1. Spectroscopic insight into the shape coexistence in 76,78Sr, (78),80Zr
Letter of Intent for
P. Boutachkov, C. Domingo-Pardo, H. Geissel, J. Gerl, M. Gorska,
E. Merchan, S. Pietri, T.R. Rodriguez, C. Scheidengerger, H.J. Wollersheim
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
G. de Angelis, D.R. Napoli, E. Sahin, J.J. Valiente-Dobon
INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy
S. Aydin, D. Bazzacco, E. Farnea, S. Lenzi, S. Lunardi, R. Menegazzo,
D. Mengoni, F. Recchia, C. Ur
Dipartimento di Fisica and INFN, Sezione di Padova, Padova, Italy
A. Dewald, C. Fransen, M. Hackstein, T. Pisulla, W. Rother
Institut fuer Kernphysik der Universitaet zu Köln, Köln, Germany
A. Algora, A. Gadea, B. Rubio, J.L. Tain
IFIC Instituto de Fisica Corpuscular, Valencia, Spain

2. Spectroscopic insight into the shape coexistence in 76,78Sr, (78),80Zr
Scientific Motivation

3. Shape coexistence along Z=38 and Z=40
Beyond Mean Field calculations show shape coexistence and evolution in p-rich Strontium isotopes:

4. Shape coexistence along Z=38 and Z=40
Beyond Mean Field calculations show shape coexistence and evolution in p-rich Strontium isotopes:

5. Shape coexistence along Z=38 and Z=40
Beyond Mean Field calculations show shape coexistence and evolution in p-rich Strontium isotopes:
and Zirconium isotopes:
A=78
N=38
A=80
N=40

6. Scientific Motivation
Beyond Mean Field calculations predict shape coexistence in 78Sr and strong triaxial effects
One observes shape-coexistence in 78Sr with the appearance of a rotational yrast band (build on top of the prolate minimum) and a vibrational band (build on the spherical minimum). The energy difference between both band heads is of about 0.7 MeV.
These two bands do not mix, the transition probabilities between states of the two different bands are neglibible, as it is reflected by the collective wave-functions.
The appearance of the rotational band as the Ground State happens after including the beyond mean field correlations (Projection in good angular momentum), which energetically favors the deformed (prolate) minimum rather than the spherical one.
Axial calculations (K=0) yield a rather rotational spectrum compared to the experiment. Including triaxial effects in the BMF calculation should bring the energy of J>0 states lower, thus giving a better agreement with the experiment.

7. Scientific Motivation
Beyond Mean Field calculations predict shape coexistence in 78Sr and strong triaxial effects
(*)
(*) L.Gaudefroy et al. Phys. Rev. C 80, 2009

8. Shape coexistence along Z=40

9. Shape coexistence along Z=40
One observes shape-coexistence in 80Zr, with one spherical minimum and one prolate minimum separated by a barrier of more than 5 MeV.
After doing the projection in good angular momentum J, (at variance with 78Sr!) the deformed minimum drops in energy but not enough to become the absolute minimum.
The deformed state is practically at the same energy as the spherical one. Theoretically, here one can speak of shape coexistence better than anywhere else!

10. Shape coexistence along Z=40

11. Scientific Motivation
Study the possible X(5) character of these N=Z=38,40 Sr and Zr isotopes
X(5) Sm
B(E2;J J-2)/B(E2;2 0)
Casten et al.,Phys.Rev.Lett. 85 (2000)
E.A. McCutchan et al. Phys.Rev.C 71 (2005)
Iachello,Phys.Rev.Lett. 85 (2000), 87 (2001)

12. Scientific Motivation
Search for the possible empirical realization of X(5) Critical Point Symmetry in 78Sr
78Sr
X(5)
10+
Rudolph et al. Phys. Rev. C, 1997
Gross et al. Phys. Rev. C, 1994
U(5)
X(5)
X(5)
SU(3)
78Sr
Lister et al., Phys. Rev. Lett. 49 (1982)

