Shell effects in atomic nucleiPart 2: shapes and superheavy elements
Laurent Gaudefroy1, Alexandre Obertelli2
1CEA DAM, DIF, France2CEA Saclay, IRFU, France
protons
neutrons
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5028
28
50
82
2082
28
20
126
Changes in the nuclear shell structure
Lecture (part 1) given by Laurent Gaudefroy
Shapes of atomic nuclei
protons
neutrons
82
5028
28
50
82
2082
28
20
126
The vast majority of all nuclei shows a non-spherical mass distribution
Z, N = magic numbers
Closed shell = spherical shape
DeformedDeformed
SphericalSpherical
8
20
28
50
2
sng
le p
arti
cle
eneg
ies
elongation
Nilsson diagram
Oblate Prolate
Nuclear structure description framework[Addendum to yesterday’s lecture]
1- Shell-model: • nucleus described in the laboratory frame• the nucleus is described as a superposition of spherical configurations• « intrinsic deformation » is implicitely contained in correlations
2- Mean-field like description:• nucleus described in its intrinsic frame• « angular momentum » is not a good quantum number• intrinsic deformation is explicit
In this lecture, the deformed mean-field approach will be followed
Nilsson diagram
nlj=1f7/2 K=1/2-
K=3/2-
K=5/2-
K=7/2-
0
• core + single particle• short range & attractive int.
• Pauli : orbit repulsion
Shapes and “deformation” parameters
),()(1)( 0 YtaRtR
quadrupole
octupole
hexadecapole
cos220 a sin2
122222 aa
oblate non-collective
prolatecollective
2 : elongation
prolate non-collective
Lundconvention
spherical
oblatecollective
: triaxiality
Generic nuclear shapes can be described
by a development of spherical harmonics
deformation parameters
Tetrahedral Y32 deformation
Dynamic vibration
Static rotation
Triaxial Y22 deformation
Shapes and “deformation” from experiment
quadrupole
Quadrupole moments via low-energy Coulomb excitation Reorientation effect
projectile
target
Intrinsic quadrupole moment IKEMIKeQ )2(5
162/1
0
J=0+
J=2+
J=4+
J=6+
J=8+
even-even
)1(2
)(2
JJIE
)(
1
)2()2()()(
)1(
JE
J
JJEJEJEJE
J
Moment of inertia via rotational-band spectroscopy / model dependent
Coulomb field*
excitationde-excitation
photon
M. Girod, CEA
N=Z
Oblate deformed nuclei are far less abundant than prolate nucleiShape coexistence possible for certain regions of N & Z
Prolate
Quadrupole deformation of nuclei
Oblate Pb & Bi
N~Z
Fissionfragments
N~28 n-rich
actinides
Shape coexistence
oblate prolate
74Kr
M. GirodM. Bender et al., PRC 74, 024312 (2006)
0+0+2+
2+
4+
4+
6+
6+8+ Configuration mixing:
oblpro2
oblpro1
0cos0sin0
0sin0cos0
electric monopole (E0) transition
)(cossin0)0(0 2obl
2pro12 EM
SPIRAL beams 76Kr 5105 pps74Kr 104 pps4.7 MeV/u
[24°, 55°] [55°, 74°] [67°, 97°] [97°, 145°]
74Kr
Shape coexistence in light Krypton isotopesCoulomb excitation of 74,76Kr
78Kr68.5 MeV/u1012 pps
74Kr4.7 MeV/u104 pps
ECRISSPIRAL target
CIME
78Kr source
CSS1
CSS2
Shape coexistence in light Krypton isotopesQuadrupole moments
24.023.053.0
sQ
4.02.08.0
sQ
3.05.03.1
sQ
21.017.024.0
sQ
9.03.03.0
sQ
)2(
)4(
1
1
I
I
Fit matrix elements (transitional and diagonal)to reproduce experimental -ray yields (as function of ) 14 B(E2) values 5 quadrupole moments
E. Clément et al., PRC 75, 054313 (2007)
first reorientation measurement with radioactive beam SPIRAL1, GANIL (France), 2005
prolate oblateQs<0prolate
Qs>0oblate
experimental B(E2;) [e2fm4]
Comparison with ‘beyond-mean-field’ theory
K=2 vibration
E. Clément et al., PRC 75, 054313 (2007)
GCM (GOA) calculationq0, q2: triaxial deformationGogny D1S
M. Girod et al.
prolate oblate
GCM calculationaxial deformationSkyrme SLy6M. Bender et al.PRC 74, 024312 (2006)
Extreme shapes and intruder orbitalssi
ngle
-par
ticle
ene
rgy
(Wo
ods-
Sax
on)
quadrupole deformation
ND
235U
SD
152Dy
Z=48
HD
108Cd i13/2
(N+1) intruder normal deformed, e.g. 235U
(N+2) super-intruder Superdeformation, e.g. 152Dy, 80Zr
(N+3) hyper-intruder Hyperdeformation in 108Cd, ?
