rotational and vibrational states in heavy nuclei described
TRANSCRIPT
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