13. Spectroscopic insight into the shape coexistence in 78Sr
What can we measure?

14. Measurables t = ? t = ? t = ? t = ? t = ? t = ? t = ? t = ? t = ?
lifetime values of yrast levels up to 10+ with high accuracy (5%/20%)
t = ?
t = ?
t = ?
t = ?
t = ?
t = ?
t = ?
t = ?
t = ?
t = 5.1(5) ps
t = ?
t = ?
t = ?
t = ?
t = 155(19) ps
78Sr
76Sr
80Zr
yrast band livetime measurements at LNL via fusion evaporation
yrare band (2+,4+) measurements at GSI via n-knockout/Coulex

15. Measurables
lifetime values of yrast levels up to 10+ with high accuracy (5%/20%)
GSI
LNL
yrast band livetime measurements at LNL via fusion-evaporation reactions
low-spin yrast and yrare band (2+,4+) measurements at GSI via n-knockout/Coulex

16. Spectroscopic insight into the shape coexistence in 78Sr
How can we measure it?

17. Experiment Sec. Frag. I@S4 (pps) 81Zr for (80Zr+n) 450
Livetime measurements via line-shape analysis (?)
AGATA S2’
FRS
Sec. beams:
100 MeV/u
81Zr 81Sr, 79Sr
SIS-18
Primary beam:
1 GeV/u 107Ag
4x109 pps
79Sr
Sec. Frag.
(pps)
81Zr for (80Zr+n)
450
77Sr for (76Sr+n)
1.5E3
79Sr for (78Sr+n)
1.4E5
78Sr + n
E’g J
79Sr
(to LYCCA)
bR=0.43
9Be-Target

18. Comparison vs. Pieter’s MC of 36K
AGATA
RISING
150 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 23.5 cm
cut qg [15,25] deg
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

19. Summary & Outlook
We plan to study deformation, shape coexistence and evolution effects in the 78,80Zr and 76,78Sr isotopes.
Both and offer complementary possibilities in order to approach this problem in a concomitant way. This means, high-spin yrast states at LNL via Fusion-Evaporation reactions, and low-spin yrast and yrare states at GSI-FRS.
The experiment proposal for concentrates on the high-spin yrast states of the 76,78Sr isotopes. Here we plan to measure the livetimes of the yrast levels up to 10+ by combining Plunger (RDDS) with Thick target (DSAM) techniques.
The experiment proposal for will concentrate on the measurment of the 0+,2+(4+) yrare states in the 78,80Zr and 76,78Sr isotopes.

20. END

21. Experiment (a) <t = 0.1 ps> t x 0.5 <t = 0.12 ps>
d = 23.5 cm
Be (1g/cm2)
AGATA S2’
<t = 0.1 ps> 2+
t x 0.5 4+
<t = 0.12 ps> 6+ 8+
10+
<t = 1 ps>
t = 5.1 ps
t = 155 ps
278 keV
78Sr
(t x 0.5)

22. Experiment (a) <t = 0.1 ps> t = 155 ps t x 0.5
d = 23.5 cm
Be (1g/cm2)
AGATA S2’
<t = 0.1 ps> 2+
t = 155 ps
t x 0.5
<t = 0.12 ps>
<t = 1 ps>
t = 5.1 ps
t = 155 ps
278 keV
(t x 0.5)

23. Experiment (a) <t = 0.1 ps> t = 5.1 ps t x 0.5
d = 23.5 cm
Be (1g/cm2)
AGATA S2’
<t = 0.1 ps> 4+
t = 5.1 ps
t x 0.5
<t = 0.12 ps>
<t = 1 ps>
t = 5.1 ps
t = 155 ps
278 keV
(t x 0.5)

24. Experiment (a) <t = 0.1 ps> t = 1 ps t x 0.5 <t = 0.12 ps>
d = 23.5 cm
Be (1g/cm2)
AGATA S2’
<t = 0.1 ps> 6+
t = 1 ps
t x 0.5
<t = 0.12 ps>
<t = 1 ps>
t = 5.1 ps
t = 155 ps
278 keV
(t x 0.5)

25. Comparison vs. Pieter’s MC of 36K
150 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 23.5 cm
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

26. Comparison vs. Pieter’s MC of 36K
150 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 23.5 cm
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

27. Comparison vs. Pieter’s MC of 36K
150 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 73.5 cm
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

28. Comparison vs. Pieter’s MC of 36K
150 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 73.5 cm
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

