D. Mücher
|
European Gammapool Workshop – Paris, 30.05.2008
Shell structure and shape changes in neutron-rich krypton isotopes
D. Mücher, University of Cologne
for the MINIBALL and REX_ISOLDE Collaboration
Motivation: Shape changes in exotic krypton isotopes, N=56 @ Z=40
Coulomb Excitation of
88Kr
and
92Kr
with MINIBALL @ ISOLDE
conclusion on N=56 "subshell closure"
consequence on deformation and octupole softness for neutron-rich
Krypton isotope
Quadrupole Moments from Coulomb Excitation data ? , GOSIA
Conclusion and Outlook
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Where we are ....
Z=40
N=56
N=50
Z=38
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
N=56 subshell closure ?
2200
Z=40
Z=36
Z=38
Z=44
1800
1600
Sr
Mo
Zr
(1)
B(E2)↑ (e2b2)
Z=42
2000
Kr
Sr
Ru
E(2+1) (keV)
1400
1200
1000
800
600
Number of Neutrons
400
strong influence of N=56 shell closure for Zr
200
and Sr nuclei, but no evidence in Mo, Ru, Cd,...
0
50
why peaks E(2+1) for
52
54
56
58
60
62
64
Number of Neutrons
(1):
H. Mach et al./Nucl. Phys. A523 (1991) 197-227
(2): K.-L. Kratz et al./Atomic Nuclei 330, (1988)
ideas
(1,2):
92Kr?
locally occuring deformed gap ,
quasi-spherical but soft against octupole
deformation
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Deformation β2 from Relativistic Mean-Field
β2
Kr (Z=36)
δ<r2> (fm2)
FRDM
0.4
0.2
Kr
2.0
Sr
0
-0.2
1.0
0.0
ETF-SI
NL-SH
expt.
70
80
90
80
90 100
-0.4
80 70
90 100
A
G.A. Lalazissis et al. Nucl. Phys. A586 (1995) 201-218
RMF (NL-SH)
80
90
A
100
D. Mücher
D. Mücher|
European
|
University
Gammapool
of Cologne
Workshop
|
Chamrousse
– Paris, 30.05.2008
2008
Changes in mean-square charge radii, octupole deformation
Description of isotope shifts: good description in RMF theory
(1)
Liquid drop model:
78-100Sr
δ<r2> (fm2)
1.5
<β22>1/2=0.4
0.3
0.2
1.0
increase of radii contains additional
contributions: „shell effect“
0.12
0
0.5
Strutinsky-type potential-energy
calculations
(2)
: "92Kr is
soft but
stable with respect to octupole
deformation"
sharp increase of charge radii at N=60:
0.0
phase-transition-like behaviour
40
(1):
50
60
Number of Neutrons
G.A. Lalazissis et al. Nucl. Phys. A586 (1995) 201-218
(2): W. Nazarewicz et al. Nucl. Phys. A429 (1984) 269-295
|
University
of Workshop
Cologne –| Paris,
Dezember
2007
D. MücherD. Mücher
|
European
Gammapool
30.05.2008
Octupole deformation in Kr-Isotopes
(1)
δ<r2> (fm2)
1.5
calculated values of radii show the
1.0
same effects like in Sr isotopes
0.5
B(E2) values: Grodzins Relation
92Kr
0
88Kr
-0.5
35
no sharp increase of radii at N=60
was found
40
45
50
55
60
Number of Neutrons
(1):
M. Keim et al./Nucl. Phys. A586 (1995) 219-239
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Experiment on
(88,92)Kr
@ REX-ISOLDE
88
Kr
⊗
θ
ϕ
Ep (MeV)
Beam energy: 2.19 MeV/u (broken 9 gap resonator)
Beam intensity: 5 *106 particles/sec
targets: 4 mg/cm² 109Ag, 2 mg/cm² 109Ag, 2mg/cm² 12C
4 days beam time for 88Kr and 2 days for 92Kr
MINIBALL spectrometer: 8 triple clusters+particle
detector
12C
annular strip number
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Particle-Gamma Time difference
prompt Peak
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Particle Gamma Time difference, gate on 2+1
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Determination of B(E2) values
First order perturbation theory :
Alder & Winther : "Electromagnetic Excitation - Theory of Coulomb Excitation with Heavy Ions"
North-Holland, 1975, Amsterdam
●
Experimental method:
●
used Coulomb Excitation codes:
●
CLX
... calculates differential cross section, incl. energy loss
GOSIA (Rochester, Warsaw)
● ... performs χ²-fitting of matrix elements to the experimental data
● ... handels projectile and target excitation simultaneously (GOSIA 2)
● ... let the user to specify the experimental setup (8 cluster+part. det.)
● ... calculates angular distributions
● ... counts for the deorientation effect
● ...
