Narrow Results

We obtained the spectrum of probability of the bremsstrahlung emission accompanying the α-decay of ²²⁶Ra(E_α = 4.8 MeV) by measuring the α-γ coincidences and using the model presented in our previous study on the α-decay of ²¹⁴Po(E_α = 7.7 MeV). We compare the experimental data with the quantum mechanical calculation and find a good agreement between theory and experiment. We discuss the differences between the photon spectra connected with the α-decay of the ²²⁶Ra and ²¹⁴Po nuclei. For the two mentioned nuclei, we analyze the bremsstrahlung emission contributions from the tunneling and external regions of the nucleus barrier into the total spectrum, and we find the destructive interference between these contributions. We also find that the emission of photons during tunneling of the α-particle gives an important contribution to the bremsstrahlung spectrum in the whole E_γ energy range of the studied ²²⁶Ra nucleus.

At RIKEN Nishina Center, a series of experiments for studying the heaviest elements has been done by using a gas-filled recoil ion separator (GARIS). Isotopes of the 112th and the 113th elements, ²⁷⁷Cn and ²⁷⁸113 by the ⁷⁰Zn induced one neutron emission reactions on the targets ²⁰⁸Pb and ²⁰⁹Bi, respectively. The former provided an independent confirmation of the production of an isotope, ²⁷⁷Cn, of the 112th element reported firstly by the GSI (Helmholtzzentrum für Schwerionenforschung GmbH, Germany) research group. The latter was the first observation of the 113th element produced by the 'cold fusion' reaction. A gas-jet transport system coupled to GARIS was successfully operated for the chemistry study of the heaviest elements.

This paper reviews the history and stages of experimental verification of the hypothesis of Wigner’s spin–isospin SU(4)-symmetry restoration in the field of heavy atomic nuclei and its implications on hypothesis of the “island of stability”. Energies of $\alpha$-decay of a number of $\alpha$-chains of new superheavy nuclei were calculated based on Wigner’s mass formula without contribution of spin–orbit interaction that correspond to the restoration of Wigner’s spin–isospin symmetry. Calculated energies of the $\alpha$-decay fit the experimental data better than other theoretical approaches. It is concluded that there is a need to continue theoretical research of the “island of stability” taking into account mechanisms of restoration of Wigner’s spin–isospin SU(4)-symmetry.

The elastic scattering data of $\alpha +{}^{16}\mathrm{O}$ and $\alpha +{}^{40}\mathrm{Ca}$ systems at $E_{\mathrm{\text{lab}}}$ = 32.2–146 MeV and $E_{\mathrm{\text{lab}}}$ = 24.1–49.5 MeV energies have been analyzed with double-folding (DF) potential in optical model formalism in order to investigate the cluster structures of ${}^{20}$Ne and ${}^{44}$Ti nuclei. The deduced DF potentials between $\alpha$ and ${}^{16}$O as well as $\alpha$ and ${}^{40}$Ca have been used for obtaining the excitation energies and $\alpha$-decay widths of ${}^{20}$Ne and ${}^{44}$Ti in Gamow code, but the reasonable results could not be obtained. Thus, the real parts of DF potentials which are in the best agreement with experimental data have been fitted with the squared-Woods–Saxon (WS2) potential parameters to calculate the $\alpha$-decay widths of ${}^{20}$Ne and ${}^{44}$Ti with Wentzel–Kramers–Brillouin (WKB) approach. The nuclear potential sets obtained in WKB calculations are also used for Gamow code calculations. We take into account the deformation and orientation of ${}^{40}$Ca nucleus to examine their influence on both the excitation energies and decay widths of ${}^{44}$Ti. Besides, by using the binary cluster model the rotational band energies and electromagnetic transition probabilities (BE2)s according to angles are also reproduced for both nuclei. The obtained results showed that the binary cluster model is very useful to understand the observables of ${}^{20}$Ne and ${}^{44}$Ti nuclei. Although only spherical calculations are made for ${}^{20}$Ne ($\alpha$ + ${}^{16}$O), the deformation in ${}^{40}$Ca would be important for the understanding of ${}^{44}$Ti ($\alpha$ + ${}^{40}$Ca) cluster structure. The mechanism presented here would also be applied to understand the cluster structures in heavy nuclei.

