Shape Isomerism in 66 Ni S. Leoni, B. Fornal, N. Marginean, M. - PowerPoint PPT Presentation

“ Shape Isomerism in 66 Ni ” S. Leoni, B. Fornal, N. Marginean, M. Sferrazza, Y. Tsunoda, T. Otsuka, et al., … University of Milano and INFN sez. Milano, Italy IFJ-PAN, The Ins=tute of Nuclear Physics, Krakow, Poland IFIN HH, Bucharest, Romania Departement de Physique, Universite libre de Bruxelles, Belgium Center for Nuclear Study, University of Tokyo, Japan

Outline o Introduction isomers in molecular chemistry o Atomic nucleus shell structure, deformation, potential energy surpace (PES) o Discovery of nuclear fission (shape) isomers o Experimental search for shape coexistence/shape isomers o The unique case of 66 Ni o Relevance for THEORY – SHELL Model MICROSCOPIC origin of Nuclear Deformation

ISOMERS in chemistry In chemistry, an isomer is a molecule with the same molecular formula as another molecule, but with different arrangement of the atoms. Subgroup: stereoisomers or spa=al isomers Sub-subgroup: conforma=onal isomers (conformers) Sub-sub-subgroup: rotamers

Butane molecule C 4 H 10 Conformational isomers C C 60 ° free energy rotation C C CH 3 CH 3 CH 3 CH 3 60 ° H C C H H H C C rotation H H H H Free energy diagram of butane as a function of dihedral angle Rotation about single bond of butane

Potential energy surface (PES) of a nucleus If we consider only quadrupole deforma<on Parametriza<on Z Z of the NUCLEAR SHAPE a β cos 20 = γ a ( 1 2 ) β sin R ( , ) R [ 1 a lm Y ( , )] ∑ 22 = γ θ ϕ = + θ ϕ 0 lm β < 0 l , m β > 0 ONE-dimensional representation TWO-dimensional contour ENERGY 5 4 3 2 1 -0.3 0.0 0.1 0.2 -0.2 -0.1 0.3 Spheroidal Deforma<on β

Where do we find secondary minima in the nuclear chart considering only sta<c deforma<on ? (no addi=onal degree of freedom involved … angular momentum, excita=ons … )

1953 Already in 1953 , Hill and Wheeler discussed possible consequences of the existence of two well separated minima in the potential energy surface for the ground state of the system. Cigare form becoms stable

1961 - discovery of the first spontaneously fissioning isomer in 242 Am with a half-life 14 msec 82 C. M. Polikanov et al., Zh. Eksp. Teor. Fiz. 42, 1464 126 (1962) [Sov. Phys.- JETP 15, 1016 (1962)]. 50 82 28 50 20 8 28 20 2 2 8

1968 1973 Liquid Drop Model

Shape isomers in actinides 82 o HIGH Poten<al BARRIER 126 o Nucleus trapped In the second minimum o Spontaneous fission from the second minimum 50 82 28 50 20 8 28 20 2 2 8 TWO EXCEPTIONS

SHAPE ISOMERS very peculiar metastable states o HIGH Poten<al BARRIER o Nucleus trapped In the minimum o very retarded photon decay ( 10 7 hindrance ) 236,238 U Structures living in “separate worlds” 5% MAIN FINGER PRINT: 95% γ hindrance of deexciSng transiSons B ( E2 ) = 1 . 54 x 10 - 7 W.u. !!! Can OTHER (lighter) nuclei exhibit these features ?

SEARCH for SHAPE ISOMERS in LIGHTER nuclei: o MOST CLEAR-CUT cases of SHAPE Coexistence o a PROBE of MICROSCOPIC origin of nuclear deforma<on within a pure SHELL Model Approach Ideal Cases are 0 + states – to avoid ambiguity given by spin effects (Ac<nides are NOT doable by SHELL Model …)

SHAPE Coexistence in Atomic Nuclei Appearence of different shapes at low excitaSon energy K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011) Prolate Spherical Oblate 186 Pb Shape Isomers in acSnides Polikanov - 1973 82 0 + 126 0 + 3 2 0 + 1 70 Ni 50 A. Andreyev et al., Nature 405 (2000) 430 82 28 50 20 8 28 20 2 2 8 Through the last 40 years of experimental acSviSes, the concept has evolved: 1) exo<c rarity (1970’) 2) islands of occurrence (1990’) 3) current believe: occurrence in all (but the lightest) nuclei