N+2 shell
N+3 shell
N shell
N+1 shell
Fermi level
En
erg
y
Deformation
The quest for high-spin superdeformation: 152Dy
first discrete superdeformed band energy spacing: E = 47 keV
TESSA3 (12 detectors), Daresbury (UK)P. Twin et al., Phys. Rev. Lett. 57, 811 (1986)
TESSA Ge array
Extracted moment of inertia
0+
2+
4+
6+
8+
even-even
)1(2
)(2
JJJE
20 years laterArgonne National Lab.Gammasphere108 Ge detectors
T. Lauritsen et al., Phys. Rev. Lett. 88, 042501 (2002)
The quest for high-spin superdeformation: 152Dy
Properties of the superdeformed band firmly established
Pushing the limits: The quest for nuclear hyperdeformation
Hyperdeformation favored at high-spin Competition with fission
Fission barrier vs. High spin
stable beam
n-rich beam
Need for intense neutron-rich beams Spiral2 : intense Kr and Sn neutron-rich beams
The AGATA germanium array
• 180 large volume 36-fold segmented Ge crystals in 60 triple-clusters • Digital electronics and sophisticated signal processing algorithms (PSA)• Operation of Ge detectors in position sensitive mode -ray tracking
> Efficiency ~ 40 %Huge gain in γγ, γγγ, … efficiency
> Cristal rate up to 50 kHz Allow larger beam intensity
http://www-w2k.gsi.de/agata/
New generation gamma-detection array based on the tracking method
Existence and structure of heavy elements
208Pb
238U~4.5 109 y
Limits of stability ?Shell structure ?Next magic number ?
Chart from http://www.nndc.bnl.gov/chart/
Synthesis of heavy elements in the universe
B. Pfeiffer et al., NPA (2001)
Cassiopea A supernova
Why SHE do not exist on earth ?1- not stable2- not formed during the r-process
Upper limit of stability : positron emission
Nuclei for Z larger than 173 become unstable against positron emission.
The most deeply bound electrons from the 1s1/2 shell reach an energy of -511 keV
W. Pieper, W. Greiner Z. Phys. A 218 (1968) 327J. Reinhardt et al, Z. Phys. A 303 (1981) 173
Limits of stability : fission
• B(A,Z) = av A volume – nuclear attractive force
- as A2/3 less binding at the surface
- ac Z2/A1/3 Coulomb – proton repulsion
- aa (A-2Z)2/A asymmetry
+δ A-1/3 pairing
R ab
V= 4/3R3
S=4R2
a=R(1+)b=R(1+)-1/2
V=4/3ab2
S=4R2(1+2/52+…)
1b2
a2
Surface prefers spherical nuclei Coulomb favours deformation
If BE(ε) -BE(ε=0)> 0: gain in energy with deformation fission
Limits of stability from liquid drop model
Stability = balance between surface and coulomb
• Fissility parameter x = Ecoulomb/ 2 Esurface
• ~ 1/50 Z2 / A• scaling of the fission barrier• x > 0.8 : no survival
• Possible definitions of SHE : No macroscopic fission barrierBf < 1 MeVx > 0.8
State of the art
Superheavy elements synthesized in laboratory
Shell effects balance fission andare responsible for the existence of superheavies!
Superheavy elements Z 104
H 1
Li 3
Be 4
Na 11
Mg 12
Fr 87
Ra 88
119
120
K 19
Ca 20
Rb 37
Sr 38
Cs55
Ba 56
Sc 21
Ti 22
Y 39
Zr 40
La57
Hf 72
V 23
Cr 24
Nb 41
Mo 42
Ta73
W 74
Mn 25
Fe 26
Tc 43
Ru 44
Re75
Os 76
Co 27
Ni 28
Rh 45
Pd 46
Ir77
Pt 78
Cu 29
Zn 30
Ag 47
Cd 48
Au79
Hg 80
Ds Rg 112
Ga 31
Ge 32
In 49
Sn 50
Tl81
Pb 82
113
114
115
As 33
Se 34
Sb 51
Te 52
Bi83
Po 84
Br 35
Kr 36
I 53
Xe 54
At85
Rn 86
116
117
118
F 9
Ne 10
Cl 17
Ar 18
N 7
O 8
P 15
S 16
B 5
C 6
Al 13
Si 14
He 2
Ce 58
Th 90
Pr 59
Pa 91
Nd 60
U 92
Pm 61
Np 93
Sm 62
Pu 94
Eu 63
Am95
Gd 64
Cm 96
Tb 65
Bk 97
Dy 66
Cf 98
Ho 67
Es 99
Er 68
Fm 100
Tm 69
Md 101
Yb 70
No 102
Lu 71
Lr 103
Lanthanides
Actinides
Ac 89
Rf 104
Db 105
Sg 106
Bh 107
Hs 108
Mt 109 110 111
Point of view of chemist :Actinides 90 Z 103Transactinides 104 Z 121 (?)
