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Spontaneous Fission Properties of Superheavy Nuclei

Spontaneous Fission Properties of Superheavy Nuclei. Fritz Peter Heßberger GSI – Helmholtzzentrum für Schwerionenforschung mbH, D-64291 Darmstadt, Germany Helmholtz – Institut Mainz, D-55099 Mainz, Germany. ECT Workshop Trento, Italia, April 9 – 13, 2018. Version 29. 5. 2018. Layout.

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Spontaneous Fission Properties of Superheavy Nuclei

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  1. Spontaneous Fission Properties of Superheavy Nuclei Fritz Peter Heßberger GSI – Helmholtzzentrum für Schwerionenforschung mbH, D-64291 Darmstadt, Germany Helmholtz – Institut Mainz, D-55099 Mainz, Germany ECT Workshop Trento, Italia, April 9 – 13, 2018 Version 29. 5. 2018

  2. Layout  Motivation  General considerations  Fission barriers  SF half-lives  Nuclearstructureand SF – SF hindranceofodd-massnuclei  <TKE> measurementsandsystematics  Fission modes  Specificfeaturesof SF  SF of K – isomers  EC delayedfission  SF ofeven-evennuclei after EC decay – Z identificationof SHE  Summary andconclusions

  3. The Strong Force Oneofthefourbasicinteractions, playingamongothers an essential rolefor • Quark – Gluon - Plasma • Development of the universe • Formation and development of stars • Synthesis of the chemical elements • Structure of the atomic nuclei • Stability and/or decay properties of atomic nuclei

  4. Spontaneous Fission – General Considerations Liquid Drop Model: nuclear stability ends at Z ≈ 106 due to vanishing fission barriers Spontaneousfissionis an essential decaymodeofmanynuclides in the transuraniumregion. It was and still isbelievedtoterminatetheupper end ofthechartsofnuclei. Nuclear Shell Model: fission barriers in heaviest nuclei determined by shell effects; nuclei Z > 106 may exist

  5. Macroscopic – MicroscopicPredictionsof Shell Effects Stability limit of a droplet against prompt fission

  6. Fission BarriersofHeaviest Nuclei Seemingly there is a strong relation between ground-state shell effects and fission barriers A.Baran et al. subm. to NPA (2015) (arXiv:1503.01608 (2015))

  7. Fission Barriers 232Th 6.8 MeV 5.44 MeV -0.60 MeV P. Möller et al. ADNDT 59, 185 (1995) Emic 7.4 MeV E From P. Möller et al. PRC 91, 024310 (2015)

  8. Fission Barriers Fission barriers of Cn, Fl and Lv isotopes calculated within HFB – approach using the finite-range density-dependent Gogny force with the D1S parameter set. Two different approaches for the fission path: a) axial symmetric ( = 0) and reflection symmetric (Q3 = 0) fission path (AS-RS, full line) b) axial symmetric and non-reflection symmetric (Q3 ≠ 0) fission path (AS-NRS, dashed line) Lv Fl In SHE – region have to be treated rigorously including shapes, deformations, potential energy surfaces, inertias etc. Simplifications by just taking ‚shell effects‘ ends up in misleading results, as e.g. done in S.Hofmann et al. EPJA 52:116 (2016) M. Warda, J.L. Egido PRC 86, 014322 (2012)

  9. Fission Barriers Comparison of fission barriers from different models Comparison of fission barriers and shell effects Z = 116

  10. Fission Barriers

  11. Velocity separator SHIP SHIP Separation time: 1 – 2 μs Transmission: 20 – 50 % Background: 10 – 50 Hz Det. E. resolution: 18 – 25 keV Det. Pos. resolution: 150 μm Dead time: 25 μs Mastertitelformat bearbeiten

  12. SF ActivitiesInvestigated at SHIP

  13. SF ActivitiesInvestigated at SHIP

  14. SF half-lifesystematicsofee - nuclei Features → strong enhancement of TSF at the deformed neutron shell N = 152 for No, Fm, Cf, (Cm) → enhancement at N = 152 vanishes at Z = 104 (Rf) due to change of the shape of the fission barrier → steep decrease of fission halflives on the ‚neutron deficient‘ side and partly on the neutron rich side → rather flat behavior of fission half- lives at N = 152 – 158 for Rf and Sg → increase of fission half-lives towards the deformed neutron shell N = 162 indicated for Rf, Sg, Hs, (No) based on Yu.Ts. Oganessian et al. NPA 239, 157 (1975) New SHIP Data marked by squares

