We have conducted a thorough analysis of the potential energy surfaces (PES) in ^236 U and ^233 Th using the Cassini-ovals parameterization within the macro–micro approach. We employed the state-of-the-art immersion water flow (IWF) method to study the saddles on four-dimensional energy grids encompassing reflection-asymmetric shapes. For ^233 Th, we computed the adiabatic potential energy surfaces by minimizing configurations with one blocked neutron within ten levels below and above the Fermi level. Our results show satisfactory agreement with empirical and experimental estimates for both nuclei, specifically regarding the first and second fission barriers. This suggests that our method holds promise in efficiently describing non-compact shapes while reducing the dimensionality of the space without sacrificing accuracy. Interestingly, employing Cassinian oval parameterization fails to reveal a pronounced, hyper-deformed third minimum in the potential energy landscape. Instead, only a shallow third minimum is observed for ^233 Th, while in ^236 U, this minimum ultimately vanishes. This finding holds significant importance when considering the modeling of fission cross-sections.

We employ a statistical approach to investigate the influence of axial asymmetry on the nuclear level density and entropy along the fission pathways of a superheavy nucleus, explicitly focusing on the $^{296}$Lv isotope. These pathways are determined within multidimensional deformation spaces. Our analysis reveals a significant impact of triaxiality on entropy. Additionally, suppressing shell effects can alter the fission scenario depending on the available excitation energy. We derive the deformation-dependent level density parameter, which plays a crucial role in estimating the survival probability of a superheavy nucleus. Furthermore, we utilize a set of master equations to obtain the time-dependent fission probabilities and calculate the ratio of decay probabilities for both axial and triaxial paths.

The probabilities of $xn$-, $pxn$-, and $αxn$-evaporation channels in excited superheavy nuclei were evaluated using the Monte Carlo method. The calculations utilized microscopically determined nuclear level densities and were compared with results obtained from the phenomenological Jackson formula. Effective temperatures derived from the microscopic approach were incorporated into the Jackson formula for different evaporation channels at low and moderate excitation energies. Additionally, an analytical formula was introduced to estimate the average kinetic energy of emitted particles in multi-step processes.

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.

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, a(f), as well as those for neutron, a(n), proton, a(p), and alpha-particle, a(alpha), emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with Z = 112-120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the "immersion water flow" technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the a(f)/a(n) ratio, the a(p)/a(n) and a(alpha)/a(n) ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of alpha decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.

For the Ca-48 and Ra/actinide-based complete fusion reactions, the excitation functions for the production of isotopes of superheavy nuclei with charge numbers 108-116 are calculated and compared to the available experimental data. The calculated production cross sections clearly indicate the border nucleus Ds between the island of stability of superheavy nuclei and the mainland with a relatively large number of neutrons.

Excitation functions are predicted for the production of isotopes of a superheavy nucleus with charge number Z=112 in the (2-5)n -evaporation channels of the complete fusion reactions ^48 Ca+ ^233,235 U for future experiments. The calculated production cross section of the ^277 Cn isotope in the hot fusion reaction ^48 Ca+ ^233 U is compared with the experimental one in the cold fusion reaction ^70 Zn+ ^208 Pb. The strong correlation between the fusion probability and asymmetry in the entrance reaction channel is revealed. The possibility of filling the gap between the isotopes of superheavy nuclei with Z=112 produced in cold and hot fusion reactions is indicated.

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 $$\ge 910$$ 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 $$\ge 844$$ 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.

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 Qα 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. Calculated ground-state mass excess, nucleon separation- and Qα energies, total, macroscopic (normalized to the macroscopic energy at the spherical shape) and shell corrections energies, and deformations are given for each nucleus in Table 1. Table 2 contains calculated properties of the saddle-point configurations and the fission barrier heights. In 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.

The production cross sections of superheavy nuclei with charge numbers 114− 117 are predicted in the (5 − 9)n-evaporation channels of the Ca-induced complete fusion reactions for future experiments. The estimates of synthesis capabilities are based on a uniform and consistent set of input nuclear data provided by the multidimensional macroscopic-microscopic approach. The contributions of various factors to the final production cross section are discussed. As shown, the specific interplay between survival and fusion probabilities unexpectedly leads to a relatively slow decline of the total cross-sections with increasing excitation energy. This effect is supported by a favorable arrangement of fission barriers protecting the compound nucleus against splitting concerning energetic thresholds for the emission of successive neutrons. In particular, the probabilities of the formation of superheavy nuclei in the 5n-, 6n-, and in some cases even in 7n-evaporation channels are still promising. This may offer a new opportunity for the future synthesis of unknown neutron-deficient superheavy isotopes. PACS numbers: 25.70.Hi, 24.10.-i, 24.60.-k

We systematically study the nuclear level densities of superheavy nuclei, including odd systems, using the single-particle energies obtained with the Woods-Saxon potential diagonalization. We applied minimization over many deformation parameters for the global minima-ground states, and the "imaginary water flow" technique on a many-deformation energy grid for the saddle points, including nonaxial shapes. The level density parameters are calculated by fitting the obtained results with the standard Fermi gas expression. The total potential energy and shell correction dependencies of the level-density parameter are analyzed at the ground state and saddle point. These parameters are compared with the results of a phenomenological approach. As shown, this expression should be modified for the saddle points, especially for small excitation energy. The ratio of the level-density parameter at the saddle point to that at the ground state is shown to be crucial for the survival probability of a heavy nucleus.

