Alpha decay energies and half-lives for possibly synthesized superheavy elements

We investigate the ground state properties of some superheavy nuclei, which may be synthesized in future experiments. Special emphases are placed on the alpha decay energies and half-lives. The alpha decay energies and half-lives from different theoretical models are compared and discussed comprehensively. Through these calculations and comparisons, the optimal superheavy elements to be synthesized in future experiments are proposed theoretically.

Alpha decay of heavy and super heavy nuclei with a generalized electrostatic potential

Half-lives ofαdecay for Z≥84 nuclei are calculated based on the WKB theory applied for a phenomenological potential barrier composed of a centrifugal contribution and a screened electrostatic interaction represented by a Hulthen potential.For favored decays,the model has a single adjustable parameter associated with the screening of the electrostatic potential.The description of half lives for unfavored decays requires an additional hindrance term.A good agreement with experimental data is obtained in all considered cases.The evolution of the screening parameter for each nucleus revealed its dependence on shell filling.The model is also used for theoretical predictions on a few nuclei with uncertain or incomplete decay information.

Theoretical approaches to alpha decay half-lives of super-heavy nuclei

We consider the systematics of α-decay half-lives of super-heavy nuclei versus the decay energy and the total α-kinetic energy. We calculate the half-lives using the experimental Qα values. The computed half-lives are compared with the experimental data and with existing empirical estimates and are found to be in good agreement. Also, we obtain α-preformation factors from the ratio between theoretical and experimental results for some super- heavy nuclei and evaluate the standard deviation. The results indicate the acceptability of the approach.

Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Qα value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the DensityDependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.

Investigation of decay modes of superheavy nuclei

A detailed investigation of different decay modes,namely alpha decay,beta decay,cluster decay including heavy particle emission(Z_(c)>28),and spontaneous fission,was carried out,leading to the identification of new cluster and beta-plus emitters in superheavy nucle with 104≤Z≤126.For the first time,we identified around20 beta-plus emitters in superheavy nuclei.Heavy-particle radioactivity was observed in superheavy elements of atomic number in the range 116≤Z≤126.^(292-293)Og were identified as ^(86)Kr emitters,and ^(298)122 and ^(300)122 were identified as ^(94)Zr emitters,whereas heavy-particle radioactivity from ^(91)Y was also observed in ^(299)123.Furthermore,the nuclei ^(300)124 and ^(306)126 exhibit ^(96)Mo radioactivity.The reported regions of beta-plus and heavyparticle radioactivity for superheavy nuclei are stronger than those for alpha decay.The identified decay modes for superheavy nuclei are presented in a chart.This study is intended to serve as a reference for identifying possible decay modes in the superheavy region.

An angle-dependent potential and alpha-decay half-lives of deformed nuclei for 67≤Z≤91

The half-lives of deformed nuclei are reported for 67≤Z≤91. We consider an angle-dependent potential which yields multiple approximations. The results are in better agreement with the experimental data when the multiple approximation is solely considered for the daughter nuclei.

Study of various ground state decay mechanisms of Actinide nuclei

The special property of the actinide mass region is that nuclei belonging to this group are radioactive and undergo different ground state processes,such as alpha decay,cluster radioactivity(CR),heavy particle radioactivity(HPR),and spontaneous fission(SF).In this study,the probable radioactive decay modes of the heavy mass region(Z=89−102)are studied within the framework of the preformed cluster model(PCM).In the PCM,the radioactive decay modes are explored in terms of the preformation probability(P0)and penetration probability(P)at the turning point Ra,where the penetration of fragments is initiated[Ra=RT(touching state)+ΔR(neck length parameter)].First,the alpha decay half-lives are calculated for light and heavy nuclei,and Ra points are obtained by optimizing the neck length parameter.These Ra points are further employed to fix the Q-value dependent turning point(Ra(Q)).Then,using the(Ra(Q))relation,the decay half-lives are computed,and the calculated results are compared with the available theoretical and experimental data.The isotopical trend of P0 and P is studied with respect to the mass number of the parent and daughter nucleus,respectively.The CR and HPR channels are also explored,and a comparison of calculated data is conducted with the available literature.Comparative analysis of the fragmentation potential and preformation probability is carried out for alpha decay and SF.The mass distribution of the nuclei is studied as a function of fragment mass(A2)by considering the spherical and hot-compact deformation of the decaying fragments.Finally,the most probable fission fragments are identified using the fragmentation structure,and the corresponding fission fragment total kinetic energy of the identified fragments is calculated and compared with available data,wherever applicable.

