Introduction

The concept of superheavy elements (elements with Z ≥ 104) was first introduced in 1958 [1]. The synthesis, decay, and identification of superheavy nuclei (SHN) have emerged as significant and popular topics in nuclear physics. The existence of stable nuclei with large Z values as a result of nuclear shell effects was supported by several theoretical investigations conducted in the 1960s [2, 3]. Despite the immense Coulomb repulsion in the superheavy region, SHN can exist owing to shell closure effects. The shell effect was found to be especially strong for nuclei with Z = 126 and N = 184, pointing to the prediction of an area known as the "island of stability" around higher atomic numbers. This discovery compels scientists to explore the possibility of synthesizing superheavy elements near the predicted magic numbers. In recent studies, proton numbers (Z values) of 114, 120, 124, and 126 and neutron numbers (N values) of 172 and 184 have been predicted to be magic numbers [4-8]. Hot fusion [9] and cold fusion [10] have been used in experiments to produce superheavy elements up to Og (Z = 118). Currently, different trials are in progress to create superheavy elements with Z = 119 and 120. Hofmann et al. [11] investigated the reaction of ⁵⁴Cr projectiles on ²⁴⁸Cm targets to examine their production and decay parameters and synthesize a new superheavy element with Z = 120. Khuyagbaatar et al. [12] also performed experiments to synthesize isotopes with Z = 119 and 120 using the reactions ⁵⁰Ti+²⁴⁹Bk and ⁵⁰Ti+²⁴⁹Cf at the Gesellschaft fur Schwerionenforchung (GSI). Strong theoretical foundations are required to create new elements that can assist experimentalists in conducting research.

Shell closures can be understood by studying the half-lives of various radioactive modes, such as α-radioactivity and cluster decay. The decay chains of SHN have been determined using these half-lives, as well as the fission half-lives, because they serve as experimental evidence for the production of these elements in fusion reactions. Checking the mode of disintegration of newly produced SHN is a valid way to understand their decay, which typically involves an α-decay chain accompanied by spontaneous fission (SF). Numerous theoretical investigations have been conducted to determine the probable decay mechanisms of SHN. The two types of decay experimentally observed in SHN so far are α-decay and SF. Cluster radioactivity (CR) in the trans-lead region has been studied both theoretically and experimentally [13–16]. In 2001, Royer et al. [17] studied light particle emission using the generalized liquid drop model (GLDM) and quasi-molecular shapes and introduced an analytical formula for light nuclear decay. Royer et al. [18] investigated the alpha decay, cluster radioactivity, and heavy-particle emission half-lives of known and still unknown SHN using the original GLDM and analytical formulas, and found that ^76–80Zn, ⁷⁸Ga, ^72,74–76Cu, ^69,71Ni, and ⁴⁷K nuclei are the best candidates for emission from SHN, with the daughter nuclei being doubly closed ²⁰⁸Pb or neighboring nuclei. The modified generalized liquid drop model (MGLDM), which developed by introducing the proximity 77 potential of Blocki et al. [19]to the GLDM of Royer and Remaud [20, 21], was used to investigate the emission of even–even light clusters such as Be, C, O, Ne, Mg, and Si from SHN with a Z value of 120 [22]. The concept of heavy-particle radioactivity (HPR), which permits the release of particles with Z_C > 28 from SHN with Z > 110, was proposed by Poenaru et al. [23] in 2011. This concept predicted that HPR is more probable than α decay in SHN. Zhang and Wang [24] employed the universal decay law (UDL) formula to predict the supremacy of cluster decay over α decay. The Coulomb and proximity potential model for deformed nuclei (CPPMDN) [25], which is a productive approach, was able to forecast HPR with a half-life similar to or even dominant over α decay for isotopes with Z ≥ 118. The investigation on the HPR from superheavy elements with Z = 118 and Z = 120 employing the MGLDM with a Q-value-dependent preformation factor [26, 27] was effective in obtaining half-lives comparable to αhalf-lives. In 2021, Qian et al. [28] studied the surface alpha clustering in heavy nuclei by considering the preformation factor, which behaves with a Geiger-Nuttal-like pattern (i.e., P_C has an exponent law with $Q^{-1/2}$). Later, Wan et al. [29] considered the α-decay energies and half-lives of SHN within the cluster model, along with a slightly modified Woods–Saxon potential.

