IS THE NUCLEAR LARGE AMPLITUDE COLLECTIVE DYNAMICS ADIABATIC OR NON ADIABATIC ? W. Brodziński, M. Kowal, J. Skalski National Centre for Nuclear Research(Warsaw) National Centre for Nuclear Research (Warsaw) P. Jachimowicz University of Zielona Gora

Motivation = an inherent limitations of both: hot & cold fusion reactions: Hot (well- deformed radioactive actinides (Act.) targets are used and compound nucleus is quite excited ) attempts of going beyond the reactions Act Ca by using heavier projectiles like 50 Ti, 54 Cr, 58 Fe, and 64 Ni gave no results so far. all heavier actinides with Z>98 live to short that one could perform target with them. Cold (magic nuclei as targets are used with projectiles heavier than 40 Ar and Compound system is in this case only weakly heated and is cooled down via emission of just one or two neutrons ) produced nuclei lies belong to the far “island of stability” of superheavy elements. to produce more & more heavier nuclei the mass and charge of projectile should be increased but it pulls an increase of the Coulomb repulsion what drastically reduces the cross sections.

Introduction Done: calculations for masses, shapes, fission barriers, Q-alpha etc… for even – even actinides Conclusions: quite good agreement with exp (masses & Qalpha: rms = 0.3 MeV, BfA rms=0.5 MeV, BfB=0.7MeV Hope 1 : with the same set of the parameters one can predict properties of SHE + Hope 2: one can extend calculations on odd systems General Hope: K-isomers or high–K ground states of odd & odd-odd nuclei - a chance for longer half-lives of SHE

Microscopic-macroscopic method with a possibility of many various deformations Calculated energy: The effect of intruder states lying sclose to the Fermi level is most apperent in the heavier nuclei

SPHERICAL HARMONICS PARAMETRIZATION

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).

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).

Statistical parameters for different macro – micro calculations of first (in parentheses) and second barriers.

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.

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)

K. Siwek-Wilczyńska, T. Cap, M. Kowal, A. Sobiczewski, and J. Wilczyński, Phys. Rev. C 86, (2012). T. Cap, K. Siwek-Wilczyńska, M. Kowal, and J. Wilczyński,Phys. Rev. C 88, (2013).

Second minima in actinides, Max diff = ~800 KeV! M. Kowal and J. Skalski,PRC 82, (2010). P. Jachimowicz, M. Kowal, and J. Skalski, PRC 85, (2012). N. Nikolov, N. Schunck, W. Nazarewicz, M. Bender, and J. Pei, PRC 83, (2011). Max diff = ~4 MeV!

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- „ /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+ 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- „ /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+

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

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.

Mass parameter for odd system In the diabatic scienario one can imagine that blocked state lies higher in energy than the g.s. => Negative values of mass parameter! Around the crosing region two states are close together => Mass parameter explode! Due to pairing even far awy from crossing one can imagine that on both side of fermi level quasiparticles have practicaly the same energies (if slopes of the levels are similar) => Mass parameter explode! even odd

Landau – Zener effect To CROSS or NOT to CROSS ? IS THE LASD ADIABATIC OR NON ADIABATIC ? W. Nazarewicz, Nucl. Phys A 557 (1993) Q

Central Open Questions/Problems: What are the conditions for the many – body system to give up its quantum characteristic ? How to calculate the stability of odd nuclei (fission & alpha half – lives) ? Problem of mass parameters for odd systems! How many colective variables is enough ?

Status of third minimum in actinides: Theory: Experiment: Shallow minima (0.5 MeV or less ) Deep minima (3 - 4 MeV) self-consistent models mac-mic model P. Moller et, al. mac-mic model S. Ćwiok et, al. Blons et, al. (231,232,233Th) Debrecen-Munich (232,234,236U) ? ? ?

B A

The dipole deformation b1 is omitted there, as corresponding to a shift of the origin of coordinates which leaves energy (always calculated in the center of mass frame) invariant. However, this is true only for weakly deformed shapes. For large elongations, b1 acquires a meaning of a real shape variable.

IIIrd minima – type: A minima with larger octupole deformations (A) have quadrupole moments Q=170 b, disturbingly close to the scission region. minima (A) are just intermediate congurations on the scission path, whose energy was calculated erroneously because of limitations of the admitted class of shapes. One can nd continuous 8D paths start ing at the supposed IIIrd minimum and leading to scission, along which energy decreases gradually. M. Kowal, J. Skalski, PRC 85, (R) (2012)

IIIrd minima – type: B

P. Jachimowicz, M. Kowal, J. Skalski, PRC 87, (2013)

MODIFY FUNNY-HILLS PARAMETRIZATION eg. : Krzysztof Pomorski, Johann Bartel, Int. J. Mod. Phys. E, Vol. 15, No. 2 (2006) 417.

MODIFY FUNNY-HILLS PARAMETRIZATION 232 Th c × h × α × η = gird points 0.5 MeV

MODIFY FUNNY-HILLS PARAMETRIZATION 236 U c × h × α × η = gird points no third minimum

THREE QUADRATIC SURFACE PARAMETERIZATION

eg. : Peter M ̈ oller et al., Phys. Rev. C,79 (2009) eg. : Peter M ̈ oller et al., Phys. Rev. C, 79 (2009)

● Heights of the first and second fission barriers as well as the excitation of the second minimum are convergent with those three classes of nuclear shape parameterizations. ● We found the similar depth of the third minimum of the order of several hundred of keV for all tested parameterizations. This is still in a sharp contrast with the experimental status of the III-rd minima in those nuclei. Their experimental depth of 3 – 4 MeV contradicts all realistic theoretical predictions. ● Among all investigated parameterizations the most effective and efficient (the smallest amount of required dimension without apparent loss of the described shapes) is the modify Funny – Hills prescription.