We have investigated shapes and sizes of selected two- and four-quasiparticle \mbox{high-$K$} states in nobelium and rutherfordium isotopes within the microscopic-macroscopic model with the deformed Woods-Saxon potential. Excited nuclear configurations were obtained by blocking single-particle states lying close to the Fermi level. Their energies and deformations were found by the four-dimensional energy minimization over shape variables. We have selected the most promising candidates for \mbox{$K$-isomers} by analyzing the isotopic dependence of excitation energies, and compared our results to available experimental data. We calculated differences in quadrupole moments and charge radii between nuclei in their \mbox{high-$K$} and ground states and found their quite different pattern for four-quasiparticle states in neighboring No and Rf isotopes. The leading role of the quadrupole and hexadecapole deformations as well as the importance of higher rank symmetries are also discussed. The current development of laser techniques and the resulting ability to measure discussed effects in the near future is the motivation of our study.

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 a 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 Experimental vs theory discrepancies seem to be of various natures and not easy to eliminate, especially if one cares about 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.

The production cross sections of heaviest isotopes of superheavy nuclei with charge numbers 112–118 are predicted in the xn–, pxn–, and αxn–evaporation channels of the 48Ca-induced complete fusion reactions for future experiments. The estimates of synthesis capabilities are based on a uniform and consistent set of input nuclear data. Nuclear masses, deformations, shell corrections, fission barriers and decay energies are calculated within the macroscopic-microscopic approach for even-even, odd-Z and odd-N nuclei. For odd systems the blocking procedure is used. To find saddle points, the Imaginary Water Flow technique is used and non-axiallity is taken into account. As shown, our calculations, based on a new set of mass and barriers, agree very well with the experimentally known cross-sections, especially in the 3n–evaporation channel. The dependencies of these predictions on the mass/fission barriers tables, the ratio af/a, and fusion models are discussed. A way is shown to produce directly unknown superheavy isotopes in the 1n– or 2n–evaporation channels. The synthesis of new superheavy isotopes unattainable in reactions with emission of neutrons is proposed in the promising channels with emission of protons (σpxn≃10−200 fb) and alphas (σαxn≃50−500 fb).

A. Tucholski,1 Ch. Droste,2 J. Srebrny,1 C. M. Petrache,3 J. Skalski,4 P. Jachimowicz,5 M. Fila,2 T. Abraham,1 M. Kisieliński,1 A. Kordyasz,1 M. Kowalczyk,1 J. Kownacki,1 T. Marchlewski,1 P. J. Napiorkowski,1 L. Próchniak,1 J. Samorajczyk-Pyśk,1 A. Stolarz,1 A. Astier,3 B. F. Lv,3 E. Dupont,3 S. Lalkovski,6 P. Walker,7 E. Grodner,4 and Z. Patyk4 1Heavy Ion Laboratory, University of Warsaw, Pasteura 5a, 02-093 Warsaw, Poland 2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland 3Centre de Sciences Nuclaires et Sciences de la Matire, CNRS/IN2P3, Université Paris-Saclay, Batiment 104-108, 91405 Orsay, France 4National Centre for Nuclear Research, Hoża 69, 00-681 Warsaw, Poland 5Faculty of Physics and Astronomy, University of Zielona Gora, Licealna 9, 65-417 Zielona Gora, Poland 6Nuclear Engineering, Faculty of Physics, Sofia University “St. Kl. Ohridski”, 5 James Bourchier Boulevard, Sofia 1164, Bulgaria 7Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom

Background: The gamma softness of Nd-136 makes it possible to study the shape changes induced by two-proton or two-neutron excitation. Purpose: We measure the lifetimes of two-quasiparticle states of the bands based on the 10(+) states at 3296 and 3279 keV to investigate the shape change induced by the alignment of two protons or two neutrons in the h(11/2) orbital. Methods: The recoil-distance Doppler shift method was used for the study of Nd-136 studies, which was formed by the fusion reaction Sn-120(Ne-20, 4n)Nd-136, at E-beam = 85 MeV. Calculations were performed within the microscopic-macroscopic approach, based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy. Results: The lifetime of the 10(+) state at 3279 keV of Nd-136 was measured to be T-1/2(10)+ = 1.63(9) ns. The lifetimes of the 2(+) state at 374 keV and of the 12(+) state at 3686 keV of the ground band were also measured to be T-1/2(2+) = 26.5(14) ps and T-1/2(12+) = 22.5(14) ps. Conclusions: The measured lifetime of 10(+) the state at 3279 keV together with other observables confirm the structure change in Nd-136. A rather small reduced hindrance of the electromagnetic decay of the 10(+) state at 3279 keV would be consistent with its K-mixed character.

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 $K^{\pi} = 20^{+}$ 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.

After shortly analyzing data relevant to fission hindrance of odd-A nuclei and high-$K$ isomers in superheavy (SH) region we point out the inconsistency of current fission theory and propose an approach based on the instanton formalism. A few results of this method, simplified by replacing selfconsistency by elements of the macro-micro model, are given to illustrate its features.

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 <= Z <= 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 10th below to the 10th 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 nonaxiality. The ground states (g.s.) were found by energy minimization over configurations and deformations. We find that the nonaxiality significantly changes first and second fission saddle in many nuclei. The effect of the mass asymmetry, known to lower the second, very deformed saddles 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 triaxiality does not play any role, which 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.

We search for effects of tetrahedral deformation beta(32) over a range of similar to 3000 heavy and superheavy nuclei, 82 <= Z <= 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 nonzero tetrahedral distortion, both absolute and conditional-with the quadrupole distortion constrained to zero. In order to assure reliability of our results we include the ten 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 >= 120 for N = 173-188, as a result of a combined action of two octupole deformations: beta(32) and beta(30), in the ratio beta(32)/beta(30) approximate to root 3/5. The resulting shapes are moderately oblate, with the superimposed distortion beta(33) with respect to the oblate axis, which makes the equator of the oblate spheroid slightly triangular. Almost all found conditional minima are excited; a handful of them are degenerate with the axial minima.