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

1. Equilibrium shapes 2. Fission barriers 3. Q alpha of Z=98-126 (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.

136 144 152 160 168 176 184 192

98100102104106108110112114116118120122124126 min

20

-0.50-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.0500.050.100.150.200.250.30

N

Z

SDO

OBLATE

PROLATE

SPHERICAL

Ground state shapes, even-even

20

:

0.5

3.

2

SDO

Axis ratio

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, 054302 (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, 084305 (2012).M. Kowal, P. Jachimowicz and A. Sobiczewski, PRC 82, 014303 (2010) .

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)

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B

f [M

eV]

N

HN FRLDM RMF SkM*

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HN FRLDM RMF SkM*

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Bf [

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HN FRLDM RMF SkM*

HN – Woods-SaxonFRLDM – 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 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

P. Jachimowicz, M. Kowal, and J. Skalski, PRC 89, 024304 (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=101-118

mean 217 keV 196 keVerror

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-Kclose-lying orbitals,like:9/2+ and 5/2- protonsbelow Z=108 or 11/2- and 9/2+ neutronsbelow N=162

Z N Omega(n) Omega(p) K113 173 5/2+ 7/2- 6-112 173 15/2- 15/2-111 170 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- „ 12-108 163 „ 13/2- 157 11/2- 11/2-107 163 13/2- 5/2- 9+ 157 11/2- „ 8+106 163 13/2- 13/2- 157 11/2- 11/2-105 157 11/2- 9/2+ 10- 151 9/2- 9/2+ 9-104 157 11/2- 11/2-105 157 11/2- 7/2- 9+ 151 9/2- 7/2- 8+ 149 7/2+ 7/2- 7-101 157 11/2- 1/2- 6+

protons

neutrons

156 158 160 162 164 166 168 170

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GS->GS GS->EX

Z=109

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Z=113 Z=111 Z=109 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.

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G.S. configuration:P:11/2+ [6 1 5]N:13/2- [7 1 6]

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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:

}

1{})({),()(

4444)(

4242)(

2222

80806060404020200

YYY

YYYYRcR

• β20 & β22 on the mesh, minimalization in {β40 β60 β80 β42 β44 }.

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

Stability for Z>126W. Brodziński, J. Skalski, Phys. Rev C 88, 044307 (2013)

Macroscopic energy

vs axial elongation

in the beta-gamma plane

200 300

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 Royeret 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: Qα≈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-macro Hartree-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