●
●
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Counts
4 mg/cm2
88Kr
and
92Kr
on
109Ag
109Ag
Target
2 mg/cm2
109Ag
2000
2000
1500
1500
1000
1000
500
88Kr
2+1 -> 0+1
92Kr
2+1 -> 0+1
0
0
Energy resolution after Doppler Correction: ~ 8 keV for
88Kr
on
12C
when normalizing to target excitation: A(92Kr,2+->0+)≈2·A(88Kr,2+->0+) !!
Exact calculation (integration over full CD range):
88Kr:
B(E2;2+1->0+1)=7.7(8) W.u.
92Kr: B(E2;2+ ->0+ )=16.9(5) W.u.
1
1
500
(smaller error from
12C
data...)
Counts
Spectra of
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Consequences for nuclear structure in neutron-rich krypton isotopes
(1)
δ<r2> (fm2)
1.5
92Kr
(Exp)
B(E2) values do not follow Grodzins
relation!
1.0
Exp. B(E2) value gives new δ<r2> from
liquid drop model and octupole degree of
0.5
92Kr
0
88Kr
(Grodzins)
freedom has not to be included
E(2+1) in
(Exp)
92Kr
still a mystery, but
deformation seems to set in smoothly, so
-0.5
N=56 is not active
evolution of deformation towards N=60?
35
40
45
50
55
Number of Neutrons
60
->
(94,96)Kr
@Isolde ...
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
N=56 subshell closure...
Slide from Ari Jokinen
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Where we are ....
Z=40
N=56
N=50
Z=38
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Quadrupole moment of
88Kr
cross section (a.u.)
<2|M(E2)|2>=- 0.4 eb
<2|M(E2)|2>=+0.4 eb
lab. scattering angle [deg]
a negative value for <2|M(E2)|2> fits better to the cross section
due to defect strips only quater of the full statistics was used so far
for
92Kr:
no separation of Target-and Projectile excitation -> Det. of Q not possible
--> for future experiments: heavier and thinner targets !
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Relative determination of matrix elements in GOSIA
deorientation
Error calculation is
done separately for
target and proj. !
88Kr
GOSIA-2
Normalisation Constant
109Ag
dependencies of matrix elements: Minimization and error calculation with Gosia
actuell problems: normalization constant can not be fixed and has no error!
Problems when Aproj > Atarget
for the future: Gosia can make it possible to determine e.g. quadrupole moments
without knowing the lifetimes, but we need an upgrade of GOSIA
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
Summary and outlook
The nuclear structure of the A=100 region shows a complex interplay between
microscopic and macroscopic features: N=50,56 shell gaps vs phase transition
to deformed nuclei for N>58
In the past: Differences in mean square radii in Kr isotopes were explained by
octupole softness
We determined B(E2;2+1->0+1) values for
88Kr
and 92Kr
for 92Kr deformation starts to set in and no octupole softness has to be assumed
There is still the question why E(2+1) peaks for 92Kr !!
The determination of the (sign of) the quadrupole moment might be possible with
RIB@Isolde without knowing lifetimes of the projectile, but we need an upgrade
of GOSIA for this
For the future: evolution of deformation towards 96Kr
D. MücherD. Mücher
|
European
|
University
Gammapool
of Workshop
Cologne –| Paris,
April
30.05.2008
2008
D. Mücher IKP Cologne, Germany
J.Iwanicki (Spokesperson) Heavy Ion Laboratory, Warsaw University
P.Van Duppen, M.Huyse, P.Mayet, I. Stefanescu, J. Van de Walle IKS, Leuven, Belgium
A. Blazhev, J.Jolie, N.Warr IKP Cologne, Germany
N.Amzal, C.Andreoiu, A.Andreyev, P.Butler, R-D.Herzberg, G.Jones, G.Rainovski, Oliver Lodge
Laboratory, Liverpool, UK
U.Bergmann,J.Cederkäll, S.Franchoo, T.Nilsson, T.Sieber, F.Wenander, B.Wolf, CERN, Geneva,
Switzerland
W.Korten, E.Bouchez, Y.Le Coz, Ch.Theisen, CEA, Saclay, France
F.Becker, J.Gerl, S.Mandal GSI Darmstadt, Germany
T.Czosnyka † , J.Kownacki, P.Napiorkowski, M.Zielinska HIL Warsaw, Poland
J.Eberth, A.Scherillo, D.Weiß haar, C. Fransen IKP Cologne, Germany
F.Ames, D.Habs, O.Kester, LMU Munich, Germany
R. Krücken, T. Kröll, T. Faestermann, R. Gernhaeuser, TU Munich, Germany
D.Schwalm, H.Scheit, MPI Heidelberg, Germany
T.Davinson, Z.Liu, P.Woods, University of Edinburgh, UK
D.Jenkins, University of York, UK
Thanks for your attention!