Alpha-decay half-lives of the even–even superheavy isotopes with proton numbers $120\le Z\le 126$ have been calculated within the cluster model. The alpha-daughter potential was constructed by employing the density-dependent double-folding model with a realistic nucleon–nucleon interaction whose exchange part has a finite range approximation. The half-lives were calculated using Wentzel–Kramers–Brillouin (WKB) approximation with the alpha preformation factor. The results have shown that the computed alpha-decay half-lives were in good agreement with their counterpart calculated by different semi-empirical approaches. The obtained results have also shown a negative linear relationship between the logarithm of the preformation factor and the fragmentation potential for the understudy isotopes. Also, the calculated results have shown that isotopes ${}^{304,296,318}120$, ${}^{296,300,306,318,326}122$, ${}^{312,318,324,332}124$ and ${}^{308,316,322}126$ had longer half-lives than their adjacent isotopes, which indicates that the corresponding neutron or proton numbers have a magical or semi-magical properties. Furthermore, we have studied the competition between alpha-decay and spontaneous fission to predict possible decay modes from the even–even isotopes $Z=120\text{–}126$. The results revealed that the isotopes ${}^{308\text{–}332}126$, ${}^{308\text{–}320}124$, ${}^{300\text{–}312}122$ and ${}^{290\text{–}308}120$ had alpha-decay as a predominant mode of decay and the nuclei ${}^{334\text{–}338}126$, ${}^{324\text{–}338}124$, ${}^{314\text{–}334}122$, and ${}^{310\text{–}328}120$ could not survive from the spontaneous fission. We hope that the theoretical prediction could be helpful for future investigation in this field.

Theoretical predictions of $\alpha$-decay properties of several isotopes of the superheavy nucleus of $Z=126$$({}^{318\text{–}327}126)$ and their consecutive $\alpha$-decay chains are presented. Based on the double-folding model, the $\alpha$–daughter interaction potential is constructed microscopically using a realistic M3Y–Paris nucleon–nucleon (NN) interaction. The $\alpha$-decay half-lives are computed for both spherical and deformed shapes of daughter nuclei within the density-dependent cluster model. The effect of deformation is found to decrease the $\alpha$-decay half-lives compared to spherical shapes. The calculated $\alpha$-decay half-lives are in satisfactory agreement with their counterparts using other theoretical methods. The prediction of the dominant decay mode for the isotopes ${}^{318\text{–}327}126$, which have not yet been experimentally synthesized, is presented through the competition between $\alpha$-decay and spontaneous fission. We have found that the isotopes ${}^{318\text{–}327}126$ survive fission and have relatively long half-lives which span the order $10^{-6}$–$10^{-3}$. Moreover, the correlation between the logarithm of the preformation probability deduced from the cluster formation model and the fragmentation potential for even–even ${}^{304\text{–}338}126$ isotopes is elucidated showing a negative linear relation. The feasibility of cluster emission from the superheavy isotope ${}^{318}126$ is investigated using different theoretical approaches. The predictions can provide useful guidance for future experimental researches.

The $\alpha$-decay and spontaneous fission (SF) half-lives for even–even isotopes of superheavy nuclei in the range $106\le Z\le 124$ are predicted using nuclear double-folding and Coulomb potentials. The $\alpha$-decay half-lives are computed based on WKB approximation for tunneling probability through potential barrier. The half-lives of SF have also been calculated using a semi-empirical relation constructed by Santhosh et al. [Nucl. Phys. A832, 220 (2009)]. Our calculated half-lives of cold SF and $\alpha$-decay are compared with the available experimental data. This comparison indicates that our obtained half-lives are in good agreement with the available experimental data. The competition between $\alpha$-decay and SF is also analyzed in detail and the decay modes are predicted for the unknown cases. Variation of $\alpha$-decay and SF half-lives with mass number of the parent isotopes for each nucleus revealed the major role played with shell effect.