  15. Experimental andCalculated Fission Halflives •  MM calculationsreproduce SF- halflives • fairlyaround N = 152, increasingdisagree- • menttowards N = 162 and at N > 162 • HFB – calculations (D1S, SkM*) do not • describe experimental halfliveswell • strong disagreementbetweenthemodels • aroundthe (predicted) neutronshells • at N = 162 and N = 184 MM D1S SkM* - A. Staszczak et al. PRC 87, 024320 (2013) Gogny D1S – M. Warda, J.L. Egido, PRC86, 014322 (2012) MM –R.Smolanczuk et al., PRC52, 1871 (1995), R.Smolanczuk, PRC 56, 812 (1997) F.P. Heßberger, EPJ A 53:75 (2017)

  16. Shell strengthand SF propertiestowards N = 162 N = 162 – shell more localized or weaker than predicted ?? N-Z = 50 isotopes Theory: R. Smolanczuk et al. PRC 52, 1871 (1995) isoptop e discovered after 1995

  17. Nuclear structure and spontaneous fission HF = Tsf/Tunh(N,Z) Tunh(N,Z) = (Tsf(N-1,Z) x Tsf(N+1,Z))1/2 Due to angular momentumconservation fissionofnucleiwithodd Z, odd N cannot follow themostenergeticfavourablepath → effectiveenhancementoffission barrier (‚specalizationenergy‘) → enhancementoffissionlife-times →‘hindrance‘ offissionfornucleiwith oddnumbersof n and/or p • Hindrance factors tend to decrease with increasing • fissility • No evidence for relation between HF and spin/parity of • fissioning level • In spin-up states (↑) HF of more fissile nuclei tend to be • lower, while in spin-down states (↓)HF of more fissile • nuclei tend to be higher; accidential or nuclear structure effect ?? D. Vretenar, Priv. comm. (2012) F.P. Heßberger, EPJ A 53:75 (2017)

  18. Nuclear structure and spontaneous fission Global dependency of HF from energy change ΔE of single particle levels at deformation visible: ‚upsloping‘ levels tend to exhibit higher hindrance factors than ‚downsloping‘ levels. Examples: 235U (7/2-[743], from 1j15/2) HF = 520 (down) 255Fm (7/2+[613], from 1i11/2) HF = 7.3x105 (up) downsloping levels upsloping levels Note: E(β2) = 0.5 isan arbitraryreferencevalue

  19. <TKE> Measurement of255,256,258Rf Implantation depthof ER < rangeof SF products p(sf1+sf2) ≈ 40% large PHD (pulse-heightdefect) due to high ionisationdensity preliminary <TKE> = 198.8 ± 1.2 MeV SF1 SF2‘ <TKE> E = 198.9±4.4 MeV (J.F.Wild JAC213/214,86 1994) <TKE> = 197.0 ± 1.3 MeV SF1‘ ER <TKE> E = 197.6±1.1 MeV (J.F.Wild JAC213/214,86 1994) SF2 ≈ 7μm for 258Db Stopdetektor (SD) Esf(SD) / MeV

  20. TKE - Distributions 267,268Rf, 267Db, 271Sg Compact Fission Shapes Elongated Fission Shapes 279,281Ds, 282,284Cn, 286Fl, 266Hs, 279Ds, 283,284Cn ■ D.C. Hoffman, M.R. Lane, RCA 70/71, 125 (1995) Viola85: V.E. Viola et al. PRC 31, 1550 (1985) Unik73: J.O. Unik et al., Proc. IAEA Symp. Phys. Chem. of Fission, Rochester 1973, IAEA Wien, Vol. II,19 (1974) ■ SHIP-Results: J.Khuyagbaatar et al. EPJA 46,59(2010); J.Khuyagbaatar et al. EPJA 37, 177 (2008); F.P.Heßberger et al. GSI Sci. Rep. 2014; S.Antalic et al. EPJA 51:41 (2015); K.Nishio et al. EPJA 29, 281 (2006); S.Hofmann, EPJA 32, 251 (2007); S. Hofmann et al. EPJA 48:62 (2012) Sg-262,Hs-266: prelim. results from SHIP exp. R282 ♦Yu. Ts. Oganessian, J.Phys. G: Nucl. Part. Phys. 34, R175 (2007)

