arXiv subjects

J. Skalski

Publications and source records attributed to J. Skalski.

At least 19 recordsLinked to original sources

arXiv2025

Candidates for three-quasiparticle $K$-isomers in even-odd Fm-Cn nuclei

Following our study of possible $K$-isomers in odd-even Md-Rg nuclei, here we continue with searching for three-quasiparticle 1$ν$2$π$ and 3$ν$ isomer candidates in even-odd Fm - Cn nuclei. We use the same approach to calculate energies of different nuclear configurations using a microscopic-macroscopic model with the Woods-Saxon potential. We used two versions of pairing: quasi-particle BCS method and particle number projection formalism. The optimal deformations for both ground states and high-$K$ configurations are determined through a four-dimensional energy minimization process. We point out the most promising candidates for high-$K$ isomers and compare them, where possible, with existing experimental data.

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arXiv2023

Candidates for three-quasiparticle $K$-isomers in odd-even Md-Rg nuclei

We performed a search for three-quasiparticle high-$K$ isomer candidates in odd-even Md - Rg nuclei by considering the lowest lying 1$π$2$ν$ and 3$π$ excitations. Our approach involves calculating the energies of different nuclear configurations using a microscopic-macroscopic model with the Woods-Saxon potential. We explore three pairing scenarios: blocking, quasi-particle BCS method, and particle number projection formalism. The optimal deformations for both ground-states and high-$K$ configurations are determined through a four-dimensional energy minimization process. By analyzing the obtained excitation energies, we discuss the most promising candidates for high-$K$ isomers and compare them, where possible, with existing experimental data. We also discuss a possible isomer $α$-decay hindrance using calculated $Q_α$-hindrances.

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arXiv2021

First observation of high-$K$ isomeric states in $^{249}$Md and $^{251}$Md

Decay spectroscopy of the odd-proton nuclei $^{249}$Md and $^{251}$Md has been performed. High-$K$ isomeric states were identified for the first time in these two nuclei through the measurement of their electromagnetic decay. An isomeric state with a half-life of $2.8(5)$ ms and an excitation energy $\geq 910$ keV was found in $^{249}$Md. In $^{251}$Md, an isomeric state with a half-life of $1.4(3)$ s and an excitation energy $\geq 844$ keV was found. Similarly to the neighbouring $^{255}$Lr, these two isomeric states are interpreted as 3 quasi-particle high-$K$ states and compared to new theoretical calculations. Excited nuclear configurations were calculated within two scenarios: via blocking nuclear states located in proximity to the Fermi surface or/and using the quasiparticle Bardeen-Cooper-Schrieffer method. Relevant states were selected on the basis of the microscopic-macroscopic model with a deformed Woods-Saxon potential. The most probable candidates for the configurations of $K$-isomeric states in Md nuclei are proposed.

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arXiv2020

Properties of heaviest nuclei with $98\leq Z \leq 126$ and $134 \leq N \leq 192$

We systematically determine ground-state and saddle-point shapes and masses for 1305 heavy and superheavy nuclei with $Z=98-126$ and $N=134-192$, including odd-$A$ and odd-odd systems. From these, we derive static fission barrier heights, one- and two-nucleon separation energies, and $Q_α$ values for g.s. to g.s transitions. Our study is performed within the microscopic-macroscopic method with the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy taken as the smooth part. We use parameters of the model that were fitted previously to masses of even-even heavy nuclei. For systems with odd numbers of protons, neutrons, or both, we use a standard BCS method with blocking. Ground-state shapes and energies are found by the minimization over seven axially-symmetric deformations. A search for saddle-points was performed by using the "imaginary water flow" method in three consecutive stages, using five- (for nonaxial shapes) and seven-dimensional (for reflection-asymmetric shapes) deformation spaces. The results are collected in two main tables. Calculated ground-state mass excess, nucleon separation- and $Q_α$ energies, total, macroscopic(normalized to the macroscopic energy at the spherical shape) and shell corrections energies, and deformations are given for each nucleus in \mbox{Table 1}. \mbox{Table 2} contains calculated properties of the saddle-point configurations and the fission barrier heights. In \mbox{Tables 3-7}, are given calculated ground-state, inner and outer saddle-point and superdeformed secondary minima characteristics for 75 actinide nuclei, from Ac to Cf, for which experimental estimates of fission barrier heights are known. These results are an additional test of our model.