Using the MGLDM, we studied heavy-cluster emissions (Z_C > 28) from Z = 118 [26] and Z = 120 [27], leading to doubly magic ²⁰⁸Pb or its neighbor (the obtained half-lives were comparable to the α half-lives) and doubly magic ¹³²Sn or its neighbor (with minimum half-lives). In a previous study [22] we considered the cluster decay of various isotopes of Z = 120 emitting light clusters (Z_C < 14) ranging from ⁸Be to ³⁴Si using the MGLDM. It should be noted that in this study, the residual nuclei formed were neither doubly magic ²⁰⁸Pb, ¹³²Sn, nor neighboring nuclei.

The goal of the current study was to examine every possible combination of cluster daughters in heavy clusters for isotopes ^297–300119 and compute all the heavy-cluster decay half-lives using the MGLDM with the Q-value-dependent preformation factor. Section 2 outlines the theoretical framework of the study. The findings of this study and their significance are presented in Sect. 3. Finally, Sect. 4 concludes the study.

MGLDM

In the MGLDM, the total energy of the decaying nucleus is found as follows: $E=E_{\text{V}}+E_{\text{S}}+E_{\text{C}}+E_{\text{R}}+E_{\text{P}}.$ (1)

For the post-scission zone, the volume, surface, and Coulomb energies were provided by Royer et al. [20] as follows: $E_{\text{V}}=-15.494\left[\left(1-1.8I_1^2\right)A_1+\left(1-1.8I_2^2\right)A_2\right]$ (2) $E_{\text{S}}=17.9439\left[\left(1-2.6I_1^2\right)A_1^{2/3}+\left(1-2.6I_2^2\right)A_2^{2/3}\right],$ (3) $E_{\text{C}}=\frac{0.6e^2{Z}_1^2}{R_1}+\frac{0.6e^2{Z}_2^2}{R_2}+\frac{e^2{Z}_1{Z}_2}{r},$ (4) where $A_i$ represents the mass, $Z_i$ represents the charge, $R_i$ represents the radius, $I_i$ represents the relative neutron excess of the two nuclei, and $r$ represents the separation between the mass centers. The nuclear proximity energy [19] is found as follows: $E_{\text{p}}\left(z\right)=4\pi \gamma b\left[\frac{C_1{C}_2}{\left(C_1+C_2\right)}\right]\Phi \left(\frac{z}{b}\right),$ (5) where $\gamma$ is the nuclear surface tension coefficient, and $\Phi$ is the universal proximity potential [30].

Tunneling probability P [20] is found as follows: $P=\text{exp}\left\{-\frac{2}{\hslash }\underset{R_{\text{in}}}{\overset{R_{\text{out}}}{{\displaystyle \int }}}\sqrt{2B\left(r\right)\left[E\left(r\right)-E\left(\text{sphere}\right)\right]}\text{d}r\right\},$ (6) where $R_{\text{in}}=R_1+R_2$, R_out=e₂Z₁/Z₂/Q, and mass inertia B(r) = μ, the reduced mass.

The partial half-life can be computed as follows: $T_{1/2}=\left(\frac{\ln 2}{\lambda }\right)=\left(\frac{\ln 2}{\nu P_{\text{C}}P}\right).$ (7)

Here P_C, the preformation probability [31], is found as follows: $P_{\text{C}}={10}^{aQ+b{Q}^2+c}$ (8) with a = –0.25736, b = 6.37291 × 10^-4, and c = 3.35106. For alpha decay, the preformation factors [32] (P_C=0.94 for even–even nuclei, P_C =0.85 for odd–A nuclei, and P_C=0.67 for doubly odd nuclei) were obtained using the MGLDM values and experimental data of 318 nuclei in the range of Z = 74 to 93. Assault frequency $\nu =\frac{\omega }{2\pi }=\frac{2E_v}{h}$, where $E_v$ is the zero-point vibration energy, which is given as follows [16]: $E_v=Q\left\{0.056+0.039\exp \left[\frac{\left(4-A_2\right)}{2.5}\right]\right\},\text{ for }{A}_2\ge 4.$ (9)

