Introduction

The exploration of nuclear structures is a prevalent area in nuclear physics [1-8]. α decay, as the dominant decay mode of heavy and superheavy nuclei, has long been regarded as a reliable pathway for obtaining rich nuclear information such as the decay energy [9-12], half-life [13-18], shell effect [19], and deformation [20-27]. This decay process was explained by Gamow [28] and Condon and Gurney [29] as a quantum tunneling effect back in 1928. Subsequently, numerous phenomenological models have been proposed to study α decay, such as the density-dependent cluster model [30, 31], two-potential approach (TPA) [16, 32], generalized liquid-drop model [33-35], and unified fission model [36]. These methods suitably reproduce the experimental half-lives and are widely used to further predict the half-lives of unknown nuclei for subsequent experimental studies.

In recent years, with the development of experimental equipment, many studies have been devoted to heavy and superheavy nuclei to extract valuable nuclear structure information from such extreme nuclei [37-41]. Superheavy elements 110–118 have been successfully synthesized using different fusion reactions, advancing toward the superheavy stable island [42-45]. On the other hand, increasing experimental data suggest that nuclei around magic numbers are relatively more stable in heavy and superheavy regions. These include neutron magic numbers, N, of 126, 152, and 162 [46-48]. In fact, the traditional liquid-drop model indicates that superheavy nuclei cannot exist because of their strong Coulomb potentials. In the 1980s, corresponding experiments confirmed that a region of deformed superheavy nuclei exists near proton and neutron numbers of 108 and 162, respectively [49]. Many studies have shown that the shell effect in the deformed regions contributes to maintain the stability of superheavy nuclei [50, 51]. As a magic number is usually a good indicator of the shell structure, the α-decay properties of nuclei should be investigated around neutron magic numbers in the heavy and superheavy regions. First, nuclei around neutrons contain important nuclear structure information. Second, research based on α-decay properties can be extended to predict the half-lives of unknown nuclei to provide reasonable references for subsequent experiments. In addition, relevant studies have suggested that N values of 178 and 184 are candidate neutron magic numbers in superheavy regions [15, 35, 52]. Similarly, the corresponding decay properties of related nuclei should be unveiled.

In α decay, the α-particle preformation factor represents the relative probability of four nucleons forming an α cluster on the surface or inside the parent nucleus [53, 54]. As this factor largely depends on the structures and states of the parent and daughter nuclei, it is often regarded as a useful probe for studying nuclear structures [55-58]. In a recent study, by combining the experimental decay energy and half-life, we systematically extracted the α-particle preformation factor of heavy and superheavy nuclei using the TPA. The TPA [16, 32, 48] is a phenomenological model that can describe α decay, and it has been extended to describe proton radioactivity [59], with the calculated half-lives suitably agreeing with experimental data. In the present study, by combining experimental half-life and decay energy data, we further extended the TPA to extract the α-particle preformation factor of nuclei around neutron magic numbers, N, of 126, 152, and 162. Useful nuclear structure information was obtained from the relevant α-decay properties. In addition, we extended the model to predict the α-decay half-lives of the nuclei around N of 178 and 184 with Z of 119 and 120. Our findings may provide useful guidelines for future synthetic experiments.

The remainder of this paper is organized as follows. Section 2 details the TPA framework and α-particle preformation factor. The results and discussion are presented in Sect. 3. Finally, a summary of the study and findings is presented in Sect. 4.

