Shape evolution in neutron-rich Zr isotopes through secondary fragmentation reaction S. Pietri, J. Gerl et al. (GSI Darmstadt), A. Bruce et al. (Univ. Brighton), Z. Podolyak et al. (Univ. Surrey), A. Algora et al. (IFIC Valencia), D. Sohler et al. (Debrecen) presented at AGATA Physics Workshop 2010 Istanbul, Turkey May 6, 2010

Shape evolution in neutron rich nuclei How to explain collective phenomena from individual motion? What are the phases, relevant degrees of freedom, and symmetries of the nuclear many-body system? Investigate the evolution of shapes and shape changes in nuclei Neutron-rich medium heavy nuclei are predicted to exhibit dramatic shape effects

Nuclear shapes phase transitions of the equilibrium shapes octahedral nuclear shapes rapid shape changes and shape coexistence

Most dramatic shape changes in heavy Zr nuclei rapid deformation change from  ≈ 0.1 to  = 0.47

Rapid shape changes in medium heavy nuclei from spherical via triaxial to prolate deformed rigid rotor vibrator

Shape coexistence in heavy Zr nuclei? Hartree-Fock Bogolyubov 9/2-[514]  5/2+[420] K  = 5 - ~100 ns isomer PES for 106 Zr: triaxiality Alignment of g 9/2 protons and h 11/2 neutrons produce oblate structure Liquid drop with shell correction oblate prolate

X(5) Critical point nuclei Interacting Boson Model X(5) Dynamical symmetry shape transitional nuclei unexplored Sr to Mo region Vibrator X(5) Rotor Deformation

Shape evolution controversy ? prolate excited states known Figure 1: The lo cation of predicted m ulti-quasiparticle states in this region [1]. Pro- late m ulti-quasiparticle states are predicted in 110 ; 112 ; 114 Zr and oblate m ulti-quasiparticle states in ev en-ev en N=66 n uclei from 100 Se to 112 Pd. The red line marks the limit of n uclei in whic h excited states ha v e b een observ ed (see text for details). implications for the mean-eld p oten tials used to calculate the n uclear shap e and the conguration-constrained calculations used to calculate the m ulti-quasiparticle states. 2.2 X(5) Critical p oin t n uclei. Benc hmarks of collectiv e n uclear b eha viour are the harmonic vibrator [6], axially de- formed rotor [7], and triaxially soft rotor [8]. They corresp ond to limits of the in teracting b oson mo del (IBM) and an algebraic description of the nature of the transition b et w een these limits has b een dev elop ed indirect analogy with classical phase transitions [9]. Recen tly, it has b een suggestedthat a useful approac h is to nd an analytic appro xima- tion of the critical p A recen t pap er [4] p oin ted out that a necessarycondition for X(5) b eha viour is that the n um b er of in teractions b et w een v alence protons and neutrons is sucien t to induce collectiv ec haracteristics but not so large asto push the n ucleus to full rotational b e- ha viour. This is reected in the P-factor [14] P= NpNn/(Np+Nn) where Np and Nn are the n um b ers of v alence protons and neutrons, resp ectiv ely. Substan tial collectivit y no excited states known prolate oblate shape change sudden deformation triaxial shapes shape coexistence multi quasi-particle states dynamical symmetries... Ideal testing ground for theoretical models

Proposed experiment Goal: Identify low and medium spin yrast and near-yrast states in Zr, and in surrounding n-rich Sr and Mo isotopes, and determine lifetimes Technique:secondary fragmentation, relativistic DSAM Beam: 238 U at 750 AMeV, 4x10 9 /spill → 110 Mo at 150 AMeV, 7x10 2 /spill Set-up: AGATA (  detection) LYCCA (channel identification)

Rates (8 + ) Cr secondary fragmentation of 55 Ni on 9 Be at 140 AMeV DSAM lineshapes 108 Zr 106 Zr 104 Zr 102 Zr ions /spill excitation /shift6x x x x  -yield /shift max. spin (>10% of 2 + ) An example of Mikes run from the early RISING days without mass selection

112 Sn →Au Relativistic Coulomb excitation / fragmentation excited nucleus Coulomb interaction Prefragment Equilibrated nucleus

Zs. Podolyak et al. 148 Tb I = 27 + R = 3.2 (3) % Fragmentation of 208 Pb Fragmentation of 238 U Isomeric ratios I R [%] 211 Fr 29/ (2) 212 Fr (2) 213 Fr 29/ (8) 214 Ra (2) 215 Ra 43/ (6) High Spin population in massive fragmentation massive fragm. I (hbar)

Secondary fragmentation of 55 Ni on 9 Be at 140 MeV/u Mirror symmetry at N  Z (8 + ) Cr 46 Ti Ni Co Fe Mn Cr Ca Ti Ar S Si E dE First observation of higher spin states at relativistic energies extract lifetimes from lineshapes Mike Bentley et al.