Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce Liverpool, Daresbury, Lyon, Grenoble, Strasbourg, Debrecen, Padova, Camerino Euroball IV 4/22/2019 Lund Conference June 2005 : E.S. Paul

Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce 4/22/2019 Lund Conference June 2005 : E.S. Paul

The Nucleus is a Mesoscopic System at the Femtoscale Mesoscopic: The atomic nucleus consists of a large, yet finite, number of strongly interacting constituent fermions (nucleons) Femtoscale: The size of the nucleus is of the order of femtometres (10-15 m) Similar to nanoscale (10-9 m) mesoscopic systems, e.g. metallic clusters, the properties (shell structure, deformation) are determined by the finite number of constituents 4/22/2019 Lund Conference June 2005 : E.S. Paul

At the Limits of Angular Momentum: Band Termination Fundamentally, nuclear angular momentum is generated by the (finite number of) constituent nucleons Hence there must be a “maximum” value for a given nucleus, or rather nucleonic configuration Experimentally this is seen as “termination” of a rotational band in nuclei when the nuclear angular momentum is generated entirely from the constituent nucleons rather than collective excitations of the nucleus 4/22/2019 Lund Conference June 2005 : E.S. Paul

Experimental Band Termination A band terminates when all valence particles outside a doubly magic (spherical) core are aligned 4/22/2019 Lund Conference June 2005 : E.S. Paul

Superdeformed Shell Structure New shell gaps appear when the lengths of the nuclear axes occur in the ratio of small integers: 2:1 (A = 150, dysprosium) 3:2 (A = 130, cerium) 3:1 (“hyperdeformation”) But they occur at different particle numbers to the spherical case 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul To Terminate or Not? For modest (i.e. small) deformation, solutions of the Harmonic Oscillator suggest that configurations will terminate into a noncollective oblate state where the spin is simply given by the sum of the angular momenta of the ‘pure’ single particle configuration: Imax For large deformation (e.g. 2:1 superdeformation), however, spin above Imax can be generated The SD Ce deformation (3:2 axes ratio) occurs at the intersection of these two regimes The (experimental) question is: will the SD bands in cerium nuclei ‘terminate’ or not? 4/22/2019 Lund Conference June 2005 : E.S. Paul

Superdeformation in 132Ce The first SD band was discovered in 132Ce: PJ Nolan et al., J. Phys G 11, L17 (1985) Its “enhanced” quadrupole moment showed it to correspond to the 3:2 shape AJ Kirwan et al., Phys. Rev. Lett. 58, 467 (1987) The TESSA3 array at Daresbury 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul EUROBALL IV Results A BGO inner ball calorimeter allowed measurement of the total (summed) γ ray energy and also the number of emitted γ rays in an event Gating on these quantities enhanced the yield of 132Ce (top) 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul Yrast SD Band in 132Ce (SD1) Top: triples (double gated) γ-ray spectrum of SD1 in 132Ce with a high ‘sum-energy/fold’ condition Bottom: triples γ-ray spectrum from the whole data set 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul SD1 in 132Ce The lowest energy (yrast) superdeformed band in 132Ce spans 50ħ (from 20ħ to 70ħ) of angular momentum (in a finite fermionic system) ! 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul SD2 and SD3 in 132Ce 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 132Ce SD1 Rigid-Rotor Plot The yrast SD band in 132Ce shows similarities to smoothly terminating bands in A ~ 100 nuclei. It is approaching the maximum spin for its configuration (termination at 78ħ) 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul Theory: Protons (Z = 58) Important orbitals (relative to Z = 50): h11/2 ‘intruder’ levels (particles) - red g9/2 ‘extruder’ levels (holes) - blue Cerium has a 10 particle 2 hole configuration A ‘finite’ number of valence protons to generate angular momentum 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul Theory: Neutrons (N = 74) Important orbitals (relative to N = 82): h9/2 and f7/2 intruder orbitals – blue i13/2 intruder orbitals – green h11/2 holes – red Again a finite number of ‘constituents’ to generate the angular momentum 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 132Ce SD1 Theory Cranked Nilsson Strutinsky calculations have been performed The yrast SD1 band in 132Ce cannot be described over its whole range by a single configuration Look at dynamic moment of inertia 4/22/2019 Lund Conference June 2005 : E.S. Paul

Dynamic Moments of Inertia 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 131Ce SD1 and SD2 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 131Ce SD1 – SD2 Links 100% 90% 10% 4/22/2019 Lund Conference June 2005 : E.S. Paul

131Ce: SD1 & SD2 Extension + Links The excited band in 131Ce (SD2) has the same configuration as the yrast band in 132Ce (SD1) 131Ce SD2 becomes favoured (yrast) at high spin 131Ce SD2 has a larger quadrupole moment (8.2 eb) compared to all other bands in 131,132Ce (7.3 eb) 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 131Ce Theory 4/22/2019 Lund Conference June 2005 : E.S. Paul

Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce The End 4/22/2019 Lund Conference June 2005 : E.S. Paul

Gammasphere Expt (Nov 2004) (AC Milan) 4/22/2019 Lund Conference June 2005 : E.S. Paul

Lund Conference June 2005 : E.S. Paul 132Ce SD1 Decay & Links Aled Evans 4/22/2019 Lund Conference June 2005 : E.S. Paul