Spectroscopic insight into the shape coexistence in 76,78 Sr, (78),80 Zr P. Boutachkov, C. Domingo-Pardo, H. Geissel, J. Gerl, M. Gorska, E. Merchan, S.

Spectroscopic insight into the shape coexistence in

76,78Sr, (78),80Zr

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-DobonINFN, 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. RotherInstitut fuer Kernphysik der Universitaet zu Köln, Köln, Germany

A. Algora, A. Gadea, B. Rubio, J.L. TainIFIC Instituto de Fisica Corpuscular, Valencia, Spain

Letter of Intent for AGATA@GSI

Spectroscopic insight into the shape coexistence in

76,78Sr, (78),80Zr

Scientific Motivation

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



A=78

N=38

A=80

N=40

and Zirconium isotopes:

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.

Scientific Motivation • Beyond Mean Field calculations predict shape coexistence in 78Sr and strong triaxial effects

(*) L.Gaudefroy et al. Phys. Rev. C 80, 2009

(*)

Shape coexistence along Z=40

A=78

N=38

A=80

N=40


A=80

N=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!


A=78

N=38

A=80

N=40

Scientific Motivation • Study the possible X(5) character of these N=Z=38,40 Sr and Zr isotopes

E.A. McCutchan et al. Phys.Rev.C 71 (2005)

Casten et al.,Phys.Rev.Lett. 85 (2000)

B(E

2;J

J-

2)/B

(E2;

2

0)

X(5) 152Sm

Iachello,Phys.Rev.Lett. 85 (2000), 87 (2001)

5

np

np

NN

NNP

Scientific Motivation • Search for the possible empirical realization of X(5) Critical Point Symmetry in 78Sr

X(5)

78Sr X(5)

X(5)

U(5)

SU(3)

78Sr

10+

Lister et al., Phys. Rev. Lett. 49 (1982)

Rudolph et al. Phys. Rev. C, 1997

Gross et al. Phys. Rev. C, 1994

5

np

np

NN

NNP

Spectroscopic insight into the shape coexistence in 78Sr

What can we measure?

Measurables• lifetime values of yrast levels up to 10+ with high accuracy (5%/20%)

= 155(19) ps

= 5.1(5) ps

= ?

= ?

= ?

78Sr 80Zr

= ?

= ?

= ?

= ?

= ?

76Sr

= ?

= ?

= ?

= ?

= ?

• yrast band livetime measurements at LNL via fusion evaporation

•yrare band (2+,4+) measurements at GSI via n-knockout/Coulex


• 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

LNL GSI


How can we measure it?

Experiment• Livetime measurements via line-shape analysis (?)

SIS-18

Primary beam:

1 GeV/u 107Ag

4x109 pps

79Sr

AGATA S2’

9Be-Target

R=0.43

E’79Sr

78Sr + n

FRS

Sec. beams:

100 MeV/u

81Zr 81Sr, 79Sr

(to LYCCA)

Sec. Frag. I@S4 (pps)81Zr for (80Zr+n) 450

77Sr for (76Sr+n) 1.5E3

79Sr for (78Sr+n) 1.4E5

Comparison vs. Pieter’s MC of 36K

d = 23.5 cm

cut [15,25] deg

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

= 0 ps

= 15 ps

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/uAGATA RISING

Summary & Outlook

• We plan to study deformation, shape coexistence and evolution effects in the 78,80Zr and 76,78Sr isotopes.

• Both AGATA@LNL and AGATA@GSI 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 AGATA@LNL 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 AGATA@GSI will concentrate on the measurment of the 0+,2+(4+) yrare states in the 78,80Zr and 76,78Sr isotopes.