Arbitrary point of view : Superheavies: existence due to shell effects
Cn (2010)
copernicium
200720101996
2004
Chemist point of view
238U~4.5 109 y
238U
Peninsula vs island of stability
Deformed 254No, 270Hs
Spherical 298114
LDM
LDM
LDM
LDM
LDM
LDM
162
184
152
M. Bender et al . PL B515 (2001) 42Z N
W.S 114 184
HFB 126 184
RMF 120 172
Note 1 :Up to 208Pb : proton and neutron magic numbers identical.Note 2 : Models rely on extrapolations –parameters are adjusted on known cases
Modern-theory predictions
Theoretical challenges
Level density increases with A, Z
M.
Ben
der
et a
l., P
hys.
Let
t. B
515
(20
01)
42
132Sn :Large gap
Super-heavies :Gap function of modelsand not marked
Why is it so difficult to get information on SHE?
times needed to observe on
average 1 event
present sensitivity:
limit 1 pbarn
beam dose:
1.51018 projectiles
10 days
1 minute
1 hour
1 day
1 second
known
CN277112
273110
269Hs
265Sg
261Rf
257No
11.45 MeV280 s
11.08 MeV110 s
9.23 MeV19.7 s
4.60 MeV (escape)7.4 s
8.52 MeV4.7 s
253Fm8.34 MeV15.0 s
Date: 09-Feb-1996Time: 22:37 h
277112
70Zn 208Pb 277112
n
kinematic separationin flight identification
by - correlationsto known nuclides
Synthesis and Identification of SHE
JINR/FLNRDubna, Russia
GSI
State-of-the-art worldwhile
294118: Yu. Oganessian et al., J. Phys. G R165 (2007)294117: Yu. Oganessian et al., Phys. Rev. Lett. 104, 142502 (2010)
RIKENTokyo, Japan
Spectroscopy of Transfermium elements
Access to high j deformed orbitals : probe of higher lying spherical orbitals
R.-D. Herzberg et al., Nature 442, 896-899 (2006)S.K. Tandel et al., PRL 97, 082502 (2006)
(courtesy of P.-H. Hennen)
Prompt and/or decay spectroscopy
M Block et al., Nature 463, 785-788 (2010)
Cyclotron resonance curve of 253No2.
Bridging the gap from heavies to superheavies
253,254,255Nomass measurement
The S3 spectrometer at SPIRAL2
A spectrometer for the high intensity stable ion beams of SPIRAL2 (from 2012)
Isotopic explorationIsotopic exploration40-4840-48Ca+Ca+238238UU275-283275-283112+3,4n112+3,4nSS33 (I=20pµA) (I=20pµA) 40evt/week/pb40evt/week/pb
New elementsNew elements5454Cr+Cr+248248CmCm299299120+3n120+3nSS33 (I=10pµA) (I=10pµA) 1evt/month@1evt/month@σσestest~0.01pb~0.01pb
?
Closed-shell deformed nucleus ???Closed-shell deformed nucleus ???4040Ar+Ar+238238UU274274Ds (+4n) Ds (+4n) 270270Hs + Hs + ααSS33 (I=50pµA) (I=50pµA) 190evt/week@190evt/week@σσthth=2pb=2pb
Summary
superheavy elements exist only because of shell effects theory predicts deformed + spherical shell gaps next proton magic number still to be discovered
very low production cross sections direct production and undirect experimental techniques SPIRAL2 and S3 spectrometer
shape coexistence: interplay between shell effects and macroscopic propertiesessential to constrain collective nuclear models
Very large deformations encoutered at high spin superdeformation evidenced / hyperdeformation still to be discovered AGATA high-resolution germanium array
most nuclei are deformed prolate quadrupole deformation are the most common
Key questions and shell effects in nuclei
• What is the shape of a nucleus, how large can be nuclear deformation?hyperdeformation, shape-coexistence
• Is there any island of stability for superheavy elements?Next proton magic number, stabilizing deformed shell gaps
• Next-generation facilities and innovative detectors worldwhile built this decade
• How does shell structure evolve away from stability? magic numbers, shell-model, spin-orbit, tensor
• How do nuclear clusters and molecules form?few-body systems, halos, clusters