235 U target Z=50 0.3 N=82 0.2 0.4 241 Pu target 0.3 0.1 N=60 100 Zr Z=28 0.2 N=50 0.1 0.0 0.0 0 + B(E2) 69 W.u. 0 + B(E2) 2 + 0 + 2 + 63 W.u. B(E2) 2 + 93 W.u. 0 + 0 + 0 + 98 Sr 102 Mo 100 Zr

E. Clément, M. Zielińska et al ., Phys.Rev. Lej. 116, 022701 (2016) Z=50 235 U target N=82 241 Pu target N=60 N=50 B(E2)=16 W.u. 98 Sr B(E2)=93 W.u. 96 Sr No retardaSon in γ decay is observed !!!! Poten<al barrier NOT sizable enough to prevent fast shape changes

PredicSons for SHAPE ISOMERS - Mean Field Based Macro-Microscopic Model – P. Moeller et al. 2012 Global Calculation Searching for Nuclear Shape Isomers Study of 7206 nuclei from A=31 to A=209 2012 64 Ni 66 Ni 68 Ni actinides 1989 Ni 66 Ni Microscopic Hartree-Fock 1989 plus BCS calculations Barrier hight Energy of second minimum 66 Ni 64 Cr 66 Fe 68 Ni 72 Zn

PredicSons for SHAPE ISOMERS – SHELL Model Based [ Otsuka group and Nowacki, Lenzi, Poves, …] state-of-the-art SHELL Model : possible for A <= 100 new calcula<ons scheme, very powerfull computer Inves<ga<on of MICROSCOPIC NATURE - wave func<ons, B(E λ /M λ ), … Monte Carlo SHELL Model (T. Otsuka’s Group – K computer 10 6 processors) 66 Ni – 78 Ni: FULL pf + g 9/2 + d 5/2 for both neutrons and protons 66 Ni 68 Ni 70 Ni oblate oblate prolate prolate spherical spherical Z=28 70 Ni 68 Ni 78 Ni 66 Ni 64 Ni N=50 N=40 stable Y. Tsunoda et al., PRC 89 (2014) 031301R

Experimentally … No retardaSon is found in 68 Ni and 70 Ni B(E2) 2.4 W.u. prolate B(E2) 7 W.u. prolate oblate spherical spherical 70 Ni 68 Ni B. P. Crider et al., Phys. LeP. B 763, 108 (2016)

PredicSons of four models à shape isomerism in 66 Ni Microscopic Hartree-Fock-Bogoliubov Microscopic Hartree-Fock plus BCS 66 Ni 1989 Barrier hight 1989 Energy of second minimum 66 Ni 64 Cr 66 Fe 68 Ni 72 Zn 2012 66 Ni 66 Ni 2016 Monte Carlo Shell Model Macro-Microscospic Model

MONTE CARLO SHELL MODEL Calculations Y. Tsunoda and T. Otsuka, Univ. of Tokyo State-of-the-art Shell Model calculations possible by employing new calculations schemes and very powerful computing systems (K computer -10 6 processors) prolate 0 +4 82 126 0.006 W.u. 0 +3 spherical 50 0.01 W.u. 82 0 +2 oblate 28 4.1 W.u. FULL 50 20 pf + g 9/2 + d 5/2 8 28 for both neutrons and protons 20 2 2 8 Detailed Microscopic Inves<ga<on: o Wave func<ons spherical 0 +1 o B(E λ /M λ ), … 66 Ni

MONTE CARLO SHELL MODEL Calculations Y. Tsunoda and T. Otsuka, Univ. of Tokyo prolate 0 +4 0.006 W.u. 0 +3 spherical 0.01 W.u. 0 +2 oblate 4.1 W.u. Circles: MCSM basis vectors projected on PES (T-Plot) spherical A quadruplet of 0 + states !!!! 0 +1 66 Ni

