Spectroscopic insight into the shape coexistence in 76,78Sr, (78),80Zr Letter of Intent for AGATA@GSI 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

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:

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

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

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

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!

Shape coexistence along Z=40

Scientific Motivation Study the possible X(5) character of these N=Z=38,40 Sr and Zr isotopes X(5) 152Sm 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)

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)

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

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

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

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

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. I@S4 (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

Comparison vs. Pieter’s MC of 36K AGATA RISING 37Ca @ 150 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 23.5 cm cut qg [15,25] deg Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

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) <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)

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)

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)

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)

Comparison vs. Pieter’s MC of 36K 37Ca @ 150 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 23.5 cm Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

Comparison vs. Pieter’s MC of 36K 37Ca @ 150 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 23.5 cm Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

Comparison vs. Pieter’s MC of 36K 37Ca @ 150 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 73.5 cm Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

Comparison vs. Pieter’s MC of 36K 37Ca @ 150 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 73.5 cm Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

Comparison vs. Pieter’s MC of 36K 37Ca @ 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

Comparison vs. Pieter’s MC of 36K 37Ca @ 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

Comparison vs. Pieter’s MC of 36K 37Ca @ 200 MeV/u 37Ca @ 150 MeV/u 36K+n 810 keV (3+) d = 73.5 cm Be (1g/cm2) d = 70-140 cm Be (1g/cm2) GS 2+ t = 0 ps t = 15 ps

Comparison vs. Pieter’s MC of 36K 37Ca @ 200 MeV/u 37Ca @ 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

Summary of 36K lifetime studies with AGATA S2’ (no angular cut!) 37Ca @ 150 MeV/u 37Ca @ 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) 37Ca @ 200 MeV/u t = 0 ps t = 15 ps d = 23.5 cm Be (1g/cm2) 37Ca @ 200 MeV/u t = 0 ps t = 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 2+ (3+) 810 keV GS 36K+n d = 23.5 cm Be (1g/cm2) 37Ca @ 200 MeV/u q in [15,25] deg 37Ca @ 200 MeV/u All q‘s t = 0 ps t = 15 ps t = 0 ps t = 15 ps

AGATA S2’: angular differential lineshape effect study

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

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

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

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

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

Spectroscopic insight into the shape coexistence in 78Sr Scientific Motivation

Scientific Motivation Search for the possible empirical realization of X(5) Critical Point Symmetry in 78Sr X(5) 152Sm 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) 2 4 6 8 10 Iachello,Phys.Rev.Lett. 85 (2000), 87 (2001)

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)

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

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

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

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

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 400 mg/cm2 Au-Degrader 10.5 mg/cm2

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 2 mm 4 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

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 0.06 mm 0.10 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

Experiment (a) t ~ 1 ps (t x 0.8) t ~ 1 ps (t x 0.8) AGATA Demonstrator (5 triple cluster) + Köln Plunger d = 0.008 mm 0.01 mm 0.02 mm t ~ 1 ps (t x 0.8) t ~ 1 ps (t x 0.8) 712 keV + Information from thick-target measurement

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)

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

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

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 = 5 days

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

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

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

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 = 5.6 days

Theoretical Framework BMF (from T.R. Rodriguez)

Theoretical Framework BMF (from T.R. Rodriguez)

Theoretical Framework BMF (from T.R. Rodriguez)

Theoretical Framework BMF (from T.R. Rodriguez)