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arXiv2020

Instanton-motivated study of spontaneous fission of odd-A nuclei

Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the adiabatic cranking approximation which serves as the basis in calculations of fission probabilities. Selfconsistent instanton equations, with and without pairing, are reviewed and then simplified to non-selfconsistent versions with phenomenological single-particle potential and seniority pairing interaction. Solutions of instanton-like equations without pairing and actions they produce are studied for the Woods-Saxon potential along realistic fission trajectories. Actions for unpaired particles are combined with cranking actions for even-even cores and fission hindrance for odd-A nuclei is studied in such a hybrid model. With the assumed equal mass parameters for neighbouring odd-A and even-even nuclei, the model shows that freezing the K π configuration leads to a large overestimate of the fission hindrance factors. Actions with adiabatic configurations mostly show not enough hindrance; instanton-like actions for blocked nucleons correct this, but not sufficiently.

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arXiv2019

Static fission properties of actinide nuclei

Fission barriers heights and excitation energies of superdeformed isomeric minima are calculated within the microscopic - macroscopic Woods - Saxon model for 75 actinide nuclei for which the experimental data are known. State - of - the - art methods were used: minimization over many deformation parameters for minima and the imaginary water flow on many - deformation energy grid for saddles, including nonaxial and reflection-asymmetric shapes. We obtain 0.82 - 0.94 MeV rms deviation between the calculated and experimental barriers and 0.53 MeV rms error in the excitation of superdeformed minima (SD). Experimental vs theory discrepancies seem to be of various nature and not easy to eliminate, especially if one cares for more than one or two observables. As an example, we show that by strengthening pairing in odd systems one can partially improve agreement in barriers, while spoiling it for masses. We also discuss the "thorium anomaly" and suggest its possible relation to a different way in which the Ac and Th barriers are derived from experimental data.

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arXiv2018

Hindered alpha decays of heaviest high-K isomers

To find candidates for long-lived high-K isomers in even-even Z=106-112 superheavy nuclei we study dominant alpha-decay channel of two- and four-quasi-particle configurations at a low excitation. Energies are calculated within the microscopic - macroscopic approach with the deformed Woods-Saxon potential. Configurations are fixed by a standard blocking procedure and their energy found by a subsequent minimization over deformations. Different excitation energies of a high-K configuration in parent and daughter nucleus seem particularly important for a hindrance of the alpha-decay. A strong hindrance is found for some four-quasi-particle states, particularly $K^π = 20^{+}$ and/or $19^{+}$ states in $^{264-270}$Ds. Contrary to what was suggested in experimental papers, it is rather a proton configuration that leads to this strong hindrance. If not shortened by the electromagnetic decay, alpha half-lives of $\sim$ 1 s could open new possibilities for studies of chemical/atomic properties of related elements.

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arXiv2017

Effect of tetrahedral shapes in heavy and superheavy nuclei

We search for effects of tetrahedral deformation $β_{32}$ over a range of $\sim 3000$ heavy and superheavy nuclei, $82\leq Z \leq 126$, using a microscopic-macroscopic model based on the deformed Woods-Saxon potential, well tested in the region. We look for the energy minima with a non-zero tetrahedral distortion, both absolute and conditional - with the quadrupole distortion constrained to zero. In order to assure reliability of our results we include 10 most important deformation parameters in the energy minimization. We could not find any cases of stable tetrahedral shapes. The only sizable - up to 0.7 MeV - lowering of the ground state occurs in superheavy nuclei $Z\geq 120$ for $N=173-188$, as a result of a {\it combined} action of two octupole deformations: $β_{32}$ and $β_{30}$, in the ratio $β_{32}/β_{30}\approx \sqrt{3/5}$. The resulting shapes are moderately oblate, with the superimposed distortion $β_{33}$ {\it with respect to the oblate axis}, which makes the equator of the oblate spheroid slightly triangular. Almost all found conditional minima are excited and not protected by any barrier, a handful of them are degenerate with the axial minima.

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arXiv2016

Adiabatic fission barriers in superheavy nuclei

Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98\leq Z \leq 126$, including even - even, odd - even, even - odd and odd - odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10-th below to the 10-th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the "Imaginary Water Flow" method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole non-axiallity. The ground states were found by energy minimization over configurations and deformations. We find that the non-axiallity significantly changes first and second fission barrier in many nuclei. The effect of the mass - asymmetry, known to lower the second, very deformed barriers in actinides, in the heaviest nuclei appears at the less deformed saddles in more than 100 nuclei. It happens for those saddles in which the triaxiallity does not play any role, what suggests a decoupling between effects of the mass-asymmetry and triaxiality. We studied also the influence of the pairing interaction strength on the staggering of $B_f$ for odd- and even-particle numbers. Finally, we provide a comparison of our results with other theoretical fission barrier evaluations and with available experimental estimates.

