Analytical Superasymmetric Fission Research Articles

Empirical formula for heavy cluster decay in the superheavy region

In this paper, an empirical formula to describe the heavy cluster decay with [Formula: see text] ([Formula: see text] is the charge number of the emitted cluster) from superheavy elements is proposed. The predictions of our formula are compared with the predictions of Coulomb and Proximity Potential Model (CPPM), the predictions of Analytical Super Asymmetric Fission (ASAF) model and the predictions by UDL formula of Qi et al. Excellent agreement is found between the predictions of CPPM and ASAF models and those of the present formula. Using our formula, we have calculated the decay half-lives of various heavy cluster emission from superheavy elements leading to doubly magic [Formula: see text]Pb and compared with the predictions of CPPM. The predictions of UDL formula deviate considerably from the predictions of this formula, CPPM and ASAF model, giving much lower decay half-lives, as the order of decay half-life increases. Possible heavy cluster emissions from [Formula: see text] and 122 nuclei leading to [Formula: see text]Pb and [Formula: see text]Bi are also predicted.

Proton radioactivity of nuclei with atomic numbers Z = 51–91 and mass number 104–211

Proton radioactivity of neutron-deficient nuclei with atomic numbers [Formula: see text]–91 and mass number 104–211 is investigated using the analytical super-asymmetric fission (ASAF) model — a model used to study [Formula: see text]-decay and cluster radioactivity since 1984. The experimental [Formula: see text] values are compared with calculated ones based on WS4 (Y. Z. Wang et al., 2014–2015), and in few cases KTUY05 (H. Koura et al., 2005) mass models. Proton drip-line and neutron drip-line are determined using the WS4 mass model. We compare the calculated results with experimental half-lives, showing good agreement.

Alpha decay and cluster radioactivity of super heavy nuclei 303,304120

The heaviest nuclei produced until now are few isotopes of the oganesson (atomic number Z = 118). We performed calculations of α-decay half-lives using the models AKRA (Akrawy, 2017), ASAF (Analytical Super-Asymmetric Fission, 1980), UNIV (Universal Formula, 2006), and semFIS (Semi-empirical formula based on Fission Theory, 1983). Cluster radioactivity half-lives are calculated with ASAF and UNIV models. The most important result of our calculations shows that 92,94Sr cluster radioactivity of 303,304120 has a branching ratio relative to α-decay of −0.10 and 0.49, respectively. We hope that future measurements will prove that cluster decay may compete with α decay.

Systematic studies of α and heavy-cluster emissions from superheavy nuclei

The probabilities of \ensuremath{\alpha} decay and heavy-cluster decay in the superheavy region are investigated. The preformation probabilities for \ensuremath{\alpha} and cluster emissions are evaluated with a new formula which depends on the $Q$ value of the decay. The formula shows a better agreement with the experimentally extracted cluster preformation probabilities in the heavy region. The \ensuremath{\alpha} half-lives using our model are compared with the experimental results and it is found that the present model can be employed successfully to predict \ensuremath{\alpha} half-lives in the superheavy region. The probable heavy-cluster radioactivity from superheavy nuclei is also studied using the same model. A comparison of the heavy-cluster half-lives using the present model, the half-lives given by Poenaru et al. [Eur. Phys. J. A 54, 14 (2018)] (analytical superasymmetric fission) and Zhang et al. [Phys. Rev. C 97, 014318 (2018)] are performed. The agreement between these three formalisms is evident from the study. A further study on the competition between \ensuremath{\alpha} decay and heavy-cluster radioactivity leading to $^{208}\mathrm{Pb}$ is performed. The study suggests that heavy-cluster radioactivity may be comparable to or even dominant over \ensuremath{\alpha} decay for some of the isotopes with $Z\ensuremath{\ge}118$. The study shows that the present model can be used effectively to obtain the \ensuremath{\alpha} as well as the heavier cluster decay half-lives in the superheavy region.