Theoretical framework

Results and discussion

An N value of 126 is a classical neutron magic number [46]. Thus, the α-decay properties of nuclei around N of 126 can be considered as a reference for larger neutron magic numbers in the heavy and superheavy regions. Using Eq. (11), the α-particle preformation factors for Rn, Ra, and Th isotopes were obtained as listed in Table 2. The first three columns indicate the α transition, neutron number of the parent nucleus, and experimental decay energy. The fourth column indicates the prediction factors extracted from experimental data, denoted by $P_{\alpha }^{\text{Extract}}$. The last two columns denote the logarithmic form of the experimental α-decay half-lives and those calculated using Pα = 1.0. To visualize the nuclear structure information reflected by the corresponding decay properties, the variations in the experimental α-decay energies (panel (a)), half-lives (panel (b)), and extracted preformation factors (panel (c)) according to neutron number N are shown for Rn, Ra, and Th isotopes in Fig. 1. Panels (a) and (b) show that the decay energies for each isotope chain generally decreases with increasing neutron number. A clear reversal occurs at N of 126 with a rapid increase until N of 128. In addition, the half-life of each isotope chain generally increases with increasing neutron number. However, a substantial decline begins at N of 126 until N of 128. At N of 126 in the classic neutron shell closure, a sharp peak in the decay energy and minimum in the half-live at N of 128 indicate the “magicity” of the daughter nuclei for N of 126. These results also indicate that the nuclei are more stable with closed shells. Similar results were reported in [62] and [63]. In panel (c), the preformation factors show the lowest values for Rn, Ra, and Th isotopes for N of 126. This indicates the difficulty of forming an α particle on the surface or inside the parent nucleus when the nucleons occupy the shell closure [47, 48, 55].

Fig. 1Full-screen View

(Color online) α-decay properties of nuclei around neutron magic number N of 126. (a) Variations in experimental α-decay energy according to neutron number of parent nuclei. Variations in (b) experimental half-lives and (c) extracted preformation factors according to neutron number of parent nuclei. The red circles, blue stars, and black squares represent the results of Rn, Ra, and Th isotopes, respectively

Overall, we evaluated the α-decay properties of nuclei around N of 126, finding that the variations in α-decay energies and half-lives exhibited an obvious change when the nuclei were near the shell closure. The preformation factors suggested that the shell effect contributed to maintain nuclear stability. These features provide guidelines for future research. Below, we analyze the α-decay properties of nuclei around N values of 152 and 162.

In [12, 15, 48, 51], we showed that the deformed shell effect around N of 152 was mainly concentrated in the region near a Z value of 100. Combined with the latest experimental data, we focused on the Cf–No (Z values from 98 to 102) isotope chains to study the α-decay properties because available experimental data were insufficient to support analyze other isotope chains. The α-particle preformation factors for Cf, Fm, and No isotopes were obtained as listed in Table 3. The first three columns indicate the α transition, neutron number of the parent nucleus, and experimental decay energy. The fourth and fifth columns indicate the extracted preformation factors from the relevant experimental data and values estimated using Eq. (12), denoted as $P_{\alpha }^{\text{Extract}}$ and $P_{\alpha }^{\text{Eq}}$, respectively. The sixth column shows the experimental half-lives. The last two columns indicate the calculated half-lives in logarithmic form with the corresponding preformation factors derived at P₀ = 1.0 from Eq. (12), denoted as ${{\displaystyle \log }}_{10}{T}_{1/2}^{\text{cal}1}$ and ${{\displaystyle \log }}_{10}{T}_{1/2}^{\text{cal}2}$, respectively. The estimation of the preformation factors and predictions of the half-lives are discussed below. The variations in the α-decay energies (panel (a)), half-lives (panel (b)), and preformation factors (panel (c)) according to neutron number N are shown for Cf, Fm, and No isotopes in Fig. 2. The variations in the decay energies and half-lives differ for N of 152. Similarly, the nuclei near neutron magic number N of 152 have longer half-lives than the corresponding adjacent nuclei. Microscopically, the preformation factors revealed useful nuclear structure information, that is, smaller prediction factors indicated a higher difficulty of forming an α particle inside the nucleus. Under these conditions, the relevant decay processes were inhibited. These results provide valuable guidelines for experimental designs in this region.

