10,12Be

Analogy with one nucleon knockout

σ-α → Spectroscopic factorMomentum distribution p → l

4He

p en MeV/cN

bde

cou

ps

8He

p en MeV/c

Nb

de c

oups

12Be(12C,8He+4He) 492 MeV

Molecular states of 10,12Be

Analogy with one nucleon knockout

σ-α → Spectroscopic factorMomentum distribution p → l

Future

22O

20O

18C

16C

- 12C → α + 8Be

Test october 2005

-

Theory under progress ....Comparison with a Glauber's model

Shell evolution

Shell model ( ~1950):

Nucléon = independant particle move in an average potential created by the ensemble of the other nucleons

Reproduces many properties of the nuclei

Magic numbers : (2,8,20,28,50,82,…)

Shell model

1s1/2

1h

1s

1p

1d2s

1f2p

1g2d

3s

2p1/2

2p3/2

1f7/2

1g7/2

1p3/2

1p1/2

1d5/2

2s1/21d3/2

1f5/2

1g9/2

2d5/2

1h11/2

3s1/2

2d3/2

28

20

8

2

50

82

N=0

N=1

N=2

N=3

N=4

N=5

ħω

ħω

ħω

ħω

ħω

2

8

20

40

70

H.O. Surface correction spin-orbite

1s1/2

Maria Goeppert MayerJ. Hans D. Jensen

Nobel prize 1963Discovery of the magic numbers

2

8

20

40

2 8

2028

50

MagicNumbers

MagicNumbers

prot

ons

num

ber

Neutrons number

50

Weakening of shell N=20, 28already observed far from stability

N = 20

T. Otsuka et al., Phys. Rev. Lett. 87 (01) 082502

New magic numbers

- N = 34 neutron proton interaction πf7/2 - υf5/2

- N = 16 neutron proton interaction πd5/2 - υd3/2Experimental Evidence from - in beam fragmentation, PRC 69 (2004) 034312

- longitudinum momentum distribution

- Vστ monopole interaction: coupling of proton-neutron spin-orbit partners

but missing in n-rich nucleithe spin orbit partner of the valence neutrons are not occupied by protons

28O (N=20 ) ?

Evolution of magicity with increasing N/ZStudy of Z magic nuclei: O, Ca, Ni, Sn isotopic chains

N ∼ Z

Diffuse surfaceN >> Z

Dobaczewski et al., PRL 72, 981 (1994)

HO

40

70

40

70

50

82

N ∼ Z N >> Z

h11/2

g7/2d3/2s1/2d5/2g9/2

p1/2f5/2

h11/2d3/2s1/2g7/2d5/2

g9/2p1/2f5/2

N = 3

N = 4

N = 5

of spin orbit potentialweakening

ex: 68Ni (N=40) B(E2) small - magic nuclei ?

O. Sorlin et al., PRL 88, 092501 (1994)

Shopping List of Nuclei

SPIRAL II, FAIR > EURISOL

N = 16 24O, 25O, 25F, 26Ne

N = Z = 50 100Sn

Nickel isotopes chainZ = 28 56Ni........68Ni....... 78Ni

N = 40 N = 50

Calcium isotopes chainZ = 20 48Ca........54Ca....... 60Ca

N = 34 N = 40

N = 20 all nuclei in the region of 32Mg, called the magic inversion land

Is it so boring ?

Vladimir,

T. Otsuka et al., Phys. Rev. Lett. 87 (01) 082502 A. Ozawa et al., Phys. Rev. Lett. 84 (00) 5493

Modification de la structure en couches loin de la stabilité

Observation complémentaire:Augmentation des sections efficaces de réaction dans la même région de noyaux.

(N-Z)/21/23/25/27/29/2

2345

N = 16N = 34

30Si14 16

π υ1f5/2 1f5/2

1d5/2 1d5/2

2s1/22s1/2

2p1/2 2p1/22p3/22p3/2

1d3/2 1d3/2

1f7/21f7/2

8 8

2020

28 28

24O8 16

π υ1f5/2 1f5/2

1d5/2 1d5/2

2s1/22s1/2

2p1/2 2p1/22p3/22p3/2

1d3/2

1d3/21f7/21f7/2

8 8

1620

28 28

Modification de la structure en couches loin de la stabilité

—Inversion des couches 1p1/2 et 2s1/2 pour les noyaux riches en neutrons

J. Winfield et al, Nucl. Phys. A683(2001) 48

11Be(p,d)10Be

10Be(0+)x(2s)10Be(2+)x(1d)

Tools for structure studies

Halo nucleiHalo nuclei

11Be10Be

n

11Li9Lin

n

6Heαn

n

6He, 11Li, 14BeBorroméen

17B, 19C, 8B one neutron, one proton halo22C, 17Ne borromean

Faisceaux

68Ni : 105 pps rapport spiral II, p7

GANIL - SISSI fragmentation : (déjà mesurés)

GANIL - SPIRAL II :

16C 40 MeV/A : 18O 63 MeV/A + 9Be 800 mg/cm2 ----> 104 pps20O 43 MeV/A : 40Ar 77 MeV/A + 12C 360 mg/cm2 ----> 5 103 pps22O 46 MeV/A : 36S 77 MeV/A + 12C 540 mg/cm2 ----> 1200 pps25F 40 MeV/A : 36S 77 MeV/A + 12C 530 mg/cm2 ----> 200 pps

GANIL - SISSI fragmentation : (estimation code LISE)

18C 40 MeV/A : 40Ar 77 MeV/A + 12C 360 mg/cm2 ----> 3 103 pps

Fonction d’onde de l’6He: t + t ?