Results and discussion

The possible heavy-particle radiations from SHN with Z = 119 and 297 ≤ A ≤ 300 were investigated using the MGLDM with a Q-value-dependent preformation factor. In our previous work [31], we studied cluster radioactivity from various heavy nuclei using the MGLDM with Q-value-dependent preformations. In this study, we estimated the accuracy of our predicted half-lives and found that they matched the $T_{1/2}^{\text{Exp}.}$ values with a standard deviation of 0.755. We have also studied the α decay of various SHN [33] using the MGLDM and the predicted half-lives were found to have the values, with a least standard deviation of 0.34.

The preformation factor is not a measurable quantity but a hypothetical and model-dependent one. The Q value differs for various clusters radiating from the same mother nucleus and for the same cluster emitted from different mother nuclei. This has been confirmed experimentally [34, 35]. The relevance of Q values, which characterize the decay process, led to the study [36] of the variation of the Q value with the cluster preformation probability extracted from experimental data [34, 35], with their obtained relation given in Eq. (8). The constants in this equation were obtained by the least-squares fitting of the experimental cluster decay data [34, 35]. In the expression for the tunneling probability, Eq. (6), the inner turning point, R_in, is considered the contact point, which is valid for alpha emission. In the case of heavy-particle emission, we considered the contribution of the overlapping region (the internal part of the barrier) when developing the Q-dependent preformation factor, as shown in Eq. (8).

All of the cluster–daughter decay combinations for ²⁹⁷119, ²⁹⁸119, ²⁹⁹119, and ³⁰⁰119, which had positive Q values, were evaluated. The disintegration energy is given by the following: $Q=\text{Δ}{M}_{\text{p}}-\left(\text{Δ}{M}_{\text{d}}+\text{Δ}{M}_{\text{c}}\right),$ (10) where $\text{Δ}{M}_{\text{p}}$ is the difference in the mass excess of the parent, and $\text{Δ}{M}_{\text{d}}$ and $\text{Δ}{M}_{\text{c}}$ are the differences in the mass excesses of the two decay products. These data were taken from the AME2020 mass tables of Wang et al. [37], and on a few occasions, the KTUY05 table [38] was used for some nuclei whose experimental values were unavailable. A comprehensive study of the α-decay energies, Q values, and half-lives of 121 SHN with Z > 100 was performed using twenty mass tables by Wang et al. [39]. The results showed that the KUTY05 mass model was the best at reproducing the experimental Q values of the SHN, and the standard deviation in the estimation of the Q value was 0.352.

Our current research had the goal of understanding the characteristics of SHN, specifically those for Z = 119 with 297 ≤ A ≤ 300. We examined all the potential cluster–daughter combinations using a cold reaction valley plot, which connects the driving potential with the mass number of the cluster. This plot was used to analyze the valleys or low-energy regions in the driving potential. Driving potential refers to the overall energy difference between the interaction potential (V) and the disintegration energy (Q value) associated with the reaction process. The driving potential (V–Q) is computed for the parent nucleus by taking into account the variations in mass and charge asymmetries, ${\eta }_A=\frac{A_1-A_2}{A_1+A_2}$ and ${\eta }_Z=\frac{Z_1-Z_2}{Z_1+Z_2}$, for the touching configuration.

In the touching configuration, the distance between fragments (r) is equal to the sum of the Sussman central radii (C₁ and C₂). For a certain value of mass asymmetry (${\eta }_{\text{A}}$) and separation among the fragments (r), the charges of the fragments are determined by minimizing the driving potential. In other words, for a given set of masses (A₁, A₂) in the mass–asymmetric coordinate system, the specific set (Z₁, Z₂) that yields the lowest driving potential is found. The minimum driving potential corresponds to the most probable decay for a specific pair (A₁, A₂).

