ocl oblate nuclear shapes and shape coexistence in neutron ... · multi-step coulomb excitation...

INTC 16.2.2009Andreas Görgen 1

OCL

Oblate nuclear shapes and shape coexistence

in neutron-deficient rare earth isotopes

Andreas Görgen

Service de Physique Nucléaire

CEA Saclay

Sunniva Siem

Department of Physics

University of Oslo


OCL

Context

ultimate goal:

comprehensive microscopic description

of all nuclei and low-energy reactions

from the the basic interactions between

the constituent nucleons

ultimate goal:

comprehensive microscopic description

of all nuclei and low-energy reactions

from the the basic interactions between

the constituent nucleons

specific goal:

provide experimental data on nuclear

shapes and collectivity in a sensitive

region of shape transition and shape

coexistence for benchmarking

specific goal:

provide experimental data on nuclear

shapes and collectivity in a sensitive

region of shape transition and shape

coexistence for benchmarking

Inter-Nucleon

NN, NNN Interactions

AV18, EFT, Vlow-k

Theory of Light Nuclei

Verification: NCSM=GFMC=CC

Validation: nuclei with A≤16

Density Functional TheoryImproved functionals

remove computationally-imposed constraints

global properties of nuclei with A≥16

Dynamic Extensions of DFT

LACM, GCM, TDDFT, QRPA, CI, CC

Level densities

Low-energy Reactions

Hauser-Feshbach

Feshbach-Kerman-Koonin

Fissionmass and energy distributions


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Mean field and beyond: an example

Self-consistent HFB constrained to collective coordinate, e.g. (q20 ,q22)

set of basis states

potential energy surface qΦ

dqqf qii Φ=Ψ ∫ )(

Correlations beyond mean field

configuration mixing

properties of excited states: Ex, Qs, B(E2), … M. Bender et al.,

PRC 74, 024312 (2006)

Approaches / choices

collective coordinates: e.g. axial, triaxial, octupole, …

relativistic or non-relativistic

effective interaction: Skyrme, Gogny

Experiment: Ex, Qs, B(E2) from low-energy Coulomb excitation

Qs<0 Qs>0

experiment

E. Clément et al.,

PRC 75, 054313 (2007)

theory

prolate oblate γ vib.


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Multi-step Coulomb excitation

safe energy ⇒ purely electromagnetic excitation

transitional matrix element ⇒ B(E2)

diagonal matrix element ⇒ Qs reorientation effect ⇒ sensitive to nuclear shape

multi-step excitation

de-excitation γ-ray yields ⇒ dσσσσ/dθθθθ χ2 minimization of matrix elements to reproduce

experimental γ-ray yields

0+

6+

4+

2+0+

2+

4+

0+2+

[25°,54°] [54°,81°] [81°,115°] [115°,150°]


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3.3

2.5

2.0

1.0

E(4+) / E(2+)

148Dy

146Gd

144Sm

142Nd

140Ce

138Ba

136Xe

134Te

132Sn

150Er

146Dy

144Gd

142Sm

140Nd

138Ce

136Ba

134Xe

132Te

130Sn

148Er

144Dy

142Gd

140Sm

138Nd

136Ce

134Ba

132Xe

130Te

128Sn

142Dy

140Gd

138Sm

136Nd

134Ce

132Ba

130Xe

128Te

126Sn

140Dy

138Gd

136Sm

134Nd

132Ce

130Ba

128Xe

126Te

124Sn

134Sm

132Nd

130Ce

Region of interest

128Ba

126Xe

124Te

122Sn

828078767472

66

64

62

60

58

56

54

52

50

68

U(5)SU(3)2.0 3.33

E(5)

X(5)

Spherical

γ-softO(6)

2.2

2.5

2.9

3.3

Deformed


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Nuclear shapes

Oblate

Prolate

M. Girod,

CEA Bruyères-le-Châtel

Gogny HFB

G.A. Lalazissis et al. Nucl. Phys. A 597, 35 (1996)

RMF

region of

oblate shapes

rapid shape transition

shape coexistence ?

region of

oblate shapes

rapid shape transition

shape coexistence ?

oblate shapes in

medium / heavy nuclei

just beneath shell closure

holes in Ω=1/2 orbitals

oblate shapes in

medium / heavy nuclei

just beneath shell closure

holes in Ω=1/2 orbitals


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extensive studies at high spin

e.g. magnetic dipole bands

E.O. Lieder et al.

