Shell effects in atomic nucleiPart 2: shapes and superheavy elements

Laurent Gaudefroy1, Alexandre Obertelli2

1CEA DAM, DIF, France2CEA Saclay, IRFU, France

protons

neutrons

82

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

Shape coexistence in light Krypton isotopes

0+0+2+

2+

4+

4+

6+

6+8+

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

Fission barrier – liquid drop

Deformation β

Liqu

id d

rop

ener

gy (

MeV

/A)

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