Figures 1(a), 2(a), 3(a), and 4(a) plot the driving potentials with the mass numbers of clusters for ²⁹⁷119, ²⁹⁸119, ²⁹⁹119, and ³⁰⁰119 respectively. Decay combination [¹³⁶Xe (N=82) + ¹⁶¹Tb] exhibits the lowest driving potential among all the possibilities for isotope ²⁹⁷119, suggesting that it is the most likely decay to occur. Likewise, other combinations such as [¹³⁵I (N=82) + ¹⁶²Dy] and [¹³⁷Cs (N=82) + ¹⁶⁰Gd], where the cluster nuclei possess a magic number of neutrons, demonstrate relatively lower driving potentials. For ²⁹⁸119, [¹³⁵I (N=82) + ¹⁶³Dy] is the combination with the minimum driving potential. The decay combination [¹³⁴I (N=81) + ¹⁶⁴Dy] also has a comparatively low driving potential. The decay combination [¹³⁴Te (N=82) + ¹⁶⁵Ho] shows the minimum driving potential compared to all the other possibilities for isotope ²⁹⁹119. For ³⁰⁰119, the decay combination involving [¹³³Te (N=81) + ¹⁶⁷Ho] shows the least driving potential. Based on all these cases, it can be concluded that the decay combination with the minimum driving potential, which is the most likely degradation, is formed in a manner where the cluster nuclei possess a magic number of neutrons.

Fig. 1Full-screen View

(a) Plot of driving potential vs. mass number of clusters for ²⁹⁷119 for touching configuration r=C₁+C₂. (b) Variation of logarithm of half-life with mass number of clusters for probable heavy-cluster decay from ²⁹⁷119

Fig. 2Full-screen View

(a) Plot of driving potential vs. mass number of clusters for ²⁹⁸119 for touching configuration r=C₁+C₂. (b) Variation of logarithm of half-life with mass number of clusters for probable heavy-cluster decay from ²⁹⁸119

Fig. 3Full-screen View

(a) Plot of driving potential vs. mass number of clusters for ²⁹⁹119 for touching configuration r=C₁+C₂. (b) Variation of logarithm of half-life with mass number of clusters for probable heavy-cluster decay from ²⁹⁹119

Fig. 4Full-screen View

(a) Plot of driving potential vs. mass number of clusters for ³⁰⁰119 for touching configuration r=C₁+C₂. (b) Variation of logarithm of half-life with mass number of clusters for probable heavy-cluster decay from ³⁰⁰119

The half-lives were calculated using the MGLDM for all the possible heavy-particle emissions linked to each Z = 119 isotope after the fragment combination was determined. The obtained T_1/2 values of the possible heavy clusters for ^297–300119 are listed in Tables 1 and 2. Columns 1 and 5 give the probable clusters. Columns 2 and 6 give the daughters. Columns 3 and 7 give the Q values, and columns 4 and 8 give the heavy-particle decay half-lives in seconds. For the half-life of any heavy cluster (Z_C ≥ 32) predicted in Tables 1 and 2 that is within experimentally observable limits. Our findings were consistent with the predictions of Poenaru et al. [23] that SHN with Z> 110 release heavy clusters with Z_C > 28. In some circumstances, the likelihood of heavy-particle decay is greater than the probability of alpha decay according to the heavy-particle radioactivity concept of Poenaru et al. [23]. Given the measurable half-lives (≤10¹² s) obtained, more advanced nuclear beam sources such as China's High-Intensity Heavy-Ion Accelerator Facility (HIAF) are required to assess the potential for heavy-cluster radioactivity. Poenaru et al. [40] studied cluster and α emissions for SHN with Z =119 and 120. Two models, the analytical super asymmetric fission model (ASAFM) and universal formula (UNIV) were used by the authors to calculate the half-lives of cluster radioactivity.

Table 3 compares the half-lives obtained using the present formalism for clusters ⁸⁹Rb, ⁹¹Rb, and ⁹²Rb from parents ²⁹⁷119, ²⁹⁹119, and ³⁰⁰119, respectively, along with the values reported by Poenaru et al. [40]. Our predictions match the values reported by Poenaru et al., emphasizing the reliability of our calculations.