29. Comparison vs. Pieter’s MC of 36K
150 MeV/u
bRecoil at de-excitation time:
36K+n
810 keV
(3+)
d = 73.5 cm
Be (1g/cm2)
t = 15 ps GS 2+
t = 0 ps
t = 15 ps
t = 0 ps

30. Comparison vs. Pieter’s MC of 36K
200 MeV/u
bRecoil at de-excitation time:
36K+n
810 keV
t = 15 ps
(3+)
d = 73.5 cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps
t = 0 ps

31. Comparison vs. Pieter’s MC of 36K
200 MeV/u
150 MeV/u
36K+n
810 keV
(3+)
d = 73.5 cm
Be (1g/cm2)
d = cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps

32. Comparison vs. Pieter’s MC of 36K
200 MeV/u
200 MeV/u
36K+n
36K+n 2+
(3+)
810 keV GS
810 keV
(3+)
d = 73.5 cm
Be (1g/cm2)
d = 23.5 cm
Be (1g/cm2) GS 2+
t = 0 ps
t = 15 ps
t = 0 ps
t = 15 ps

33. Summary of 36K lifetime studies with AGATA S2’ (no angular cut!)
150 MeV/u
150 MeV/u
t = 0 ps
t = 15 ps
t = 0 ps
t = 15 ps
d = 23.5 cm
Be (1g/cm2)
d = 73.5 cm
Be (1g/cm2)
d = 73.5 cm
Be (1g/cm2)
200 MeV/u
t = 0 ps
t = 15 ps
d = 23.5 cm
Be (1g/cm2)
200 MeV/u
t = 0 ps
t = 15 ps

34. AGATA S2’:Efficiency vs. Theta for several distances

35. AGATA S2’:Efficiency vs. Theta for several distances

36. AGATA S2’: lineshape effect with and w/o angular cut2+
(3+)
810 keV GS
36K+n
d = 23.5 cm
Be (1g/cm2)
200 MeV/u
q in [15,25] deg
200 MeV/u
All q‘s
t = 0 ps
t = 15 ps
t = 0 ps
t = 15 ps

37. AGATA S2’: angular differential lineshape effect study

38. AGATA S2’: angular differential lineshape effect study
d = 23.5 cm
Be (1g/cm2)
q in [15,25] deg
q in [25,35] deg
t = 0 ps
t = 15 ps
q in [35,45] deg
q in [45,55] deg

39. Level Scheme of 78Sr
D.Rudolph et al. Phys. Rev. C, 1997

40. Previous Experimental Work on 78Sr
Year
Author
Laboratory
Detector
Reaction
Results on 78Sr
1982
Lister
et al.
Brookhaven N.L.
Ge, Ge(Li)
n-detector
58Ni(24Mg,2p2n)
100 MeV
yrast J=0 to 10
t2+, t4+
1989
Gross
SERC Daresbury
(BGO)Ge
110 MeV
yrast J=0 to 18
1994
Daresbury Nuc.Str. Facility
EUROGAM
40Ca(40Ca,2p)
128 MeV
yrast J=0 to 22
1997
Rudolph et al.
L.Berkeley N.L.
Gammasphere (57CS Ge + Microball)
58Ni(28Si,2p2n)
130 MeV
yrast J=0 to 26
negative parity side bands
2007
Davies
Argonne N.L.
Gammasphere (101 CS Ge + Microball)
40Ca(40Ca,2p2n)
165 MeV
76Sr

41. Measurables t = ? t = ? t = ? t = 5.1(5) ps t = 155(19) ps
lifetime values of yrast levels up to 10+ with high accuracy (5%/20%)
t = ?
t = ?
t = ?
Expected lifetimes (ps):
SU(3)
X(5)
U(5)
BMF 2+
155 (19) (exp. value) 4+
5.1(0.5) (exp. value) 6+
1.0
0.76
0.50
1.27 8+
0.19
0.12
0.07
0.39
10+
0.20
0.11
0.05
0.16
t = 5.1(5) ps
t = 155(19) ps
78Sr