END

Experiment (a)• AGATA S2’

= 155 ps

d = 23.5 cm

Be (1g/cm2)

x 0.5)

= 5.1 ps

x 0.5

278 keV

2+

4+

6+8+ 10+

= 1 ps>

= 0.12 ps>

= 0.1 ps>

78Sr


= 155 ps

d = 23.5 cm

Be (1g/cm2)

x 0.5)

= 5.1 ps

x 0.5

278 keV

2+

= 1 ps>

= 0.12 ps>

= 0.1 ps>

= 155 ps


= 155 ps

d = 23.5 cm

Be (1g/cm2)

x 0.5)

= 5.1 ps

x 0.5

278 keV

4+

= 1 ps>

= 0.12 ps>

= 0.1 ps>

= 5.1 ps


= 155 ps

d = 23.5 cm

Be (1g/cm2)

x 0.5)

= 5.1 ps

x 0.5

278 keV

6+

= 1 ps

= 0.12 ps>

= 0.1 ps>

= 1 ps


d = 23.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

= 0 ps

= 15 ps


d = 23.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

= 0 ps

= 15 ps


d = 73.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

= 0 ps

= 15 ps


d = 73.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

= 0 ps

= 15 ps


d = 73.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

36K+n

2+

(3+)810 keV

GS

Recoil at de-excitation time:

= 15 ps

= 0 ps

= 0 ps

= 15 ps


d = 73.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

36K+n

2+

(3+)810 keV

GS

Recoil at de-excitation time:

= 15 ps

= 0 ps

= 0 ps

= 15 ps


d = 73.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

36K+n

2+

(3+)810 keV

GS

= 0 ps

= 15 ps

d = 70-140 cm

Be (1g/cm2)

37Ca @ 150 MeV/u


d = 73.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

36K+n

2+

(3+)810 keV

GS

= 0 ps

= 15 ps

d = 23.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

36K+n

2+

(3+)810 keV

GS

= 0 ps

= 15 ps

Summary of 36K lifetime studies with AGATA S2’ (no angular cut!)

d = 73.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

= 0 ps

= 15 ps

d = 23.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u

= 0 ps

= 15 ps

d = 73.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u

d = 23.5 cm

Be (1g/cm2)

37Ca @ 150 MeV/u = 0 ps

= 15 ps

= 0 ps

= 15 ps

AGATA S2’:Efficiency vs. Theta for several distances

AGATA S2’:Efficiency vs. Theta for several distances

AGATA S2’: lineshape effect with and w/o angular cut

36K+n

d = 23.5 cm

Be (1g/cm2)

37Ca @ 200 MeV/u37Ca @ 200 MeV/u

= 0 ps

= 15 ps

= 0 ps

= 15 ps

in [15,25] deg

2+

(3+)810 keV

GS

All‘s

AGATA S2’: angular differential lineshape effect study

in [25,35] deg

in [35,45] deg

= 0 ps

= 15 ps

in [15,25] deg

in [45,55] deg

AGATA S2’: angular differential lineshape effect study

d = 23.5 cm

Be (1g/cm2)

Level Scheme of 78Sr

D.Rudolph et al. Phys. Rev. C, 1997

Previous Experimental Work on 78SrYear 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

2+, 4+

1989 Gross

et al.SERC Daresbury (BGO)Ge

n-detector

58Ni(24Mg,2p2n)

110 MeV

yrast J=0 to 18

1994 Gross

et al.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

et al.Argonne N.L. Gammasphere

(101 CS Ge + Microball)

40Ca(40Ca,2p2n)

165 MeV

76Sr


= 155(19) ps

= 5.1(5) 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

Expected lifetimes (ps):

78Sr


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. SahinINFN, 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. RotherInstitut für Kernphysik der Universität zu Köln, Köln, Germany

A.Gadea, A. Algora, B. Rubio, J.L. TainIFIC Instituto de Fisica Corpuscular, Valencia, Spain

(LNL Proposal 10.25)


Scientific Motivation


McCutchan et al. Phys.Rev.C 71 (2005)

Casten et al.,Phys.Rev.Lett. 85 (2000)

B(E

2;J

J-

2)/B

(E2;

2

0)

X(5) 152Sm

Iachello,Phys.Rev.Lett. 85 (2000), 87 (2001)

5

np

np

NN

NNP

2 4 6 8 10


X(5)

78Sr X(5)

X(5)

U(5)

SU(3)

10+

Lister et al., Phys. Rev. Lett. 49 (1982)

Rudolph et al. Phys. Rev. C, 1997

Gross et al. Phys. Rev. C, 1994

5

np

np

NN

NNP

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.