The emission of clusters of C, O, F, Ne, Mg, and Si from heavy nuclei ranging from ²²¹Fr to ²⁴²Cm was experimentally observed [34, 35], in which the daughters consistently exhibited a doubly magic configuration such as ²⁰⁸Pb or a neighboring one. It should be noted that several researchers have used different models to study the emission of light clusters of C, O, F, Ne, Mg, Si, etc. from SHN. In these decays, the daughter was not the doubly magic ²⁰⁸Pb or a neighboring one, but none of them succeeded in predicting a half-life equivalent to that of the α-decay. Only a few models have successfully been used to study heavy particle radioactivity (Z_C > 28) from SHN with Z > 110, in which the half-lives obtained were comparable to the alpha half-lives, and the decays led to ²⁰⁸Pb or neighboring nuclei. The first model to predict heavy-cluster decay half-lives comparable to alpha half-lives was the ASAFM of Poenaru et al. [23]; the other models were the CPPM [25] and MGLDM [26]. Recently, Ghodsi et al. [41] studied heavy-cluster decay from SHN using a double-folding formalism. Their results were compared with those of other models, including our results using the CPPM [25], and agreed with our findings. In the present work, our group considered all of the probable heavy clusters in the frame of the MGLDM and predicted half-lives comparable to those of the α half-lives (decays leading to the doubly magic ²⁰⁸Pb or a neighboring one), along with the minimum half-lives (decays leading to the doubly magic ¹³²Sn or a neighboring one). It should be emphasized that the predictions of HPR half-lives comparable to the alpha decay half-lives in the superheavy region are model-dependent. In Ref. [25], we studied the HPR (Z_C >28) from the isotopes of SHN using the CPPM with the preformation probability, which depends on the Q value of the decay. In the current study, we used the MGLDM with a Q-value-dependent preformation probability to study the HPR from isotopes of Z = 119. In Ref. [31], we analyzed the emission of light clusters (Z_C < 14) of C, O, F, Ne, Mg, and Si from various heavy nuclei with A values ranging from 221 to 242 using the MGLDM with a Q-dependent preformation factor. The former study [25] dealt with the emission of heavy clusters from SHN, whereas the latter one [31] dealt with the study of light clusters from heavy nuclei. We would like to mention that the models used for these studies were different. In the CPPM and MGLDM, the expressions used for the barrier penetrability were different (see Eq. (5) of Ref. [25] and Eq. (14) of Ref. [31], respectively).

The variation in the log₁₀T_1/2 value of the probable heavy cluster versus the mass number of the cluster for the possible HPR from ²⁹⁷119 is depicted in Fig. 1(b). The half-life decreased with increasing cluster size. In addition, the predicted heavy-cluster decay half-life exhibited peaks and dips. The stability of the mother nucleus was represented by the half-life peak, whereas the durability of the decay fragments was represented by the half-life drop. When decay fragments have closed shells, they are more likely to be stable and undergo radioactive decay. In Fig. 1(b), the small dip in the half-life corresponds to the fragment combinations [⁸⁶Kr (N=50) + ²¹¹Bi], [⁸⁹Rb + ²⁰⁸Pb (N=126)], [¹²⁴Sn (Z=50) + ¹⁷³Tm], [¹³⁶Xe (N=82) + ¹⁶¹Tb], and [¹³⁷Cs (N=82) + ¹⁶⁰Gd]. This indicates that if the daughter or cluster possesses a magic number of neutrons or protons, a dip in the decay half-life can be observed.

The same observation was made for ²⁹⁸119, ²⁹⁹119, and ³⁰⁰119. In Fig. 2(b), the small dip in half-life corresponds to fragment combinations [⁹⁰Rb + ²⁰⁸Pb (N=126)], [¹²⁶Sn (Z=50) + ¹⁷²Tm], [¹³⁵I (N=82) + ¹⁶³Dy], and [¹³⁷Cs (N=82) + ¹⁶¹Gd]. As shown in Fig. 3(b), fragment combinations [⁹²Sr + ²⁰⁷Tl (N=126)], [¹²⁶Sn (Z=50) + ¹⁷³Tm], and [¹³⁶Xe (N=82) + ¹⁶³Tb] exhibited the lowest half-lives. The minimum T_1/2 values for fragment combinations [⁹³Sr + ²⁰⁷Tl (N=126)], [¹²⁶Sn (Z=50) + ¹⁷⁴Tm], and [¹³⁶Xe (N=82)] + ¹⁶⁴Tb] are shown in Fig. 4(b). The predicted heavy cluster or its residual nuclei are extremely stable because of the closed-shell effect, which is one of the distinctive characteristics of heavy-particle radioactivity.

