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Four groups (even-even, even-odd, odd-even and odd-odd) of heavy and super-heavy nuclei are of interest for the synthesis of the isotopes with $Z=119, 120$. We report calculations of $\alpha$~decay half-lives using four models: AKRA (Akrawy); ASAF (Analytical Super-Asymmetric Fission); UNIV (Universal Formula), and semFIS (Semi-empirical formula based on Fission Theory). We compare the experimental $Q_\alpha$ values either with AME16 atomic mass evaluation (whenever available) and with the theoretical model WS4, able to give masses of not yet measured nuclides. For $^{92,94}$Sr cluster radioactivity of $^{300,302}$120 we predict a branching ratio relative to $\alpha$~decay of -0.10 and 0.49, respectively, meaning that it is worth trying to detect such kind of decay modes in competition with $\alpha$~decay., Comment: 28 pages, 4 figures and 14 tables. arXiv admin note: substantial text overlap with arXiv:1702.05598

A new semi-empirical formula for calculations of $\alpha$~decay halflives is presented. It was derived from Royer relationship by introducing new parameters which are fixed by fit to a set of experimental data. We are using three sets: set A with 130 e-e (even-even), 119 e-o (even-odd), 109 o-e, and 96 o-o, set B with 188 e-e, 147 e-o, 131 o-e, and 114 o-o, and set C with 136 e-e, 84 e-o, 76 o-e, and 48 o-o alpha emitters. A comparison of results obtained with the new formula and the following well known relationships: semFIS (semiempirical based on fission theory), ASAF (analytical superAsymmetric fission) model, and UNIV (universal formula) is made in terms of rms standard deviation. We also introduced a weighted mean value of this quantity, allowing to compare the global properties of a given model. For the set B the order of the four models is the following: semFIS, UNIV, newF, and ASAF. Nevertheless for even-even alpha emitters UNIV gives the 2nd best result after semFIS, and for odd-even parents the 2nd is newF. Despite its simplicity in comparison with semFIS the new formula, presented in this article, behaves quite well, competing with the others well known relationships., Comment: 20 pages, 3 figures

In a previous article published in Phys. Rev. C 94 (2016) 014309 we have shown for the first time that the best dynamical trajectory during the deformation toward fission of the superheavy nucleus $^{286}$Fl is a linearly increasing radius of the light fragment, $R_2$. This macroscopic-microscopic result reminds us about the $\alpha $ or cluster preformation at the nuclear surface, assumed already in 1928, and proved microscopically many times. This time we give more detailed arguments for the neighboring nucleus $^{282}$Cn. Also similar figures are presented for heavy nuclei $^{240}$Pu and $^{252}$Cf. The deep minimum of total deformation energy near the surface is shown for the first time as a strong argument for cluster preformation., Comment: 18 pages, 11 figures and 2 tables. arXiv admin note: substantial text overlap with arXiv:1609.00847

In 1928 G. Gamow as well as Condon and Gurney gave the first explanation of alpha decay as a quantum tunnelling of a preformed particle at the nuclear surface. Soon after experimental discovery in 1984 by Rose and Jones of cluster radioactivity, confirming earlier (1980) predictions by Sandulescu, Poenaru and W. Greiner, a microscopic theory also explained the phenomenon in a similar way. Here we show for the first time that in a spontaneous cold fission process the shell plus pairing corrections calculated with Strutinsky's procedure may give a strong argument for preformation of a light fission fragment near the nuclear surface. It is obtained when the radius of the light fragment, $R_2$, is increased linearly with the separation distance, $R$, of the two fragments, while for $R_2=$~constant one gets the well known two hump potential barrier., Comment: 4 pages, 3 figures

A broad extension of periodic system into the sector of antimatter could be possible sometimes in a remote future. We expect that anti-alpha spontaneous emission from an antimatter nucleus will have the same Q-value and half-life as alpha emission from the corresponding mirror nucleus. This is the consequence of the invariance of binding energy as well as of the surface and Coulomb energy when passing from matter to antimatter nuclei with the the same mass number and the same atomic number. The Q-values and half-lives of all measured up to now 27 cluster radioactivities are given together with Q-values and half-lives of the most important competitor --- $\alpha$ decay. The lightest anti-alpha emitter, $^8\bar{Be}$, will have a very short half-life of about $81.9\cdot 10^{-18}$ s., Comment: 11 pages, 2 figures

