Rotational and vibrational states in heavy nuclei described

Jacek Dobaczewski

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Rotational and vibrational states

in heavy nuclei described within the

energy density functional methods

Jacek DobaczewskiUniversity of Warsaw & University of Jyväskylä

Seminarium „Struktura jądra atomowego”Uniwersytet Warszawski

22 marca 2012

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The Jyväskylä theory team on January 10, 2012

Standing, from left: Markus Kortelainen, Jacek Dobaczewski

Seated, from left: Francesco Raimondi, Jussi Toivanen, Yuan Gao

Newcomer: Vaia Prassa

Former members: Gillis Carlsson, Alessandro Pastore, Nicolas Michel, Petr Veselý

Visitors: Dimitar Tarpanov, Yue Shi, Karim Bennaceur,Tamara Nikšić

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Precise Penning-trap mass measurements beyond 132Sn Tilted-axis cranking determination of ultra-high-spin triaxial rotational

bands in 158Er Incompressibility of finite nuclei studied within modern QRPA

calculations Rotational bands in superheavy nuclei around 252No Low-lying vibrational (2+ and 3-) states in semi-magic nuclei

(Calsson, Toivanen) QRPA correlation energies up to multipolarity 7 (Calsson, Toivanen) Beta-decay rates in spherical nuclei (Veselý) Beta-decay rates in deformed nuclei (Toivanen, Pastore) Pseudopotentials and equation of continuity in higher-order EDF’s

(Raimondi) Adjustments of higher-order functionals to data (Prassa, Carlsson, Veselý,

Kortelainen) Error propagation in EDF approach (Gao) Approximate restoration of broken symmetries by the Lipkin method

(P. Toivanen, Gao) Particle- and Quasiparticle-phonon coupling (Tarpanov, Toivanen) Regularization of zero-range effective interactions (Bennaceur, Raimondi)

Projects

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Precise Penning-trap mass measurements

beyond 132Sn

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arXiv:1203.0958v2 [nucl-ex] 6 Mar 2012

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En

erg

y

N-2 N-1 N N+1 N+2

D(3

) od

d

D(3

) od

dD(3

) ev

en

Odd-even mass staggering

W. S

atu

ła e

t a

l., P

hy

s.R

ev

.L

ett

. 8

1, 3

59

9(1

99

8)

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Experimental data around 132Sn

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Sn surSn mixSn vol

70 80 90

(b)

0.5

1.0

1.5

Sn

Te

Xe

70 80 90

Neutron Number N

D(3

) (N)

[Me

V]

SLy4 + HFB(sph)

(a)

Spherical EDF calculations around 132Sn

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(b)SLy4 + HFB(sph)

50 52 54

SLy4 + PLN(def)

(d)0.0

0.5

50 52 54

(c)

Proton Number Z

SLy4 + HFB(def)

0.0

0.5

1.0

N=81N=83

D(3

) (N)

[Me

V]

EXP(a)

Odd-even mass staggering in N=81 & 83

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Tilted-axis cranking determination of ultra-

high-spin triaxial rotational

bands in 158Er

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Jacek Dobaczewski

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X.

Wa

ng

et

al.

, Ph

ys.

Le

tt. B

70

2, 1

27

(2

01

1)

DSAM life-time measurements

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X.

Wa

ng

et

al.

, Ph

ys.

Le

tt. B

70

2, 1

27

(2

01

1)

Cranked Nilsson–Strutinsky (CNS) model

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Tilted-axis cranking

Kerman-Onishi theorem

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Incompressibility of finite nuclei studied

within modern QRPA calculations

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arXiv:1202.5617 [nucl-th] 25 Feb 2012

Ex

pe

rim

en

tal

da

ta f

rom

:T

. Li,

U. G

arg

, Y

. L

iu, e

t a

l.,

Ph

ys.

Re

v.

