why ? test the models at their limits - · test the models at their limits ... comparison with the...
TRANSCRIPT
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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 ?
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Tin Isotopes
measured masses
com
paris
onw
ithth
em
odel
ofM
olle
rand
Nix
(M
eV)
http://www-csnsm.in2p3.fr/
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measured masses
com
paris
onw
ithth
em
odel
ofM
olle
rand
Nix
(M
eV)
Tin Isotopes
http://www-csnsm.in2p3.fr/
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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
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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 ?
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Si
CsI
DEMON
12C
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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 !
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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
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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
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Energy regimes
< 5 MeV/nucleon
5-70 MeV/nucleon
100-1000 MeV/nucleon
REX-ISOLDE
GANIL SISSI-SPIRAL
GSI-FRS
Transfer
knockout
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Nuclear structure at the driplines
stable nuclei
known nuclei
skinshalos
superheavys
super novae
the magic numbersevolution of
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Halo nuclei
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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
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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
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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
????
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(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
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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
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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
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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
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Molecular states
Ne
9 31
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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
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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
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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
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Molecular states of 10,12Be
Analogy with one nucleon knockout
σ-α → Spectroscopic factorMomentum distribution p → l
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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
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Shell evolution
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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
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2 8
2028
50
MagicNumbers
MagicNumbers
prot
ons
num
ber
Neutrons number
50
Weakening of shell N=20, 28already observed far from stability
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N = 20
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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 ) ?
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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)
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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
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Is it so boring ?
Vladimir,
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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
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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
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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
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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)
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Tools for structure studies
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Halo nucleiHalo nuclei
11Be10Be
n
11Li9Lin
n
6Heαn
n
6He, 11Li, 14BeBorroméen
17B, 19C, 8B one neutron, one proton halo22C, 17Ne borromean
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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
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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
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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
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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
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♦ 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
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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-)
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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)
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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,
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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
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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