Theoretical predictions on α-decay properties of some unknown neutrondeficient actinide nuclei using machine learning

Neutron-deficient actinide nuclei provide a valuable window to probe heavy nuclear systems with large proton-neutron ratios. In recent years, several new neutron-deficient Uranium and Neptunium isotopes have been observed using α-decay spectroscopy [Z. Y. Zhang et al., Phys. Rev. Lett. 122, 192503(2019);L. Ma et al., Phys. Rev.Lett. 125, 032502(2020);Z. Y. Zhang et al., Phys. Rev. Lett. 126, 152502(2021)]. In spite of these achievements,some neutron-deficient key nuclei in this mass region are still unknown in experiments. Machine learning algorithms have been applied successfully in different branches of modern physics. It is interesting to explore their applicability in α-decay studies. In this work, we propose a new model to predict the α-decay energies and half-lives within the framework based on a machine learning algorithm called the Gaussian process. We first calculate the α-decay properties of the new actinide nucleus 214 U. The theoretical results show good agreement with the latest experimental data, which demonstrates the reliability of our model. We further use the model to predict the α-decay properties of some unknown neutron-deficient actinide isotopes and compare the results with traditional models. The results may be useful for future synthesis and identification of these unknown isotopes.

Woods-Saxon-Gaussian potential and alpha-cluster structures of alpha + closed shell nuclei

The Woods-Saxon-Gaussian （WSG） potential is proposed as a new phenomenological potential to sys- tematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of tile alpha-cluster structures in various alpha ＋ closed shell nuclei. It modifies the original Woods Saxon （WS） potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of ^212Po=^208Pb＋α. It is found that the resulting WSG potential matches the NI3Y double-folding potential at tile surface region and makes corrections to the inner part of the cluster-core l）otential. It was also determined that the WSG potential, with nearly identical parameters to that of ^212Po （except for a rescale（l radius）, could also be used to describe alpha-cluster structures in ^20Ne=^16O＋α and ^44Ti = ^40Ca＋α. In all lhrec cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data. which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha ＋ closed shell nuclei. This study is a useful complement to the existing cluster-core potentials ill literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understailding of the alpha-cluster formation, which occurs in the same general region.

Constraints on the nuclear symmetry energy and its density slope from theαdecay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process.Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state（EOS）. Each EOS is characterized by a particular symmetryenergy coefficient（asym） and a corresponding density-slope parameter L. The stepwise trends of the neutron（proton） skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym = 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay,yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.

Influence of proton-skin thickness on the α decays of heavy nuclei

We investigate the effect of proton-skin thickness on the α decay process. We consider 188 neutrondeficient nuclei belonging to the isotopic chains from Te（Z = 52） to Pb（Z = 82）. The calculations of the half-life are carried out in the framework of the preformed cluster model, with the Wentzel-Kramers-Brillouin penetration probability and assault frequency. It is shown that the proton-skin thickness（？p） of the daughter nucleus gives rise to a total α-daughter nucleus interaction potential of relatively wide deep internal pocket and a thinner Coulomb barrier of less height. This increases the penetration probability but decreases the assault frequency. The overall impact of the proton-skin thickness appears as a decrease in the decay half-life. The proton-skin thickness decreases the stability of the nucleus. The half-lives of the proton-skinned isotopes along the isotopic chain decrease exponentially with increasing the proton-skin thickness, whereas the Qα-value increases with ？p. α-decay manifests itself as the second favorite decay mode of neutron-deficient nuclei, next to the β＋-decay and before proton-decay. It is indicated as main, competing, and minor decay mode, at 21%, 7%, and 57%, respectively, of the investigated nuclei.