(*) L.Gaudefroy et al. Phys. Rev. C 80, 2009

(*)

BMF Calculation by T.R. Rodriguez


What can we measure?


= 155(19) ps

= 5.1(5) 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

Expected lifetimes (ps):

78Sr


How can we measure it?

Experiment• AGATA Demonstrator (5 triple cluster) + Köln Plunger

XTU-TANDEM

120 MeV 40Ca-Beam 1 pnA

40Ca

40Ca(40Ca, 2p)78Sr

Ca-target 400 g/cm2

Au-Degrader 10.5 mg/cm2

AGATA Demonstrator

Köln Plunger

Ca-Target Au-Degrader

40Ca

R=0.04

E’ E

78Sr

Recoil Distance Doppler Shift Method (RDDS)

http://www.ikp.uni-koeln.de/groups/dewald/plunger/plunger_at.html+pic=PLUNGER_MSU

Experiment (a)• AGATA Demonstrator (5 triple cluster) + Köln Plunger

= 155(19) ps

d = 0.2 mm 2 mm 4 mm

x 0.95)

= 155(19) ps

x 0.95

MC Code by E. Farnea and C. Michelagnoli

278 keV


= 5.1(5) ps

d = 0.03 mm 0.06 mm 0.10 mm

x 0.95)

= 5.1(5) ps x 0.95)

503 keV



d = 0.008 mm 0.01 mm 0.02 mm

+ Information from thick-target measurement

~ 1 ps

x 0.8)

~ 1 ps

x 0.8)712 keV


712 keV

503 keV

278 keV

Differential Decay Curve (DDC) Analysis Method

distance target-degrader (m)

rel.

gate

d pe

ak in

tens

ity (

a.u.

)

Experiment (b)• AGATA Demonstrator (5 triple cluster) + Thick Target

~ 0.12 ps x 0.8)

~ 0.12 ps x 0.8)

895 keV

~ 0.1 ps

( x0.8)1058 keV

~ 0.1 ps( x0.8)



How much beam-time is needed?

Beam-Time estimate

J E (keV) (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 8.7

6+ 712 1.0 0.008 1037 7.7

0.010 1036 7.6

0.020 992 7.3

8+ 895 0.12 0 5449

5353

40

10+ 1058 0.1

Total Beam-Time Request = 5 days

PL

UN

GE

R

Thick Target

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.

Backup Slides

Level Scheme of 78Sr

D.Rudolph et al. Phys. Rev. C, 1997

yrast band

Previous Experimental Work on 78SrYear 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

2+, 4+

1989 Gross

et al.SERC Daresbury (BGO)Ge

n-detector

58Ni(24Mg,2p2n)

110 MeV

yrast J=0 to 18

1994 Gross

et al.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

et al.Argonne N.L. Gammasphere

(101 CS Ge + Microball)

40Ca(40Ca,2p2n)

165 MeV

76Sr

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

Beam-Time estimate

J E (keV)

(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 8.7

6+ 712 1.0 0.008 1037 7.7

0.010 1036 7.6

0.020 992 7.3

8+ 895 0.12 0 9535

9368

70

10+ 1058 0.1

Total Beam-Time = 5.6 days

PL

UN

GE

R

Thick Target

Theoretical Framework BMF

(from T.R. Rodriguez)







Spectroscopic insight into the shape coexistence in 76,78 Sr, (78),80 Zr P. Boutachkov, C. Domingo-Pardo, H. Geissel, J. Gerl, M. Gorska, E. Merchan, S.

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