SH nuclei – structure , limits of stability & high-K ground-states/isomers

1. P.Jachimowicz (UZ), W.Brodziński, M.Kowal, J.Skalski (NCBJ) ARIS 2014, Tokyo, Japan SH nuclei – structure, limits of stability & high-K ground-states/isomers Equilibrium shapes Fission barriers Q alpha of Z=98-126 (with odd and odd-odd) nuclei. 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 Mostly results of the Woods-Saxon micro-macro model; some Skyrme HFBCS results.

2. 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, PRC83, 054302 (2011).

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

4. 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.

5. Fission barriers calculated using micro-macro model (e-e nuclei) Even-even SH nuclei: barries decrease for Z>114 The highest barrier for Z=114, N=178 Performance for even-even actinides: 1-st barriers, 18 nuclei rms : 0.5 MeV 2-nd barriers, 22 nuclei rms : 0.69 MeV P. Jachimowicz, M. Kowal, and J. Skalski, PRC85, 084305 (2012). M. Kowal, P. Jachimowicz and A. Sobiczewski, PRC82, 014303(2010) .

6. Heaviest even-even fissioning nuclei: 112, 170 0.8 ms (old calc. 71 ms) 112, 172 97 ms (old calc. 4 s) 114, 172 130 ms (old calc. 1.5 s) (for Z=114, the local minimum in barrier at N=168) Old calculation: Smolańczuk, Skalski, Sobiczewski (1995)

7. Comparison of various models: some must be wrong. 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!

8. SHE masses (including odd & odd-odd) P. Jachimowicz, M. Kowal, and J. Skalski, PRC 89, 024304 (2014) • 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 Qalpha values, Z=101-118, 7 differ from exp. by more than 0.5 MeV; the largest deviation: 730 keV (blocking). Slight underestimate for Z=108; Overestimate: Z=109-113

9. Statistical parameters of the fit to masses in themodel with blocking in separate groups of even-even, odd-even, even-odd and odd-odd heavy nuclei: 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=101-118 mean 217 keV 196 keV error rms 274 keV 260 keV The same but for the method withoutblocking.

12. Z N Omega(n) Omega(p) K • 173 5/2+ 7/2- 6- • 112 173 15/2- 15/2- • 170 11/2+ 11/2+ • 169 5/2+ 9/2- 7- • 163 13/2- 3/2- 8+ • 110 163 13/2- 13/2- • 109 All 11/2+ > 11/2 • 169 9/2+ „ 10+ • 161 „ „ „ • 159 „ „ „ • 163 13/2- „ 12- • 163 „ 13/2- • 157 11/2- 11/2- • 107 163 13/2- 5/2- 9+ • 157 11/2- „ 8+ • 163 13/2- 13/2- • 157 11/2- 11/2- • 157 11/2- 9/2+ 10- • 151 9/2- 9/2+ 9- • 157 11/2- 11/2- • 157 11/2- 7/2- 9+ • 151 9/2- 7/2- 8+ • 149 7/2+ 7/2- 7- • 101 157 11/2- 1/2- 6+ 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

13. protons

14. neutrons

15. 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.

16. 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.

17. Microscopic-macroscopic method Stability for Z>126 W. Brodziński, J. Skalski, Phys. Rev C 88, 044307 (2013) • Shape parametrization: • β20 & β22 on the mesh, minimalization in {β40β60β80β42β44 }. 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, Vn= 316 MeV fm3 , Vp= 322 MeV fm3

18. Macroscopic energy vs axial elongation in the beta-gamma plane

19. 200 300 Spherical shell correction with the SLy6 force; W-S gives a very similar pattern for Z>126

20. Next doubly magic nucleus?? • 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.

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

22. Conclusions 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.