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arXiv2015

Candidates for Long Lived High-K Ground States in Superheavy Nuclei

On the basis of systematic calculations for 1364 heavy and superheavy nuclei, including odd-systems, we have found a few candidates for high-K ground states in superheavy nuclei. The macroscopic-microscopic model based on the deformed Woods-Saxon single particle potential which we use offers a reasonable description of SH systems, including known: nuclear masses, $Q_α$-values, fission barriers, ground state deformations, super- and hyper-deformed minima in the heaviest nuclei. %For odd and odd-odd systems, both ways of including pairing correlations, % blocking and the quasi-particle method, have been applied. Exceptionally untypical high-K intruder contents of the g.s. found for some nuclei accompanied by a sizable excitation of the parent configuration in daughter suggest a dramatic hindrance of the $α$-decay. Multidimensional hyper-cube configuration - constrained calculations of the Potential Energy Surfaces (PES's) for one especially promising candidate, $^{272}$ Mt, shows a $\backsimeq$ 6 MeV increase in the fission barrier above the configuration- unconstrained barrier. There is a possibility, that one such high-K ground- or low-lying state may be the longest lived superheavy isotope.

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arXiv2015

Search for octupole correlations in $^{147}$Nd

Properties of excited states in $^{147}$Nd have been studied with multispectra and $γγ$ coincidence measurements. Twenty-four new $γ$-lines and three new levels have been introduced into the level scheme of $^{147}$Nd. Lifetimes of eight excited levels in $^{147}$Nd, populated in the $β$ decay of $^{147}$Pr, have been measured using the advanced time-delayed $βγγ$(t) method. Reduced transition probabilities have been determined for 30 $γ$-transitions in $^{147}$Nd. Potential energy surfaces on the ($β_{2}$,$β_{3}$) plane calculated for $^{147}$Nd using the Strutinsky method predict two single quasiparticle configurations with nonzero octupole deformation, with K=1/2 and K=5/2. We do not observe parity doublet bands with K=5/2. For pair of opposite parity bands that could form the K=1/2 parity doublet we were able only to determine lower limit of the dipole moment, $|D_0|\geq$0.02 e$\cdot fm$.

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arXiv2014

Q-alpha values in superheavy nuclei from the deformed Woods-Saxon model

Masses of superheavy (SH) nuclei with $Z=98-128$, including odd and odd-odd nuclei, are systematically calculated within the microscopic-macroscopic model based on the deformed Woods-Saxon potential. Ground states are found by minimizing energy over deformations and configurations. Pairing in odd particle-number systems is treated either by blocking or by adding the BCS energy of the odd quasiparticle. Three new parameters are introduced which may be interpreted as the constant mean pairing energies for even-odd, odd-even and odd-odd nuclei. They are adjusted by a fit to masses of heavy nuclei. Other parameters of the model, fixed previously by fitting masses of even-even heavy nuclei, are kept unchanged. With this adjustment, the masses of SH nuclei are predicted and then used to calculate $α$-decay energies to be compared to known measured values. It turns out that the agreement between calculated $Q_α$ values with data in SH nuclei is better than in the region of the mass fit. The model overestimates $Q_α$ for $Z=111-113$. Ground state (g.s.) configurations in some SH nuclei hint to a possible $α$-decay hindrance. The calculated configuration-preserving transition energies show that in some cases this might explain discrepancies, but more data is needed to explain the situation.

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arXiv2013

8Dim calculations of the third barrier in $^{232}$Th and a conflict between theory and experiment on uranium nuclei

We find the height of the third fission barrier $B_{III}$ and energy of the third minimum $E_{III}$ in $^{232}$Th using the macroscopic - microscopic model, very well tested in this region of nuclei. For the first time it is done on an 8-dimensional deformation hypercube. The dipole distortion is included among the shape variables to assure that no important shapes are missed. The saddle point is found on a lattice containing more than 50 million points by the immersion water flow (IWF) method. The shallow third minimum, $B_{III}-E_{III}\approx 0.36$ MeV, agrees with experimetal data of Blons et al. This is in a sharp contrast with the status of the IIIrd minima in $^{232-236}$U: their experimental depth of $\geq3$ MeV contradicts all realistic theoretical predictions. We emphasize the importance of repeating the experiment on $^{232}$Th, by a technique similar to that used in the uranium nuclei, for settling the puzzle of the third minima in actinides.