42. Spectroscopic insight into the shape coexistence in 78Sr
(LNL Proposal 10.25)
C. Domingo-Pardo, T.R. Rodriguez, P. Boutachkov, J. Gerl, M. Gorska,
E. Merchan, S. Pietri, H.J. Wollersheim
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
J.J.Valiente-Dobon, G. de Angelis, D.R. Napoli, E. Sahin
INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy
S. Aydin, D. Bazzacco, E. Farnea, S. Lenzi, S. Lunardi, R. Menegazzo,
D. Mengoni, F. Recchia, C. Ur
Dipartimento di Fisica and INFN, Sezione di Padova, Padova, Italy
T. Pisulla, A. Dewald, C. Fransen, M. Hackstein, W. Rother
Institut für Kernphysik der Universität zu Köln, Köln, Germany
A.Gadea, A. Algora, B. Rubio, J.L. Tain
IFIC Instituto de Fisica Corpuscular, Valencia, Spain

43. Spectroscopic insight into the shape coexistence in 78Sr
Scientific Motivation

44. Scientific Motivation
Search for the possible empirical realization of X(5) Critical Point Symmetry in 78Sr
X(5) Sm
B(E2;J J-2)/B(E2;2 0)
Casten et al.,Phys.Rev.Lett. 85 (2000)
McCutchan et al. Phys.Rev.C 71 (2005)
Iachello,Phys.Rev.Lett. 85 (2000), 87 (2001)

45. Scientific Motivation
Search for the possible empirical realization of X(5) Critical Point Symmetry in 78Sr
78Sr
X(5)
10+
Rudolph et al. Phys. Rev. C, 1997
Gross et al. Phys. Rev. C, 1994
U(5)
X(5)
X(5)
SU(3)
Lister et al., Phys. Rev. Lett. 49 (1982)

46. Scientific Motivation
Quantum Phase Transitions can be also studied from a microscopic perspective e.g. as shown by T.Niksic et al., Phys. Rev. Lett. 99 (2007)
Beyond Mean Field calculations predict shape coexistence in 78Sr and strong triaxial effects, and can provide quantitative predictions of E(J) or BE2 values.
(*)
BMF Calculation by T.R. Rodriguez
(*) L.Gaudefroy et al. Phys. Rev. C 80, 2009

47. Spectroscopic insight into the shape coexistence in 78Sr
What can we measure?

48. Measurables t = ? t = ? t = ? t = 5.1(5) ps t = 155(19) ps
lifetime values of yrast levels up to 10+ with high accuracy (5%/20%)
t = ?
t = ?
Expected lifetimes (ps):
t = ?
SU(3)
X(5)
U(5)
BMF 2+
155 (19) (exp. value) 4+
5.1(0.5) (exp. value) 6+
1.0
0.76
0.50
1.27 8+
0.19
0.12
0.07
0.39
10+
0.20
0.11
0.05
0.16
t = 5.1(5) ps
t = 155(19) ps
78Sr

49. Spectroscopic insight into the shape coexistence in 78Sr
How can we measure it?

50. Experiment AGATA Demonstrator (5 triple cluster) + Köln Plunger
40Ca
XTU-TANDEM
120 MeV 40Ca-Beam 1 pnA
Recoil Distance Doppler Shift Method (RDDS)
Köln Plunger
Ca-Target
Au-Degrader
40Ca
bR=0.04 J
E’g Eg
40Ca(40Ca, 2p)78Sr
78Sr
Ca-target mg/cm2
Au-Degrader 10.5 mg/cm2

51. Experiment (a) t = 155(19) ps t x 0.95 t = 155(19) ps (t x 0.95)
AGATA Demonstrator (5 triple cluster) + Köln Plunger
d = 0.2 mm mm mm
t = 155(19) ps
t x 0.95
t = 155(19) ps
278 keV
(t x 0.95)
MC Code by E. Farnea and C. Michelagnoli

52. Experiment (a) t = 5.1(5) ps (t x 0.95) t = 5.1(5) ps (t x 0.95)
AGATA Demonstrator (5 triple cluster) + Köln Plunger
d = 0.03 mm mm mm
t = 5.1(5) ps
(t x 0.95)
t = 5.1(5) ps
503 keV
(t x 0.95)
MC Code by E. Farnea and C. Michelagnoli