Energie de liaison de l’6He

A. Csoto, PRC 48 (1993) 165

reproduiteavec une configuration triton-triton

Analogie avec 6Li6Li(p,3He)α: clusters α+d et 3He+t

Sα-d 0.69S3He-t 0.44

(α + d) + p 3He + α

(3He+ t) + p α + 3HeM.F Werby et al., PRC 8 (1973) 106

6Li(p,3He)4He

Ep = 18.5 MeV

0 30 60 90 120 150 1800

2

θcm(deg)

Ep = 12 MeV

Ep = 14 MeV

Ep = 16 MeV

4

6

4

6

2

4

6

2

4

6

2

dσ/dΩ

mb/

sr

Calculs microscopiques

K. Arai et al., PRC 59 (1999) 1432

Yu. F. Smirnov, PRC 15 (1977) 84TISM: St-t = 1.77

RGM: St-t = 0.49

Sα-2n = 1.12

dσdΩ

dépend de TAB : élément de matrice de la réaction

A + a B + bB+x + a B + a+x

x: nucléon(s) transféré(s)

χaA+ ΦaΦA

post

DWBA

TAB = >< χbB- ΦbΦB WbB ΨaA

+

=WbB - UbBVbB

+ VxBVaB décrit la diffusion élastique de b+B

DWBA

ici: t, 2n

ΨCRC = Σi χit-pΦ i

t Φ ip

cible

projectile

( H-E )ΨCRC = 0

χ it-p

Résolution système + conditions asymptotiques Amplitudes de diffusion ,fab fbcSection efficace différentielle de la réaction

i=a,b,c… partitions de masseExemple: 6He + p, 5He + d, 4He + t

Projection

Système d’équations intégro-différentielles couplées reliant les inconnues

sur les différents états d’une partition de masse

Voies couplées

♦ Futur

22O

20O

18C

16C

4He

p en MeV/c

Nb

de c

oups

8He

p en MeV/c

Nb

de c

oups

12Be(12C,8He+4He) 492 MeV

Etats moléculaires du 10,12Be

- distributions expérimentalesdes fragments chargés

♦ Méthodep pet

- simulation Monte-Carlo:

- comparaison modèle de Glauber (F. Carstoiu)

convolution distributions moment théoriquesavec effets expérimentaux

Fonctions de corrélation

2 Events correlation

0.92 MeV

3.04 MeV

0+(g.s)

8Be 9Be

2+

8He4He

6He

6Li7Li

p d t

Energie CsI a.u

Tot

al st

rip

ener

g y( M

eV)

• x1, x2, y1, y2

(charge division)

F1 and F2

precise position

• px1, px2, py1, py2

(strip number)rough position

(x1,y2)(x2,y1)

(x1,y1)(x2,y2)

F1 (mm)

F2 (

mm

)

Excitation Energy (MeV

Cou

nts

4He + 4He

5/2-

2.43 MeV

8Be(0+)

8Be(2+)

9Be(5/2-)

8He(p,t)6Heg.s 24 MeV 8He(p,t)6He2+ 24 MeV

8He(p,d)7He 24 MeV8He(p,p)8He 24 MeV

dσ/dΩ

(mb/

sr)

dσ/dΩ

(mb/

sr)

dσ/dΩ

(mb/

sr)

dσ/dΩ

(mb/

sr)

θcm (deg)

θcm (deg)θcm (deg)

θcm (deg)

Dispositif expérimental

SPEG

MUST

6He

(CH2)3

4He

3H

Bruyères-le-Châtel

Détection: 4He et 3H

ou

ChICh. à dérive

Plastique

6He

Cible+ MUST

3H4He

6He + p 3H + 4He

Ganil

Collaboration:

Dapnia, IPNO,

6He(p,t)4He 150 MeV

Θlab 3H

MUST: α et t en coïncidence

Θcm: 82°-121° Θcm: 55°-77°

Θcm: 39°-54°Θcm: 18°-35°

Θla

b 4 H

e

bon accord entre les données obtenues avec SPEG et MUST

θcm (deg)

dans SPEG

dσ/dΩ

(mba

rn/s

tr)

α dans SPEG

α et t dans MUST t

SingleSingle--Neutron Neutron RemovalRemoval: p: p--sd shell sd shell

Expt Expt vv ’s Glauber ’s Glauber Theory Theory + Shell Model: + Shell Model: SauvanSauvan, et al., PRC (2004), et al., PRC (2004)

Momentum distribution

Heisenberg's principle

∆x ∆p ≥ h