Fig. 2Full-screen View

(Color online) Similar comparison to that shown in Fig. 1 for α-decay properties of nuclei around neutron magic number N of 152. The red circles, blue stars, and black squares represent the results of Cf, Fm, and No isotopes, respectively

The α-decay properties of nuclei around neutron magic number N of 162 appeared to be more complex than those for other numbers. First, ²⁷⁰Hs₁₆₂ has been experimentally demonstrated to be a deformed double magic nucleus [49]. Although the shell effect around this region may also originate from the proton shell, insufficient experimental data impede further investigation of the shell effect in this region. Available experimental data for Hs, Sg, and Ds isotopes are listed in Table 4, which is organized as Table 3. No complete isotopes with N > 162 appeared, and the data distribution was very scattered. Under these conditions, it was difficult to determine the relevant nuclear structure information. Instead, we attempted to find a bridge for the scattered nuclei and predict the decay energies and half-lives of these unknown nuclei. In turn, these predictions allowed us to investigate the possible nuclear structural features in the superheavy region and might be useful for experiments in future work.

In [52], the α-decay energies extracted from the WS4 mass table [64] were the most accurate for reproducing experimental data for superheavy nuclei. The WS4 mass model has been used to predict the α-decay energies of incomplete isotopes. In addition, the α-particle preformation factors should be evaluated for unknown nuclei before predicting their relevant half-lives. In a previous study, we devised a local phenomenological formula, Eq. (12), to estimate α-particle preformation factors for heavy and superheavy nuclei. Tables 3 and 4 show that the preformation factors evaluated using Eq. (12) ($P_{\alpha }^{\text{Eq}}$) suitably agreed with the extracted ones ($P_{\alpha }^{\text{Extract}}$) and that the calculated half-lives (${{\displaystyle \log }}_{10}{T}_{1/2}^{\text{cal}2}$) were consistent with the experimental data (${{\displaystyle \log }}_{10}{T}_{1/2}^{\text{exp}}$). Accordingly, we extended the TPA to predict the half-lives of unknown nuclei around neutron magic number N of 162. The predicted results are listed in Table 5. The first two columns indicate the α transition and neutron number of the parent nucleus. The third column indicates the predicted α-decay energies extracted from the WS4 mass model. The last two columns indicate the predicted preformation factors and half-lives of the nuclei around N of 162. To clearly show the decay in this region, the variations in the corresponding α-decay energies (panel (a)) and half-lives (panel (b)) according to neutron number N are shown for Sg, Hs, and Ds isotopes in Fig. 3. The red and black symbols represent the experimental data and predicted results, respectively. The variations in the decay energies and half-lives differed for N of 162, although most of the results were derived from the predicted values. Combined with the α-decay properties of the nuclei around N values of 126 and 152, some nuclei around neutron number N of 162 should showed longer half-lives for synthesis or experimental detection. These predictions may provide useful information for future work.

Fig. 3Full-screen View

(color online) Similar comparison to that shown in Fig. 1 for α-decay properties of nuclei around neutron magic number N of 162. The red and black symbols indicate experimental data and predicted results, respectively

New elements with Z values of 119 and 120 have been experimentally investigated in recent years. Relevant studies have suggested that N of 178 is a neutron magic number, in addition to the well-known neutron magic number, N, of 184 [15, 35, 52]. Therefore, we also predicted the α-decay half-lives of nuclei with Z values of 119 and 120 around N of 178 and 184, respectively [17, 18, 65, 66]. Using the α-decay energies extracted from the WS4 mass model [64] and preformation factors estimated using Eq. (12), the TPA was applied to predict the half-lives of the unknown nuclei. The relevant decay processes were assumed to be transitions from ground-to-ground state. The predicted results are listed in Table 6, which is organized as Table 5. These predictions may provide valuable guidelines for future experiments.

Summary

We systematically investigated the α-decay properties of nuclei around neutron magic numbers N of 126, 152, and 162. By combining the experimental α-decay energies and half-lives, the α-particle preformation factors for the nuclei around these magic numbers were obtained using the TPA. Useful nuclear structure information was also obtained. More importantly, the TPA was extended to predict the α-decay half-lives of the nuclei around N values of 178 and 184 with Z values of 119 and 120. Our findings will likely provide guidelines for further synthesis experiments.