Starting from the WKB approximation, a new barrier penetration formula is proposed for potential barriers containing a long-range Coulomb interaction. This formula is especially proper for the barrier penetration with penetration energy much lower than the Coulomb barrier. The penetrabilities calculated from the new formula agree well with the results from the WKB method. As a first attempt, this new formula is used to evaluate α-decay half-lives of atomic nuclei and a good agreement with the experiment is obtained.

The Q-values and half-lives of several heavy α decaying systems are calculated using the relativistic mean field (RMF) theory-based microscopic α-daughter nucleus potential. A unified procedure is adopted, using analytic S-matrix method and treating α-decay as the decay of the resonance state of the α-daughter nucleus system. The resonance parameters are obtained from the pole positions of the S-matrix in the complex k-plane and using these Q-values and half widths are evaluated. The calculation reproduces the experimental results well. We find that the present unified approach gives a good description of the data and compare well with those obtained by empirical formulae.

The first search ever for the α-decay of ¹⁴⁶Nd into the first excited state of ¹⁴²Ce has been performed by using an ultra-low background High Purity Germanium (HPGe) detector and a Nd-sample with 97.20(1)% abundance of ¹⁴⁶Nd. No significant signal could be observed with a measuring time of 144 h. A lower limit on the half-life of this decay mode has been determined to be T_1/2 > 1.6 × 10¹⁸ years at 90% CL.

Systematic calculations on $\alpha$-decay half-lives of Bi isotopes are performed by using the generalized liquid drop model (GLDM) and several sets of Royer’s analytic formulas. In calculations, the $\alpha$ transitions include the ones of (i) ground state (g.s.) to g.s., (ii) g.s. to isomeric state (i.s.), (iii) i.s. to g.s., (iv) i.s. to i.s. According to the comparison between the calculated half-lives and the experimental data, it is found that the experimental half-lives are reproduced well by the GLDM with the cluster-like mode. This indicates that the nuclear structure details play important roles in the $\alpha$-decay half-lives. In addition, it is found that the experimental half-lives are not reproduced well by these analytic formulas because the parameters are obtained by fitting the experimental half-lives of g.s. to g.s. transitions. To give better predictions on $\alpha$-decay half-lives, the parameters in these formulas should be refitted by including the experimental $\alpha$-transition of (ii)–(iv) mentioned above.

In previous studies, we provided a novel systematization of $\alpha$-decaying even–even and even–odd nuclei starting with the classically adopted mechanism [T. Yarman et al., Eur. Phys. J. A52 (2016) 140; Eur. Phys. J. A53 (2017) 4]. Knowing beforehand the measured decay half-life, we had taken as a parameter the probability of the $\alpha$-particle as being first born in a unit period of time, within the parent nucleus before it is emitted out. We thence developed a scaffold based on shell properties of families composed of “alike nuclei”. Along the same line, we now present a systematization of odd–even (OE) as well as odd–odd (OO) nuclei. We apply our approach further to the investigation of the effect of pairing (e.g., the effect when the number of nucleons is increased by one neutron), and that of unpairing (e.g., the effect when the number of nucleons is decreased by one neutron); thus it becomes an even number for the case of odd–even nuclei $($Case OE$)$, and an odd number in the case of odd–odd nuclei $($Case OO$)$. For the first case $($OE$)$, we pick the exemplar set ${}^{161}$Re, ${}^{217}$Fr, ${}^{243}$Bk, ${}^{263}$Db; where we delineate by, respectively, Re, Fr, Bk, and Db all of the odd–even or odd–odd isotopes that neighbor the four mentioned odd–even isotopes on the proposed scaffold. We proceed in the same way for the second case $($OO$)$. Thus, we choose the exemplar set of odd–odd nuclei ${}^{172}$Ir, ${}^{218}$Ac, ${}^{244}$Es. We then gather all of the Ir, Ac, and Es odd–odd and odd–even isotopes that neighbor the three mentioned odd–odd isotopes on the proposed scaffold. We show that, in the former case, pairing, as expected, generally increases stability of the given nucleus; and in the latter case, unpairing works in just the opposite direction — i.e., it generally increases instability. We disclose “stability peaks” versus $Z$ for both sets of nuclei, we tackle here. Furthermore, we present a study to highlight an outlook of “odd-A nuclei” at hand. Contrary to the general expectation, we unveil no systematic on that.