Superheavy nuclei produced until now are decaying mainly by $\alpha$ emission and spontaneous fission. Calculated $\alpha$ decay half-lives are in agreement with experimental data within one order of magnitude. The discrepancy between theory and experiment can be as high as ten orders of magnitude for spontaneous fission. We analyze a way to improve the accuracy by using the action integral based on cranking inertia and a potential barrier computed by the macroscopic-microscopic method with a two-center shell model. Illustrations are given for $^{282}$Cn which has a measured fission half-life., Comment: 5 pages, 5 figures

The concept of heavy particle radioactivity (HPR) is changed to allow emitted particles with Z_e>28 from parents with Z>110 and daughter around 208Pb. Calculations for superheavy (SH) nuclei with Z=104-124 are showing a trend toward shorter half-lives and larger branching ratio relative to alpha decay for heavier SHs. It is possible to find regions in which HPR is stronger than alpha decay. The new mass table AME11 and the theoretical KTUY05 and FRDM95 masses are used to determine the released energy. For 124 we found isotopes with half-lives in the range of ns to ps., Comment: 4 pages, 4 figurex, revtex4-1

Analytical relationships for the surface and curvature energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. By modifying the cluster shape from a spheroid to a semi-spheroid the most stable shape was changed from a sphere to a superdeformed prolate semi-spheroid (including the flat surface of the end cap). Potential energy surfaces vs. deformation and the number of atoms, N, illustrate this property independent of N., Comment: 5 pages, 3 figurex, revtex4

A new single-particle shell model is derived by solving the Schr\"odinger equation for a semi-spheroidal potential well. Only the negative parity states of the $Z(z)$ component of the wave function are allowed, so that new magic numbers are obtained for oblate semi-spheroids, semi-sphere and prolate semi-spheroids. The semi-spherical magic numbers are identical with those obtained at the oblate spheroidal superdeformed shape: 2, 6, 14, 26, 44, 68, 100, 140, ... The superdeformed prolate magic numbers of the semi-spheroidal shape are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator: 2, 8, 20, 40, 70, 112, 168 ..., Comment: 4 pages, 3 figures, 1 table

A new version of the semiempirical formula based on fission approach of alpha decay is derived, by using the optimum values of the fitting parameters determined for even-even nuclei, combined with hindrance factors for even-odd, odd-even, and odd-odd nuclides. The deviations from experimental data for two regions of nuclear chart (493 alpha emitters with Z=52-118 and 142 transuranium nuclei including superheavies (Z=92-118), respectively) are compared with those obtained by using the universal curve and the Viola-Seaborg semiempirical relationship., Comment: 11 pages, 3 figures, revtex4

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the $^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed., Comment: 12 pages, 4 figures

Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to binary, ternary, and quaternary fission are outlined., Comment: 28 pages, 17 figures

A very general saddle point nuclear shape may be found as a solution of an integro-differential equation without giving apriori any shape parametrization. By introducing phenomenological shell corrections one obtains minima of deformation energy for binary fission of parent nuclei at a finite (non-zero) mass asymmetry. Results are presented for reflection asymmetric saddle point shapes of thorium and uranium even-mass isotopes with A=226-238 and A=230-238 respectively., Comment: 5 pages, 2 Postscript figures, REVTeX, Version 4.0

We developed a three-center phenomenological model,able to explain qualitatively the recently obtained experimental results concerning the quasimolecular stage of a light-particle accompanied fission process. It was derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment, is reached by increasing continuously the separation distance, while the radii of the heavy fragment and of the light particle are kept constant. In such a way,a new minimum of a short-lived molecular state appears in the deformation energy at a separation distance very close to the touching point. This minimum allows the existence of a short-lived quasi-molecular state, decaying into the three final fragments.The influence of the shell effects is discussed. The half-lives of some quasimolecular states which could be formed in the $^{10}$Be and $^{12}$C accompanied fission of $^{252}$Cf are roughly estimated to be the order of 1 ns, and 1 ms, respectively., Comment: 12 pages, 6 epsf, uses ws-p8-50x6-00.cls

A three-center phenomenological model able to explain, at least from a qualitative point of view, the difference in the observed yield of a particle-accompanied fission and that of binary fission was developed. It is derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment is obtained by increasing continuously the separation distance, while the radii of the light fragment and of the light particle are kept constant. During the first stage of the deformation one has a two-center evolution until the neck radius becomes equal to the radius of the emitted particle. Then the three center starts developing by decreasing with the same amount the two tip distances. In such a way a second minimum, typical for a cluster molecule, appears in the deformation energy. Examples are presented for $^{240}$Pu parent nucleus emitting $\alpha$-particles and $^{14}$C in a ternary process., Comment: 8 pages, 3 epsf, uses ws-p8-50x6-00.cls