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arXiv2012

Ground State and Saddle Point: masses and deformations for even-even superheavy nuclei with 98 < Z < 126 and 134< N < 192

We determine ground-state and saddle-point shapes and masses of even-even superheavy nuclei in the range of proton numbers $98\leq Z \leq 126$ and neutron numbers $134\leq N \leq 192$. Our study is performed within the microscopic-macroscopic method. The Strutinsky shell and pairing correction is calculated for the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential energy is taken as a smooth part. We use parameters of the model that were fitted previously to this region of nuclei. A high-dimensional deformation space, including nonaxial and reflection-asymmetric shapes, is used in the search for saddle points. Both ground-state and saddle-point shapes are found with the aid of the minimization procedure, with dynamical programming technique of search for saddle points. The results are collected in two tables. Calculated ground-state mass-excess, $Q_{α$ energies, total and macroscopic energies normalized to the macroscopic energy at the spherical shape, shell corrections (including pairing) and deformations are given for each nucleus in the table one. The second table gives the same properties, but at the saddle-point configuration. The obtained results are discussed and compared with available experimental data for alpha-decay energies ($Q_α$) and ground-state masses.

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arXiv2012

Third minima in actinides - do they exist?

We study the existence of third, hyperdeformed minima in a number of even-even Th, U and Pu nuclei using the Woods-Saxon microscopic-macroscopic model that very well reproduces first and second minima and fission barriers in actinides. Deep ($3 ÷4$ MeV) minima found previously by Ćwiok et al. are found spurious after sufficiently general shapes are included. Shallow third wells may exist in $^{230,232}$Th, with IIIrd barriers $\le$ 200 and 330 keV (respectively). Thus, a problem of qualitative discrepancy between microscopic-macroscopic and selfconsistent predictions is resolved. Now, an understanding of experimental results on the apparent third minima in uranium becomes an issue.

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arXiv2010

Low energy shape oscillations of negative parity in the main and shape-isomeric minima in actinides

We study low energy shape oscillations of negative parity in the first and second (isomeric) minima in actinides. As a main tool we use the phenomenological Woods-Saxon potential with a variety of shape deformations. This allows to include a mixing of various multipolarities when considering oscillations with a fixed $K$ quantum number. The phonon energies are determined either from the collective Hamiltonian with the microscopic-macrocopic energy and cranking mass parameters, or from its simplified version with the constant mass parameters. The results for $K^π=0^-$,$1^-$ in the first minima are in a reasonable agreement with experimental data, including predicted E1 transitions; the $K^π=2^-$ energies are systematically overestimated. In the second minimum, as compared to the data for $^{240}$Pu and $^{236}$U, our calculated $K=$1,2 energies are overestimated while the $K=0$ energies are three or more times too large. This signals either a non-collective character of the experimentally assigned $K=0$ states or a serious flaw of the model in the second minimum. More data on the $K=0$, $I^π=1^-$ collective states in the second minima of other nuclei are necessary to resolve this issue.

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arXiv2010

Superdeformed Oblate Superheavy Nuclei?

We study stability of superdeformed oblate (SDO) superheavy $Z\geq 120$ nuclei predicted by systematic macroscopic-microscopic calculations in 12D deformation space and confirmed by the Hartree-Fock calculations with the realistic SLy6 force. We include into consideration high-$K$ isomers that very likely form at the SDO shape. Although half-lives $T_{1/2}\lesssim10^{-5}$ s are calclulated or estimated for even-even spin zero systems, decay hindrances known for high-$K$ isomers suggest that some SDO superheavy nuclei may be detectable by the present experimental technique.

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arXiv2008

Nuclear fission with mean-field instantons

We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons - periodic imaginary-time solutions to time-dependent mean-field equations - that allows for a comparison with more familiar and used generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfils the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates instanton-related decay rate. The very existence of the minimum principle offers a hope for a variational search for instantons. After the inclusion of pairing, the instanton equations and the variational principle can be expressed in terms of the imaginary-time-dependent Hartree-Fock- Bogolyubov (TDHFB) theory. The adiabatic limit of this theory reproduces ATDHFB inertia.

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