Nuclear radial distance is a prerequisite for generating any alpha-decay half-life formula by taking a suitable effective potential. We study the emission process of alpha particles from an isolated quasi-bound state generated by an effective potential to a scattering state. The effective potential is expressed in terms of Frahn form of potential which is exactly solvable and an analytical expression for half-life is obtained in terms of Coulomb function, wave function and the potential. We then derive a closed-form expression for the decay half-life in terms of the parameters of the potential, Q-value of the system, mass and proton numbers of the nuclei valid for alpha-decay as well as proton-decay. From the nature of variations of half-life as a function of radial distance, we trace the radial independence region where decay time is almost constant. Finally, by overviewing our results and picking that particular radial distance, we predict the half-lives of a series of nuclei by using the closed-form expression. We also predict the half-lives of isotopes of nuclei with $Z=119$ and 120.

A set of empirical formulae have been proposed to calculate the $\alpha$-decay half-lives from ground state to ground state transitions of 356 nuclei classified to different set of e–e, e–o, o–e and o–o isotopes. Within these formulae, modification of the previous set of Royer expressions were done by introducing three different physical terms, including the orbital angular momentum and isobaric asymmetry factors. The predicted $\alpha$-decay half-lives compared with those adopted by former proposed models for the depended experimental data, and significant improvements were noticed for all the studied sets of isotopes.

In the present work, we intended to study the $\alpha$-decay half-lives of the even–even nuclei from ${}^{178}$Po to ${}^{226}$Ra in ground state. We investigated a semi-empirical, one-parameter model based on tunneling through a potential barrier with the centrifugal and overlapping effects. Half-lives of $\alpha$-decay of even–even nuclei calculated by using different versions of proximity potentials (gpp77, MCW76 and MB77) are compared to experimental data. Also, the computed half-lives are compared with the Royer formula, Akrawy and Poenaru (AKRE) formula, modify Ren (MRen B) formula and Denisov–Khudenko (DEKH) formula and with the experimental data. The results are in good agreement with the experimental data.

In this study, we have investigated the $\alpha$-decay chains of even–even superheavy nuclei $Z=120$ in the range of $290\le A\le 304$. The Hartree–Fock–Bogoliubov model is used to calculate the binding energy of these superheavy nuclei. We have included the so-called SkP skyrme function as an effective force and the quadruple deformations. The semi-empirical formulas are used in the reproducing $\alpha$-decay and spontaneous fission half-lives of these superheavy nuclei. By studying the decay chains of the Z = 120 isotopes and comparing them with the half-lives of spontaneous fission, it is predicted that the elements ${}^{278}114$, ${}^{284}114$, ${}^{274}114$, ${}^{282}116$, ${}^{280}116$, ${}^{290}116$,${}^{292}116$, ${}^{284}118$, ${}^{294}118$ and ${}^{292}120$ are more stable than the neighboring isotopes in their parent $\alpha$-decay chain. The corresponding neutron and proton numbers represent magical behavior that is in agreement with the numbers predicted before. In this range, the predicted nuclei are found to have large enough half-lives to synthesize them in a laboratory.