Nuclear structure and decay modes of Ra isotopes within an axially deformed relativistic mean field model

We examine the structural properties and half-life decay of Ra isotopes within the axially deformed Relativistic Mean-Field（RMF）theory with NL3 force parameters.We work out the binding energy（BE）,RMS radii,two-neutron separation energies（S（2n））,and some other observables.The results are in good agreement with the finite-range droplet model（FRDM）and experimental results.Considering the possibility of neutron magic number,theα-decay and cluster decay half-lives of Ra isotopes are calculated systematically using the Q-values obtained from the RMF formalism.These decay half-life calculations are carried out by taking three different empirical formulae.The calculated decay half-lives are found to be highly sensitive to the choice of Q-values.Possible shell or sub-shell closures are found at daughter nuclei with N=128 and N=126 when alpha and 8Be,12C,18O respectively are emitted from Ra isotopes.Though the cluster radioactivity is affected by the shell closure of parent and daughter,a long half-life indicates the stability of the parent,and a small parent half-life indicates that the shell stability of the daughter against decay.

Proton Emission–Recent Results and Future Prospects

Considerable progress has been made in the study of proton-emitting nuclei since the first observation of direct proton emission nearly half a century ago. This has led to improvements in our understanding of this rare decay process and provided invaluable nuclear structure data far from the valley of beta stability. This paper reviews the implications of some recent results for exotic iridium, rhenium and tantalum isotopes and considers prospects for future experimental studies of proton-emitting nuclei located at and above the N = 82 neutron shell closure.

Investigation of deformed nuclei with a new potential combination

We investigate the alpha-decay half-lives of non-spherical nuclei with the Yukawa potential as the prox- imity potential and an angle-dependent term that accounts for the deformation effects and apply the results to Ho, Tb, Lu, Tin, Ta, Hf, Yb, Re, Ir, Pt, Au, Po, etc. as examples. The comparison with the existing data is encouraging.

Research on some superheavy nuclei

Studies on some superheavy nuclei are performed. The α decay energies are calculated by an improved local binding energy formula, and the α decay half-lives are calculated by the Viola-Seaborg formula. Good agreements between theoretical and experimental results are reached.

Half-life of bismuth isotopes predicted by the Coulomb and proximity potential model; a proposition for the spherical nuclei

We know that the ground state energy, half-life, spin and parity of the heavy nuclei can be determined via the study of alpha decay. Bearing this in mind, we have calculated the penetration probability in the barrier, the decay constant and thereby the half-lives of 21 isotopes of Bi by using the proximity potential model. The comparison with the existing data is motivating.

Exploring the half-lives of extremely long-livedαemitters

Naturally occurringαemitters with extremely long half-lives are investigated using the latest experimental data.Within the time-dependent perturbation theory,αdecay with a rather narrow width is treated as a quasi-stationary problem by dividing the potential between the α particle and daughter nucleus into a stationary part and a perturbation.The experimentalαdecay half-lives of seven available long-livedαemitters with T^(total)_(1/2)>10^(14)y are reproduced with a good accuracy.It is also found that the deformation effect should be treated carefully for long-lived nuclei,especially with low Q_(α) values.Predictions of the α decay half-lives of twenty naturally occurring nuclei are provided,namely,^(142)Ce,^(145,146)Nd,^(149)Sm,^(156)Dy,^(162,164)Er,^(168)Yb,^(182,183,184,186)W,^(187,188,189,190)Os,^(192,195)Pt,and^(204,206)Pb.These nuclei are energetically unstable to α decay with low decay energies and extremely long decay half-lives.In particular,the candidates^(187)Os and^(149)Sm are strongly recommended for future experiments.