Le

tt. 9

9, 1

62

50

3 (

20

07

);P

hy

s. R

ev

. C

81

, 03

43

09

(2

01

0))

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Fast RPA and QRPA + Arnoldi method

J. Toivanen et al., Phys. Rev. C 81, 034312 (2010)

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Convergence of the Arnoldi method

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Finite-range separable pairing interaction

Y. T

ian

, Z

.Y.

Ma

, P

.Rin

g,

Ph

ys.

Le

tt. B

67

6,

44

(2

00

9)

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Nuclear incompressibility

J. P

. B

laiz

ot,

Ph

ys.

Re

p.

64

, 17

1 (

19

80

)

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Nuclear incompressibility

P. Veselý, et al., arXiv:1202.5617

Full (empty) symbols correspond to the zero-range(separable) pairing force

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Nuclear incompressibility

P.

Ve

selý

, et

al.

, arX

iv:1

20

2.5

61

7

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Centroids of GMR

P.

Ve

selý

, et

al.

, arX

iv:1

20

2.5

61

7

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P.

Ve

selý

, et

al.

, arX

iv:1

20

2.5

61

7

Nuclear incompressibility – liquid drop

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Rotational bands in superheavy nuclei

around 252No(preliminary)

(with Yue Shi and Paul Greenlees)

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P.

Gre

en

lee

s, e

t a

l.,

to b

e p

ub

lish

ed

Rotational bands in N=150 & 152 isotones

Experiment

Lines = Harris fits

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Neutron quasiparticle spectra in 251Cf153

UNEDF1 = new parameterization adjusted to heavy deformed nucleiM. Kortelainen et al., Phys. Rev. C85, 024304 (2012)

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Proton quasiparticle spectra in 249Bk152

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A. Sobiczewski, I. Muntian, Z. PatykPhys. Rev. C63, 034306 (2001)

58

60

62

64

66

68

70

72

74Z=100JexpZ=102JexpZ=104Jexp

144 146 148 150 152 154 156

Neutron Number N

Without Lipkin-Nogami

Without Lipkin-NogamiWoods-Saxon & BCS

J(1) in N=150 & 152 isotones

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With Lipkin-Nogami Without Lipkin-Nogami

251Cf153

249Bk152

J(1) in N=150 & 152 isotones

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Conclusions

1. Precise Penning-trap mass measurements beyond 132Sn call for an improved analysis of correlations in odd nuclei

2. Tilted-axis cranking determination of ultra-high-spin triaxial rotational bands in 158Er proves the instability of excited configurations.

3. Incompressibilities of finite nuclei studied within modern QRPA calculations do not provide answer to the question “Why tin is so soft”

4. Rotational bands in superheavy nuclei around 252No challenge current approaches to pairing.

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Thank you

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What is DFT?

Density Functional Theory:

A variational method that uses observables as variational

parameters.

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Rayleigh-Ritz Variational Method

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Which DFT?

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What is the DFT good for?

1) Exact: Minimization of E(Q) gives the exact E and exact Q2) Impractical: Derivation of E(Q) requires the full

variation d (bigger effort than to find the exact ground state)

3) Inspirational: Can we build useful models E’(Q) of the exact E(Q)?

4) Experiment-driven: E’(Q) works better or worse depending on the physical input used to build it.

Energy E is afunction(al) of Q

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How the nuclear EDF is built?

Local energy density is afunction of

local densityLDA

Non-local energy density is afunction of

non-local densityGogny, M3Y,…

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How the nuclear EDF is built?

Quasi-local energy density is a function of

local densities and gradientsSkyrme, BCP,

point-coupling,…

Non-local energy density is a function of

local densitiesRMF (Hartree)

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Collectivity

beyond mean field, ground-state correlations, shape coexistence, symmetry restoration, projection on good quantum numbers, configuration interaction, generator coordinate method, multi-reference DFT, etc….

True formean field

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I. Range separation and exact long-range effects

II. Derivatives of higher order:

III. Products of more than two densities:

Extensions

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Finite-range separable pairing interaction

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Nuclear incompressibility

P. Veselý, et al., arXiv:1202.5617