53. Experiment (a) t ~ 1 ps (t x 0.8) t ~ 1 ps (t x 0.8)
AGATA Demonstrator (5 triple cluster) + Köln Plunger
d = mm mm mm
t ~ 1 ps
(t x 0.8)
t ~ 1 ps
(t x 0.8)
712 keV
+ Information from thick-target measurement

54. Experiment (a) AGATA Demonstrator (5 triple cluster) + Köln Plunger
Differential Decay Curve (DDC) Analysis Method
rel. gated peak intensity (a.u.)
712 keV
503 keV
278 keV
distance target-degrader (mm)

55. Experiment (b) t ~ 0.12 ps t ~ 0.1 ps t ~ 0.1 ps (t x 0.8) (t x0.8)
AGATA Demonstrator (5 triple cluster) + Thick Target
t ~ 0.12 ps
t ~ 0.1 ps
t ~ 0.1 ps
(t x 0.8)
(t x0.8)
(t x0.8)
1058 keV
t ~ 0.12 ps
(t x 0.8)
895 keV
MC Code by E. Farnea and C. Michelagnoli

56. Spectroscopic insight into the shape coexistence in 78Sr
How much beam-time is needed?

57. Beam-Time estimate Jp Eg (keV) t (ps) d (mm) gg-Counts time (h) 2+
277.6
155
0.2
1432
5.3 2
1452
5.4 4
1509
5.6 4+
503.2
5.1
0.03
1178
8.7
0.06
1214
9.0
0.10
1182 6+
712
1.0
0.008
1037
7.7
0.010
1036
7.6
0.020
992
7.3 8+
895
0.12
5449
5353 40
10+
1058
0.1
PLUNGER
Thick Target
Total Beam-Time Request = days

58. Outlook
The proposed lifetime measurements may provide the first strong evidence of X(5) quantum phase transition in 78Sr.
These results will be complemented with further yrare band measurements on 78Sr with AGATA at GSI in 2011/2012.
Measured lifetimes or B(E2) values will allow us to study shape coexistence in 78Sr from a microscopic point of view and they will provide an stringent test for BMF calculations, the predicted triaxiality effect in this nucleus and how the triaxial degree of freedom is included in the calculation.

59. Backup Slides

60. Level Scheme of 78Sr
yrast band
D.Rudolph et al. Phys. Rev. C, 1997

61. Previous Experimental Work on 78Sr
Year
Author
Laboratory
Detector
Reaction
Results on 78Sr
1982
Lister
et al.
Brookhaven N.L.
Ge, Ge(Li)
n-detector
58Ni(24Mg,2p2n)
100 MeV
yrast J=0 to 10
t2+, t4+
1989
Gross
SERC Daresbury
(BGO)Ge
110 MeV
yrast J=0 to 18
1994
Daresbury Nuc.Str. Facility
EUROGAM
40Ca(40Ca,2p)
128 MeV
yrast J=0 to 22
1997
Rudolph et al.
L.Berkeley N.L.
Gammasphere (57CS Ge + Microball)
58Ni(28Si,2p2n)
130 MeV
yrast J=0 to 26
negative parity side bands
2007
Davies
Argonne N.L.
Gammasphere (101 CS Ge + Microball)
40Ca(40Ca,2p2n)
165 MeV
76Sr

62. Shape coexistence along Z=38
Beyond Mean Field calculations do predict shape coexistence in 78Sr and strong triaxial effects

63. Beam-Time estimate Jp Eg (keV) t (ps) d (mm) Counts time (h) 2+ 277.6
155
0.2
1432
5.3 2
1452
5.4 4
1509
5.6 4+
503.2
5.1
0.03
1178
8.7
0.06
1214
9.0
0.10
1182 6+
712
1.0
0.008
1037
7.7
0.010
1036
7.6
0.020
992
7.3 8+
895
0.12
9535
9368 70
10+
1058
0.1
PLUNGER
Thick Target
Total Beam-Time = days

64. Theoretical Framework BMF
(from T.R. Rodriguez)

65. Theoretical Framework BMF
(from T.R. Rodriguez)

66. Theoretical Framework BMF
(from T.R. Rodriguez)

67. Theoretical Framework BMF
(from T.R. Rodriguez)