α decay and cluster radioactivity of nuclei of interest to the synthesis of Z=119 , 120 isotopes

Super-heavy nuclei of interest for the forthcoming synthesis of the isotopes with $Z=119$, 120 are investigated. One of the very interesting latest experiments was performed at the velocity filter SHIP (GSI Darmstadt) trying to produce $^{299}120$ in a fusion reaction $^{248}\mathrm{Cm}(^{54}\mathrm{Cr},3\mathrm{n})^{299}120$. We report calculations of $\ensuremath{\alpha}$-decay half-lives using four models: AKRA (Akrawy), ASAF (analytical superasymmetric fission), UNIV (universal formula), and semFIS (semi-empirical formula based on fission theory). The released energy, $Q$, is calculated using the theoretical model of atomic masses, WS4. For $^{92,94}\mathrm{Sr}$ cluster radioactivity of $^{300,302}120$ we predict a branching ratio relative to $\ensuremath{\alpha}$ decay of $\ensuremath{-}0.10$ and 0.49, respectively, meaning that it is worth trying to detect such kinds of decay modes in competition with $\ensuremath{\alpha}$ decay.

Cluster and alpha decay of superheavy nuclei

We investigated cluster radioactivity and alpha decay of some superheavy nuclei with atomic numbers Z = 119, 120 , which may be produced in the future. Two models are used to calculate the half-lives against cluster radioactivity: ASAF (Analytical Super-Asymmetric Fission) and UNIV (Universal Formula). For $ \alpha$ decay half-lives we are based on four models: ASAF, UNIV, semFIS (semi-empirical formula based on Fission Theory) and AKRA (first author Akrawy). The Q -values are calculated using the theoretical model of atomic masses WS10, which sometimes is called W4.

Alpha decay calculations with a new formula

A new semi-empirical formula for calculations of α decay half-lives is presented. It was derived from the 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 (newF) and the following well known relationships: semiempirical relationship based on fission theory (semFIS), analytical superasymmetric fission (ASAF) model and universal formula (UNIV) made in terms of rms standard deviation. We also introduced a weighted mean value of this quantity, allowing us to compare the global properties of a given model. For 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 second best result after semFIS, and for odd–even parents the second is newF. Despite its simplicity in comparison with semFIS, newF, presented in this article, behaves quite well, competing with the other well known relationships.

Fission approach to cluster radioactivity

Fission theory is used to explain α decay. Also, the analytical superasymmetric fission (ASAF) model is successfully employed to make a systematic search and to predict, with other models, cluster radioactivity. The macroscopic–microscopic method is illustrated for the superheavy nucleus 286Fl. Then a few results of the theoretical approach of α decay (ASAF, UNIV and semFIS models), cluster decay (ASAF and UNIV) and spontaneous fission dynamics are described with Werner–Wheeler and cranking inertia. UNIV denotes universal curve and semFIS the fission-based semiempirical formula.

Role of nuclear deformations and proximity interactions in heavy particle radioactivity

Based on the preformed cluster model (PCM), we have extended our earlier study on cluster decays of heavy parent nuclei to analyze the effects of different nuclear proximity potentials in the ground-state clusterization of superheavy nuclei with Z = 113, 115 and 117. In order to look for the possible role of deformations, calculations are performed for spherical as well as β2-deformed choices of fragmentation. The relevance of “hot compact” over “cold elongated” configurations due to orientations is also explored, in addition to the role of Q value and angular momentum l effects. As the PCM is based on collective clusterization picture, the preformation and penetration probabilities get modified considerably, and hence do so the decay constants and half-lives of the clusters, with the use of different nuclear proximity potentials. The comparative importance of nuclear proximity potentials Prox-1977 and Prox-2000 is analyzed and the calculated decay half-lives in the framework of PCM are compared with the recent predictions of the analytical super-asymmetric fission model (ASAFM). The possible role of shell corrections is also investigated for understanding the dynamics of heavy particle radioactivity. Finally, the potential energy surfaces are compared for different proton and neutron magic numbers in superheavy mass region.