Eur. Phys. J. A 35, 135 (2008)

Previous experiments

no lifetimes known at low spin

only few non-yrast states from ββββ decay studies no experimental information on the shape at low spin

no lifetimes known at low spin

only few non-yrast states from ββββ decay studies no experimental information on the shape at low spin


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Predictions for 142Gd

configuration mixing calculation

GCM(GOA)

5-dimensional (q20,q22,α,β,γ)Gogny D1S interaction

parameter free

K=2

γ vib.

analytic solution of Bohr Hamiltonian

with square-well potential

E(5) symmetry

normalized to experimental Ex(2+)

and B(E2,2+→0+) from GCM(GOA)

oblate shape near ground state

transition to prolate at higher spin

γγγγ vibration built on oblate states

oblate shape near ground state

transition to prolate at higher spin

γγγγ vibration built on oblate states

experiment

need B(E2) values and

quadrupole moments

to test predictions

need B(E2) values and

quadrupole moments

to test predictions

M. Girod et al.



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Shape transitions

M. Girod et al.



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Shape coexistence ?

theoryexperiment

shape transitions

neutron number: spherical (N=82)⇒⇒⇒⇒ oblate (N=78) ⇒⇒⇒⇒ prolate (N<78)

proton number: prolate (Nd, Sm)⇒⇒⇒⇒ oblate (Gd, Dy)

spin: oblate near ground state (Gd)⇒⇒⇒⇒ prolate above 4+ (Gd)

shape transitions

neutron number: spherical (N=82)⇒⇒⇒⇒ oblate (N=78) ⇒⇒⇒⇒ prolate (N<78)

proton number: prolate (Nd, Sm)⇒⇒⇒⇒ oblate (Gd, Dy)

spin: oblate near ground state (Gd)⇒⇒⇒⇒ prolate above 4+ (Gd)

is there also shape coexistence ?

indication: low-lying 0+ states

(tentative) 0+ state in 140Sm at 990 keV

is there also shape coexistence ?

indication: low-lying 0+ states

(tentative) 0+ state in 140Sm at 990 keV

M. Girod et al.



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Simulation

142Gd + 208Pb

2.9 MeV / u

experimental level scheme

theoretical B(E2) and Qs

2×104 pps1 mg/cm2 208Pb

15 shifts


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Differential cross section

142Gd + 208Pb

2.9 MeV / u



[25°,54°] [54°,81°]

[81°,115°] [115°,150°]


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Sensitivity to quadrupole moments




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Proposed experiment

REX beams at maximum energy of 2.95 MeV / u

measured yields realistic beam intensities138Nd: ? (large) ~106

140Sm: 2×108 4×105142Gd: 1.2×106 2×104144Dy: ? ?

RILIS to suppress isobaric contaminants crucial

ionization schemes exist, Sm and Gd not yet tested at ISOLDE

Coulomb excitation target: 206Pb or 208Pb

(normalization point vs. spectrum simplicity)

double-sided annular silicon detector and MINIBALL

148Dy

146Gd

144Sm

142Nd

140Ce

138Ba

146Dy

144Gd

142Sm

140Nd

138Ce

136Ba

144Dy

142Gd

140Sm

138Nd

136Ce

134Ba

142Dy

140Gd

138Sm

136Nd

134Ce

132Ba

140Dy

138Gd

136Sm

134Nd

132Ce

130Ba

8280787674

66

64

62

60

58

56

shape transition and coexistence predicted for N=78 isotones

measure quadrupole moments for 21+ (22

+, 41+) in 140Sm and 142Gd

measure transition rates between all low-lying states

identify low-lying 0+ states

extend study to 144Dy and N=76 if feasible

shape transition and coexistence predicted for N=78 isotones

measure quadrupole moments for 21+ (22

+, 41+) in 140Sm and 142Gd

measure transition rates between all low-lying states

identify low-lying 0+ states

extend study to 144Dy and N=76 if feasible

beam time request

140Sm: 6+3 shifts

142Gd: 15+3 shifts

testing required to determine / improve intensity and purity

beam time request

140Sm: 6+3 shifts

142Gd: 15+3 shifts

testing required to determine / improve intensity and purity


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Collaboration

CEA Saclay, IRFU/SPhN A. Görgen, W. Korten, A. Obertelli, B. Sulignano, Ch. Theisen

University of Oslo A. Bürger, M. Guttormsen, T.W. Hagen, P. Hoff, A.C. Larsen,

H.T. Nyhus, T. Renstrøm, S. Siem, H.K. Toft, G.M. Tveten, K. Wikan

CEA DIF, Bruyères-le-Châtel J.-P. Delaroche, M. Girod

CERN-ISOLDE J. Cederkäll, J. Van de Walle

GANIL E. Clément, G. de France, J. Ljungvall

University of Liverpool P.A. Butler, M. Scheck

University of York D.G. Jenkins

University of Manchester S. Freeman

Universität Köln P. Reiter, M. Seidlitz, A. Wendt

ocl oblate nuclear shapes and shape coexistence in neutron ... · multi-step coulomb excitation...

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