  21. Fission Modes • Early theoreticalinvestigations • pointedtolocalmaxima in <TKE> • in therangeof Z = 102 – 104 and • A = 260 – 270 as a consequenceof • Z and A ofthefissionnucleusbeing • Z  2x50 and A 2x132, double value • of double magic132Sn (Z=50,N=82). • Symmetricfissionfromcompact • shapes (twospheres) expected, • resulting in high <TKE> - values. • Forheaviernuclei Z > 104, A > 270 at • least one ‚soft‘ fissionfragment • expectedleadingtodecreasing <TKE>. • High <TKE> values not a signature • for SHE H.W. Schmitt, U. Mosel NPA 186,1 (1972)

  22. Fission Modes – Bimodal Fission <TKE> < 220 MeV <TKE> > 220 MeV Transition fromasymmetricfissiontosymmetricfissionaround A = 258 in therangefromfermium (Z = 100) torutherfordium (Z = 104) Twocomponents in <TKE> distributionsof ‚low‘ energyfollowing Z2 / A1/3 – systematicsandof ‚high‘ energynearlyreachingthe Coulomb valuefortwospheres High <TKE> connectedtonarrowmassdistributions (symmetric), low<TKE> connectedtobroadmassdistributions (asymmetric, symmetric) E.K. Hulet et al. PRC 40, 770 (1989)

  23. Fission Modes L2 L2 • S. Cwiok et al., • NPA 491, 281 (1989) • Twofissionpaths: • L1 symmetric , compact • shape • L2 asymmetric, elongated • shape • 254Fm: thinnerbarrierfor L2; • asymmetricfission • 258Fm: outerbarrierbelow • gs; bothfissionmodes • arepossible; occurence • ofwhichdepends on • ‚details‘; • bothareobserved L1 L1 L2 L2 L1 L1 L1 L1 L2 L2

  24. Fission Modes • Microscopicdescriptionofmultimodefission, based on SkM* force • Respecting Q20 (elongation), Q30 (reflectionasymmetry), Q40 (necking), Q22 (traxiality) • multipole moments •  Threefissionpaths: a) asymmetricelongated, b) symmetricelongated, c) symmetriccompact Interestingfeature: a regionat Z  104 – 108, N  154 – 160 predicted, whereall threemodesmayoccur asymmetric elongated symmetric compact bimodal: asymm. elongated andsymmetric compact ‚trimodal‘ A. Stazczak et al., PRC 80, 014309 (2009)

  25. Fission Modes • Massdistributionsand total kineticenergyfrom • liquid dropmodelandStrutinskytreatmentofshell • effectstocalculatethe potential energylandscapes • usinggeneralizedCassinianovalstodescribe • nuclearshapes (N. Carjan et al. NPA 942, 97 (2015)) • Massdistributionsarecompositionoftwofission • configurationsorfissionmodes : • Relativelycompactshapes (redcurves) • Relativelyelongatedshapes (bluecurves); • coexistenceofmassasymmetricandsymmetric • distributions in 256-262Fm • Atthelowmasseselongatedshapesdominate, • atincreasingmassescompactshapesbeginto • dominate, whilemassdistributions turn from • asymmetrictosymmetric. • Twoinversionpoints • Elongated compact (A254 (Fm), A258 (Rf)) • Compact asymmetric  compactsymmetric • (A258 (Fm), A260 (Rf))

  26. Fission Modes Comparisons of experimental mass distributions with theoretical predictions. Experiment: M.R. Lane et al. PRC 53, 2893 (1996) Theory: N. Carjan et al. Nucl. Phys. A 942, 97 2893 (2015)

  27. Fission Modes Evaluation of fission energies from elongated shapes (blue lines, low <TKE> values) to compact shapes (red lines, high <TKE> values) Interesting aspect:a region where all configurations might occur with notable intensities; experimental challenge: disentangle those components on the basis of mass distributions and <TKE> measurements.

  28. Spontaneous fission of K - isomers K – isomers are multi qp – configurations and thus SF is expected to be strongly hindered 254m1No Assigned as 2qp – state with Kπ = 8- bsf =(2.0±1.2) x 10-4 → Tsf ≈ 1400 s (prev. Bsf ≤ 2x10-3 s, Yu.A. Lazarev et al. Phys. Scr. 39, 422 (1989)) Tsf,calc ≈ 1 s → HF ≈ 1400 Tsf(iso) / Tsf(gs) ≈ 0.06 254m2No Assigned as 4qp – state with Kπ = 16- or 16+ bsf ≤ 1.3 x 10-4 → Tsf ≥ 1.5 s Tsf,calc ≤ 0.5 μs → HF > 3x106 Previously known: 256mFm E* = 1425. keV, Kπ= 7-, T1/2 = 70 ns bsf = 2x10-5→ Tsf = 3.5 s Tsf = 10400 s Tsf(iso) / Tsf(gs) ≈ 0.00034 Bf =6.6±0.9 MeV (G. Henning et al., PRL 113, 262505 (2014)) Tsf(gs) ≈ 24000 s F.P.Heßberger et al. ZPA 43,55 (2010) A.J. Ward, PHD, Univ. Liverpool (2016)