Nuclear inertia and the decay modes of superheavy nuclei

Superheavy nuclei produced up to now decay mainly by α emission and spontaneous fission. For atomic numbers larger than 121 cluster decay has a good chance to compete. While calculated α decay half-lives are in agreement with experimental data within one order of magnitude and cluster decay experiments are also very well accounted for, the discrepancy between theory and experiment can be as high as ten orders of magnitude for spontaneous fission. We analyze some ways of improving the accuracy: using a semiempirical formula for α decay and changing the parameters of analytical superasymmetric fission and of the universal curve for cluster decay. For spontaneous fission we act on nuclear dynamics based on potential barriers computed by the macroscopic–microscopic method and employing various nuclear inertia variation laws. Applications are illustrated for 284Cn and Z = 118–124 even–even parent nuclei.Communicated by Steffen Bass

Extension of superasymmetric fission theory from cluster decay to nanophysics

The experimental half-lives of cluster emitters are in good agreement with our predictions within the analytical superasymmetric fission model. We extended the macroscopic-microscopic approach to study metallic cluster physics. Charged metallic clusters are ideal emitters of singly ionized trimers because both LDM and shell correction are reaching a minimum for the same mass asymmetry corresponding to the emission of a charged particle with two delocalized electrons. Maximum Q-value is obtained for transition metal clusters (high surface tension and low Wigner-Seitz radius).

Fine structure in the cluster decay of radium isotopes

Half-life times for 14C cluster emission from various radium isotopes are computed taking interacting potential as the sum of Coulomb and proximity potentials. The half-life time values are compared with experimental data and with the values reported by Poenaru et al using the analytical super-asymmetric fission model (ASAFM). The lowest half-life time for 222Ra stresses the role of the doubly magic 208Pb daughter in the exotic decay process. It is found that neutron excess in the parent nucleus slows down the exotic decay process. The high hindrance factor (HF) of the 14C branch to the ground state (9/2+) and the low HF to the first excited state (11/2+) of the 209Pb daughter are in good agreement with the experimental result. The fine structure from 223Ra gives direct evidence of the presence of a spherical component in the deformed parent nucleus.

CLUSTER RADIOACTIVITY IN TRANS-TIN REGION USING SEMIEMPIRICAL FORMULA

A semiempirical formula with only three parameters for calculating the logarithm of half-lives of heavy particle emission from a radioactive nucleus is recently proposed. The constants in the formula were obtained by fitting the available data in the trans-actinide region. The suitability of the formula in trans-tin region is studied here. The present study reveals that the semiempirical formula with only three parameters is not agreeing well with other theoretical models in the trans-tin region. Hence, one of the constants proposed earlier which acts a scaling constant is suitably replaced by a quadratic equation. The results are compared with analytical superasymmetric fission model and Shanmugham and Kamalakaran model. The semiempirical formula with new set of constants are found to have a better agreement with the available theoretical results.

CLUSTER RADIOACTIVITIES — PAST, PRESENT AND FUTURE

The half-lives of cluster emitters predicted by the analytical superasymmetric fission model have been experimentally confirmed. Potential energy surfaces of cluster emitters are showing deep valleys due to the strong shell effect of the doubly magic daughter 208 Pb . Cluster radioactivities allow us to study transitions from a deformed parent nucleus, with a complex structure resulted from mixing of several single-particle states, to a spherical daughter possessing a pure well known state. Recently, preliminary data concerning the 14 C radioactivity of 223 Ac were reported. The following modes have been experimentally confirmed: 14 C , 20 O , 24,25 Ne , 28,30 Mg , and 32,34 Si ; lower limits for 18 O , 23 F and 26 Ne are available. We give a list of some other experiments which have a good chance to be performed in the future. Applications for true ternary fission, 2α-accompanied fission, and atomic clusters are outlined.

