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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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250 No

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SD ground states ?

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ND

SD

Multipole moments

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ND

SD

p/n multipole moments

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2QP ND

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2QP SD

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ND spin isomers

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SD spin isomers

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SD collective levels

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SD 0+ collective levels

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Inner barriers

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0+ states of Pu Isotopes :

A determination of inner barrier heights

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ND moments of inertia

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ND moments of inertia

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ND moments of inertia

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ND moments of inertia

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SD

mom

ents

of

iner

tia

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SD moments of inertia

Shape evolution with rotation

240 U

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Half-lives

Fission

-back

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Third well at ID

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Mean

deformations of

collective states

in the 0-2

plane

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Mean

deformations of

collective states

in the 0-2

plane

Localisation of ID states

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ID Collective wave functions

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Third well spectroscopy

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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 ?

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Conclusion and outlook 2/2

Next:

Even-odd and odd-odd heavy actinides : g.s. properties, spin isomer energies and half-lives