  29. EC – delayed fission EC – delayed fission of 246Md QEC = 6.16 (±0.33) MeV (AME 2003) Bf(246Fm) = 6.49 MeV (Kowal et al.) Bf (246Fm) = 6.13 MeV (Möller et al.) bsf(246Fm) ≈ 0.12 (prod. by EC of 246Md) bsf(246Fm) = 0.068 ± 0.08 (direct prod. by 208Pb(40Ar,2n)246Fm (M. Venhart et al. EPJA 47:20 (2011)) Excess → EC delayed fission of 246Md; → PECDF = 0.13 ± 0.03 However: two states in 246Md → → T1/2(246Fm,sf) ≈ 7.6 s (ER-sf corr.) → T1/2(246Fm,α) ≈ 6.2 s (ER-α corr.) EC mainly from 246m2Md; probably also Small contribution from 246m1Md → PECDF(246m2Md) > 0.1 → one of highest probability for EC delayed SF in transuranium region Decay scheme of 246Md S. Antalic et al. EPJA 43, 35 (2010)

  30. Z – Identificationof SHE • α-chainsterminatedby sf • sf ofodd-odd – nucleistronglyhindered • maybeno sf ofodd-oddnucleusobserved; • but sf ofeven-evendaughteraf EC • EC is a ‚certain‘ sourcefor K-X-rays • Z – identificationbydelayed • coincidencesbetween • K – X-raysand sf •  test-case: 258Db Proton Number Predict. SF - halflives 266Rf: 23s 268Rf: 1.4s 270Rf: 20 ms Neutron Number

  31. DirectProveof EC of258Db Fromdelayedcoincidences T1/2(sf) = 13 ± 11 ms

  32. DirectProveof EC of258Db First direct Z – Identification of an SF activity in the transactinides Fromdelayedcoincidences: T1/2(sf) = 10.0 ± 1.1 ms (ground-state + isomer) F.P.Heßberger et al. EPJ A 52:328 (2016)

  33. Decay Properties of 258Db and 258Rf • SF measurementsconfirmconclusions on • existenceoftwolong-livedstates in 258Db from • α-decaystudies(F.P. Heßberger et al. EPJ A 41, 145 (2009), • M. Vostinar et al. PHD Univ. Caen (2015) andtobepublished) • Analysis of ER –(CE,γ) - (CE,γ) - SF – correlations • resulted in identificationoftwoisomericstates in • 258Rf. • previouslyreported half-livesof 258Rf represented • ‚sum‘ of half-livesofground-stateand isomer Proposed decay schemes of 258Db(1) and 258Db(2) (F.P.Heßberger et al. EPJ A 52:328 (2016))

  34. Summary and Outlook ☺SF properties of 237,238Cf confirmed, SF branching of 240Cf experimentally determined, new sf activities or sf branches (241,243Fm, 251No, 264Sg, 266Hs,283Cn) ☺ SF of 259Sg confirmed; enhanced value for SF branching; spin and parity of fissioning level assigned for the first time; strong evidence of symmetric fission of 259Sg ☺ EC delayed fission of 246m2Md identified; one of the highest EC delayed fission probabilities in the transuranium region ☺ SF branching in K isomer 254m1No measured and upper limit for 254m2No estimated; high stability of K isomers against SF demonstrated ☺ <TKE> estimated for a couple of neutron deficient isotopes at Z = 98-106 ☺ first Z, (A) – identification of an SF activity by X-ray measurements in the transactinides ☺ Investigation of SF properties nuclei Z ≥ 104 (TKE, mass split, fission modes …) ☺ Spin dependence of hindrance factors ☺ SF probabilities of K isomers → 250Fm, 252No (high gs sf branch), 253No … ☺ EC delayed fission … ☺ shape dependence of fission properties; so far (Z ≥ 92) : prolate deformation; approaching spherical shells → oblate shapes, spherical nuclei ☺ new techniques to overcome disadvantages of implantation methods for TKE and mass distribution measurements → gas cells, ion traps

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