HEAVY PARTICLE RADIOACTIVITIES

The potential energy surface for binary decay modes of 228 Th versus the distance between the fragment centers and the mass asymmetry is calculated by using the macroscopic-microscopic model with energy levels obtained within the most advanced asymmetric two center shell model. The valley due to 20 O radioactivity is evidenced as a result of the very strong shell effects due to the doubly magic daughter 208 Pb . For the first time the potential barrier of this decay mode is produced by adding the shell and pairing corrections to the phenomenological deformation energy. The half-lives of cluster emitters predicted by the analytical superasymmetric fission model have been confirmed in all measurements performed until now.

Valleys due to Pb and Sn on the potential energy surface of superheavy and lighter α-emitting nuclei

The strong shell effects of the magic nuclei 208Pb, 132Sn and 102Sn are the origin of valleys on the potential energy surfaces (PES) of the superheavy nucleus 294118 and of the alpha emitters 212Po and 106Te. We use the most advanced asymmetric two-centre shell model allowing us to obtain shell and pairing corrections which are added to the Yukawa plus exponential model deformation energy. For the first time the alpha valley of a nucleus (106Te) calculated by using the macroscopic–microscopic method is clearly seen on a PES. The α-decay half-lives calculated within fission theories (analytical superasymmetric fission model, universal curve, semiempirical formula based on fission theory) are very close to the experimental ones. The increased deviations in the neighbourhood of magic numbers of nucleons, present in other frequently used relationships (e.g. Viola–Seaborg formula), are smoothed out by the semiempirical formula based on fission theory.

α-decay half-lives of superheavy nuclei

The half-lives against \ensuremath{\alpha} decay of transuranium nuclei including superheavies are calculated by three methods: a semiempirical formula taking into account the magic numbers of nucleons, the analytical superasymmetric fission model, and the universal curves. The calculations based on $Q$ values determined by using the recently published compilations of atomic masses are compared to the experimental results.

New semiempirical formula for exotic cluster decay

A new semiempirical formula, with only three parameters, is proposed for cluster decay half-lives. The parameters of the formula are obtained by making a least squares fit to the available experimental cluster-decay data. The calculated half-lives are compared with the results of the earlier proposed model-independent scaling law and the empirically fitted analytical super-asymmetric fission model (ASAFM), showing more closeness to the ASAFM results.

Proton-rich cluster emitter half-lives

The region of even - even proton-rich cluster emitters, Ba, Ce, Nd, Sm, Gd, and Dy isotopes, leading to daughter nuclei around the double magic , is studied within our analytical super-asymmetric fission model. The half-lives of various emitters of , , , and , plotted against the corresponding external barrier penetrability on a doubly logarithmic scale, lie on a straight line, unlike in the so-called `Geiger - Nuttal' plot, where the points versus are considerably scattered. Short half-lives and large branching ratios with respect to and decay could be found for disintegration of and , as well as for decay of and , in addition to the emission of already detected. These nuclei are emitters with estimated half-lives of seconds or fractions of a second.

Cluster radioactivities from an island of cluster emitters.

We have recently developed a realistic model for studying cluster radioactivities from actinide nuclei. This model uses a cubic potential in the overlapping region connected by a Yukawa-plus-exponential potential in the post-scission region. In the present work we use this model to study {sup 4}He, {sup 12}C, {sup 16}O, and {sup 28}Si radioactivities in the region of nuclides with proton and neutron number in the range {ital Z}=56--64 and {ital N}=58--72, which has been recently identified by Poenaru {ital et} {ital al}. as a new island of such cluster emitters. It is found that charge equilibration is not needed in the study of these radioactivities and the half-lives obtained for these decays lie very close to those reported by Poenaru {ital et} {ital al}. using their analytical super asymmetric fission model.