Decay Scheme of 66 Ni R. Broda et al ., Phys. Rev. C 86, 064312 (2012) Monte Carlo SHELL Model 0.15(2) W.u. 0.07 (t,p) prolate 0 +4 0 +4 0.006(7) W.u. 0 +3 0 +3 spherical 0.0028 0 +2 1.12(9) W.u. 1.53(9) W.u. 0 +2 0.74 oblate 5.9 0.0025(4) W.u. 0.0024 spherical 0 +1 0 +1 Excited states energies à One-to-one correspondence ( including 0 + states !) à very well reproduced !! B(E2/M1) (from our Bucharest EXP)

β -decay populaSon of 66 Ni D. Pauwels, P. Van Duppen et al ., ARIS-2011 Conference Monte Carlo SHELL Model prolate 0 +4 4.5 3.1(6) 5.3(2) 0 +3 4.1 29(3) 4.4(1) spherical 0 +2 oblate 5(1) 5.5(4) 5.6 63(4) 4.8(1) 4.3 spherical 0 +1 log(l) I β (%) log(l) model predicSons: MCSM EXP General agreement with β -decay branches popula<on of 0 + and 2 + spherical states from spherical 66 Co g.s 66 Fe à 66 Co à 66 Ni

Our Bucharest Experiment (@IFIN HH) 18 O + 64 Ni à 16 O + 66 Ni ( 2n Transfer - 1 MeV below Coulomb Barrier) σ ( 66 Ni) ≈ few mb - FUSION strongly suppressed Z=28 64 Ni 66 Ni 14 HPGe - 1.1% eff ROSPHERE 11 LaBr 3 (Ce) - 1.75% eff N=40 o THICK Target – 5 mg/cm 2 γ o PLUNGER - 12 distances From 10 to 3000 µ m 16 O 66 Ni 64 Ni v/c ≈ 2.2 % TOF of 155 ps in 1 mm γ 18 O (39 MeV) > 1.5 month 30 pnA beam current

18 O+ 64 Ni à 16 O+ 66 Ni THICK TARGET 1245 gate: 1425 keV E beam = 39 MeV 1018 2n transfer below Coulomb Barrier at IFIN HH Bucarest (t,p) 1.4 ps 2971 3+ 2974 0 + THICK TARGET, gate: 1425 keV 4 (DSAM) 2671 0 + 1018 3 1245 2443 0 + 2 1546 1549 1245 1018 1425 2+ 1.5 – 15 ps 1245 1018 1425 0 + 1 77 – 465 ps 77 – 465 ps 66 Ni 1245 1245 All transi<ons belong to 66 Ni !!

18 O+ 64 Ni à 16 O+ 66 Ni THICK TARGET 1245 gate: 1425 keV E beam = 39 MeV 1018 2n transfer below Coulomb Barrier at IFIN HH Bucarest (t,p) 1.4 ps 2971 3+ 2974 2974 0 + 0 + THICK TARGET, gate: 1425 keV 4 4 (DSAM) 2671 0 + 1018 3 1245 2443 0 + 2 1546 1549 1549 1245 1018 1425 2+ 1.5 – 15 ps 1245 1018 1425 0 + 1 77 – 465 ps 77 – 465 ps 66 Ni 1245 1245 All transi<ons belong to 66 Ni !!

prolate 0 +4 2971 3+ 2974 0 +4 20(7) ps 0.006 W.u. 2671 2671 0 +3 134(9) ps 0 +3 spherical 2443 0 +2 7.6(8) ps 0.01 W.u. 1546 1549 1245 1245 0 +2 oblate 1018 4.1 W.u. 1425 2+ 1425 spherical 0 +1 0 +1 66 Ni

prolate 0 +4 !!!!!!!!!!!!! 2971 3+ 2974 0 +4 B(E2) ~ 0.2 Wu 0.006 W.u. 2671 2671 0 +3 B(E2) = 0.1 Wu 0 +3 spherical 2443 0 +2 B(E2) = 4.3 Wu 1546 0.01 W.u. 1549 1245 1245 0 +2 2 TRANSITIONS oblate 1018 4.1 W.u. BELOW 1 W.u. 1425 2+ !!!! 1425 spherical 0 +1 0 +1 66 Ni