Post on 14-Dec-2015
ESNT Saclay February 2, 2006 1
Structure properties of even-even actinidesat normal- and super-deformed shapes
J.P. Delaroche, M. Girod, H. Goutte, J. LibertCEA Bruyères-le-Châtel & IPN Orsay
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Introduction
• Contemporary issue: understanding the properties which govern stability of SHEs and synthesis
• Strategy:
1) present day: dedicated experimental and model studies of structure properties of heaviest actinides
2) Here: model studies extended to A = 226 - 262
• Goal:model validations : reliable extrapolation into the SHE mass region
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Present work
• Microscopic model analyses of a huge amount of experimental data at ND and SD shapes.(multipole moments, spin and shape isomers, SD phonons, inner+outer barriers, moments of inertia, shape isomers decay modes)
•Tools: mean field and beyond mean field methods with D1S force Constrained HFB, blocking Configuration mixing ( = + levels) WKB method
•Playgrounds:
226-236Th, 228-242U, 232-246Pu, 238-250Cm, 238-256Cf, 242-258Fm, 250-262No.
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Outline
I. HFB methods: constraints and 2qp blocking Multipole moments, potential energy curves and surfaces, spin isomers
II. Configuration mixing ( = + levels)shape isomers, SD phononsouter and inner barriers
III. Cranking HFB (Yrast bands)kinetic moments of inertia, alignments
IV. WKB method-back and fission decay modes for shape isomers
V. Third potential well at ID deformation : N ~ 154 nuclei
VI. Conclusion + outlook
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HFB under constraintsVariational principle :
Where H = i Ti + 1/2 ij Vij Vij is the nucleon-nucleon effective interaction D1S of GOGNY
< Z or N > = Z or N
< Qi > = qi
< Jz > = (I(I+1))1/2
Qi is Q20 ~ r2 Y20 or Q22 ~ r2 (Y22 +Y2-2)
<H - z Z - n N - i i Q
i - Jz >] = 0
Theory
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Blocking
Neutron and proton 2QP excitations
Trial state :
qij> = +
i +
j
q>
Minimisation :
<qijH - z Z - n N
qij>] = 0
2QP energies :
Eij2QP
= <qijH
qij> - <
qH
q>
Calculations with and without breaking time reversal symmetry
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),),ˆ ''
'
(g E(gH IKn
In
IKn
IKK
K
)(* )(ˆ)(, orthIMK
IKn
K
IMn ΦRDd) (gdd Ψ
Pot. Energy, Inertia and ZPE calculated from HFB
vibrKKl l
lIKK HIK
JIK H ˆ'
),(2
ˆˆ
'
3
1
2
'
,rot)ZPE(ΦHΦB Hj
ijji i
vibr
,ˆ),(
2
1ˆ2,0,
5D GCM + GOA
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WKB Method
Shape isomer decays: -back and fission half-lives (s)
T(f) = 2.87 10 -21 (1+ exp(2S(,f)
) / E0
S = L {2B
s(s) [ V(q(s)) – E
0]}1/2 ds
E0 = assault energy (MeV); B
s(s) = collective masse; s = curvilinear coordinate
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Mean
deformations of
collective states
in the 0-2
plane
Localisation of ID states
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B00 Potential
Band structure in the shallow ID well is governed by collective masses
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Conclusion and outlook 1/2
I. Mean field and beyond mean field methods implemented with D1Sforce provide predictions, most of which in good overall agreement withvarious measurements collected over the years for actinides (including heaviest ones).
Complex structure properties of N ~ 154 nuclei at triaxial innerbarriers are explained.
II. Items to be fixed : collective masses (beyond Inglis Beliaev formula)
III. -vibration energies: quadrupole + hexadecapole modes (?)
IV. Pairing / alignment properties at high rotational frequency:effect of octupole correlations ?