SH nuclei – structure, limits of stability & high-K ground-states/isomers 1.Equilibrium shapes 2.Fission barriers 3.Q alpha of Z= ( with odd and odd- odd) nuclei. 4.K-isomers or high–K ground states of odd & odd-odd nuclei - a chance for longer half- lives 5. Predictions for SHE with Z>126 P.Jachimowicz (UZ), W.Brodziński, M.Kowal, J.Skalski (NCBJ) ARIS 2014, Tokyo, Japan Mostly results of the Woods-Saxon micro-macro model; some Skyrme HFBCS results.

Ground state shapes, even-even Micro-macro results In contrast to many Skyrme forces, Woods-Saxon micro- macro model gives lower barriers and mostly oblate ground states for Z>=124,126 (no magic gap for 126 protons). P. Jachimowicz, M. Kowal, and J. Skalski, PRC 83, (2011).

SLy4, M. Bender, P-H. Heenen, to be published (inverted colors) Gogny force, M. Warda L. Próchniak

Possible alpha-decay hindrance: the 14- SD oblate ground state in parent. The G.S. to G.S. transition inhibited; SDO to SDO has the Q value smaller by 2 MeV.

Fission barriers calculated using micro- macro model (e-e nuclei) Performance for even-even actinides: 1-st barriers, 18 nuclei rms : 0.5 MeV 2-nd barriers, 22 nuclei rms : 0.69 MeV Even-even SH nuclei: barries decrease for Z>114 The highest barrier for Z=114, N=178 P. Jachimowicz, M. Kowal, and J. Skalski, PRC 85, (2012). M. Kowal, P. Jachimowicz and A. Sobiczewski, PRC 82, (2010).

Heaviest even-even fissioning nuclei: 112, ms (old calc. 71 ms) 112, ms (old calc. 4 s) 114, ms (old calc. 1.5 s) (for Z=114, the local minimum in barrier at N=168) Old calculation: Smolańczuk, Skalski, Sobiczewski (1995)

HN – Woods-Saxon FRLDM – P. Moller et al. SkM* - A.Staszczak et al. RMF – H.Abusara et al. FRDLM & RMF also perform well in actinides! Comparison of various models: some must be wrong.

SHE masses (including odd & odd-odd) A fit to exp. masses Z>82, N>126, number of nuclei: 252 For odd and odd-odd systems there are 3 additional parameters – macroscopic energy shifts (they have no effect on Q alpha). >>Predictions for SHE: 88 Q alpha values, Z= , 7 differ from exp. by more than 0.5 MeV; the largest deviation: 730 keV (blocking). Slight underestimate for Z=108; Overestimate: Z= P. Jachimowicz, M. Kowal, and J. Skalski, PRC 89, (2014)

Statistical parameters of the fit to masses in the model with blocking in separate groups of even- even, odd-even, even-odd and odd-odd heavy nuclei: The same but for the method without blocking. Q alpha 204 nuclei in the fit region blocking q.p.method mean 326 keV 225 keV error rms 426 keV 305 keV 88 nuclei Z= mean 217 keV 196 keV error rms 274 keV 260 keV

High-K states: a chance for longer half-lives. < Candidates for high-K g.s. in odd or odd-odd SHN in the W-S model In even-even systems one should block high-K close-lying orbitals, like: 9/2+ and 5/2- protons below Z=108 or 11/2- and 9/2+ neutrons below N=162 Z N Omega(n) Omega(p) K /2+ 7/ /2- 15/ /2+ 11/ /2+ 9/ /2- 3/ /2- 13/ All 11/2+ > 11/ /2+ „ „ „ „ 159 „ „ „ /2- „ „ 13/ /2- 11/ /2- 5/ /2- „ /2- 13/ /2- 11/ /2- 9/ /2- 9/ /2- 11/ /2- 7/ /2- 7/ /2+ 7/ /2- 1/2- 6+

protons

neutrons

Unique blocked orbitals may hinder alpha transitions. The effect of a reduced Q alpha for g.s. -> excited state (left panel) on the life-times (below) according to the formula by Royer.

G.S. configuration: P:11/2+ [6 1 5] N:13/2- [7 1 6] Fixing the g.s. configuration rises the barrier by 6 MeV. Even if configuration is not completely conserved, a substantial increase in fission half-life is expected.

Microscopic-macroscopic method Shape parametrization: β 20 & β 22 on the mesh, minimalization in {β 40 β 60 β 80 β 42 β 44 }. Hartree-Fock-BCS with SLy6 force – an „upper limit” for barrier 180 neutron & 110 proton levels Pairing: delta interaction of time-reversed pairs with a smooth energy cutoff, V n = 316 MeV fm 3, V p = 322 MeV fm 3 Stability for Z>126 W. Brodziński, J. Skalski, Phys. Rev C 88, (2013)

Macroscopic energy vs axial elongation in the beta-gamma plane

Spherical shell correction with the SLy6 force; W-S gives a very similar pattern for Z>126

In both W-S and SLy6 models -doubly magic spherical system. In the W-S model: Q alpha = 14.3 MeV. From the formula by Royer et al. T alpha = 100 s. B eff > 700 hbar^2/MeV, along a stright path (axially symmetric) one obtains T fission > 10^7 s. Next doubly magic nucleus??

β-stable, HFBCS: Q α ≈10 MeV, T alpha = 0.1 s, T fission (rough estimate) = 10^{-6} s; more for odd & odd-odd systems W-S minimum: SD-oblate Fission barrier: 2 MeV HFBCS minimum: spherical/SD- Oblate, fission barrier: 4.2 MeV Micro-macroHartree-Fock-BCS N=228 region:

W-S micro-macro model predicts reasonable barriers for actinides and SH nuclei; Q alpha also seem reasonable; Large differences in barriers between our model and the FRDLM or Skyrme-type; nobody knows what happens for Z>=120; High-K ground states of some odd and odd-odd nuclei, with blocked intruder orbitals, may be the longest-lived SHE; Z>126 systems – rather pessimistic predictions: nonaxiality ruins stability; no stability in the W-S model, while SLy6, known to give too high barriers (by up to 2.5 MeV), leads to estimated (roughly) fission half-lives:10^-6 s & alpha half-lives of 0.1 s. This does not promise much stability. Conclusions