The $\alpha$-decay half-lives, $T_{\alpha }$, for five heavy and nine superheavy even–even nuclei with $84\le Z\le 92$ and $116\le Z\le 132$, respectively, have been calculated within the density-dependent cluster model. The $\alpha$-nucleus potential was derived by employing the double-folding model with a realistic $NN$ interaction whose exchange part has a finite-range. We considered several isotopes for each $Z$-value. The behavior of $log{T}_{\alpha }$ against the neutron number variation for different isotopes of each element is investigated. We found a clear similarity in the behavior of $log{T}_{\alpha }$ for the isotopes of a number of successive elements. The proton pair in the emitted $\alpha$ particle, for these elements, comes from the same proton energy level. Also, the behavior of $log{T}_{\alpha }$ with the parent neutron number, for different isotopes of an element, was found to be governed by the existence of neutron magic number or neutron-level closure. The possibility to correlate the behavior of $log{T}_{\alpha }$ for several isotopes of a specific element with the proton and neutron energy levels of this element is investigated. Moreover, the behavior of $log{T}_{\alpha }$ when adding successive proton pairs to fill the energy level at different neutron numbers is studied. This work can be considered as a significant step forward to correlate the behavior of $log{T}_{\alpha }$ with the energy levels.

Alpha decay (AD) and spontaneous fission (SF) half-lives of superheavy nuclei ${}^{296-350}124$ have been studied within the density-dependent cluster model. The alpha-nucleus potentials were calculated using the double-folding model with the realistic M3Y nucleon–nucleon interaction. To calculate nuclear half-lives, several semi-empirical formulas were used in addition to the Wentzel–Kramers–Brillouin (WKB) approximation. The calculated AD half-lives agree well with the values computed by the analytical formulas of Royer, the semi-empirical formula of Poenaru et al. and the Viola–Seaborg systematic. To identify the mode of decay of these nuclei, the SF half-lives were calculated using the semi-empirical formula given by Xu et al. The results show that among the isotopes studied, isotopes ${}^{312-318}124$ can be survived from the SF and have a half-life greater than $10^{-6}$(s). The study predicts $4\alpha$ chains from isotopes ${}^{312,313}124$, $3\alpha$ chains from isotopes ${}^{314,315,316}124$, $2\alpha$ chains from isotopes ${}^{317,318}124$ and an AD from ${}^{319,320}124$. These isotopes have a half-life long enough to be synthesized in the laboratory. Also, in the decay chains of these isotopes, it is observed that the nuclei ${}^{284,287}110{,}^{288}112{,}^{292}114{,}^{297-302}116$ have higher half-lives than their neighbors. The neutron numbers corresponding to these isotopes are $N=163,164,165,172,174,177$ indicating the magical or semi-magical behavior of these numbers, which is in good agreement with the research results.

We study the consistency of local mass relation approach in its application to prediction of nuclear masses in the region of superheavy elements. Binding energy calculations are carried out for nuclei with $A>200$ using formulas for evaluation of residual $np$-interaction. The results are found to be in good agreement with the experimental data AME2016. We also make predictions for characteristics of $\alpha$-decay in isotopes $Z=101$–106, $N=144$–157.

In this study, the half-lives of $\alpha$-decay from some heavy nuclei in the range $82\le Z\le 90$ have been studied using the WKB semi-classical approximation. The nuclear interaction potential between the $\alpha$-particle and the daughter nuclei is obtained within the double folding model. The $\mathrm{\text{NN}}$ interactions employed are those derived from relativistic mean field (RMF) theory, called as R3Y $\mathrm{\text{NN}}$ interactions. Six different R3Y $\mathrm{\text{NN}}$ interactions are considered in the study to determine the most appropriate R3Y parametrization for heavy nuclei. Some of the R3Y interactions (such as R3Y-HS, R3Y-L1, R3Y-Z, R3Y-W) contain only linear $\sigma$, $\omega$, and $\rho$ mesons, while the others (such as R3Y-NL2, R3Y-NLSH) contain nonlinear terms, in addition to the linear terms. All the R3Y $\mathrm{\text{NN}}$ interactions used are found to be efficient in describing the $\alpha$-decay half-lives data. However, R3Y $\mathrm{\text{NN}}$ interactions containing nonlinear terms are found to perform better than those containing only linear terms of the mesons.