The probabilities of cluster emissions from each isotope of ^297–300119 with a half-life similar to that of the α-decay half-life are listed in Table 4. Columns 1–4 show the parent nuclei, probable clusters, daughter nuclei, and Q values, respectively. Columns 5 and 6 represent the heavy-cluster half-life and α-decay half-life from each isotope of ^297–300119, respectively. If the predicted heavy-cluster half-life is close to the α-decay half-life, then there is a chance that the SHN will go through heavy-cluster decay. Various isotopes of indium (Z = 49), cadmium (Z = 48), and palladium (Z = 46), which have proton numbers close to magic number Z = 50, are the principal heavy clusters with half-lives equivalent to the α half-life, as predicted from the SHN of ^297–300119 and listed in Table 4. Another probable decay mechanism involved the different isotopes of rubidium leading to daughter nuclei of lead (Z= 82), strontium leading to thallium (Z= 81), and krypton leading to bismuth (Z= 83). In all these cases, the proton number and number of neutrons in the residual nuclei were near the magic numbers (Z= 82, N= 126). This clearly illustrates the role played by the magic numbers in radioactive decay. Detecting these decays with T_1/2 values comparable to that of the α decay will be beneficial for future studies.

Table 5 lists the possible cluster–daughter combinations with the minimum half-life values among all the fragmentations of each isotope of ^297–300119. When the half-life was low, the decay probabilities increased. From the table, it can be deduced that the most probable clusters with the lowest half-lives were various isotopes of Cs, Xe, and I, with neutron number N = 82 or near it. Consequently, we could identify an area where HPR dominated the α decay in this study and all the possible heavy clusters had the magic number of neutrons (N= 82) or close to it, as listed in Table 5. This study revealed that the likelihood of decay increases when either the emitted cluster or daughter nucleus possesses stable configurations characterized by the magic number of protons or neutrons. Therefore, our study demonstrated the significance of the shell effect on nuclear decay.

Furthermore, calculations were performed to determine the yield of every possible decay combination from ^297–300119. Yield Y for a decay combination is computed as follows: $Y=\frac{P}{\sum P} \times 100\%,$ (11)

where P is the barrier penetrability for the decay, and $\sum P$ is the sum of the barrier penetrabilities of all the combinations. Tunneling possibility P was given by Eq. (6) in section 2. Table 6 presents the tabulated data for the decay combinations that exhibited the highest yield values.

Once the yield was calculated, the logarithmic yield was plotted against the number of clusters in each case. Figures 5, 6, 7, and 8 show the plots of log₁₀[Y] versus the number of clusters for all the decay combinations involving clusters with mass numbers ranging from 80 to 150 for ²⁹⁷119, ²⁹⁸119, ²⁹⁹119, and ³⁰⁰119, respectively. From all the graphs, it can be observed that the logarithm of the yield reached its maximum at two distinct positions. One peak was located in the vicinity of clusters with mass numbers ranging from 88 to 94, while the other peak was found around the clusters having 132 ≤ A ≤ 138. For ²⁹⁷119, the first maximum occurred when the isotope decayed into cluster ⁸⁹Rb, resulting in the formation of doubly magic daughter nuclei, ²⁰⁸Pb (Z = 82, N =126). The second maximum, which had the highest log₁₀[Y] value among all the decay combinations, occurred for the combination [¹³⁶Xe + ¹⁶¹Tb]. This was also the reaction with the minimum driving potential in the cold valley plot of ²⁹⁷119, making it the most probable decay. The first peak in the yield for the cluster emissions from ²⁹⁸119 and ²⁹⁹119 was achieved when the daughter nuclei, ²⁰⁸Pb, were formed, with the respective clusters generated being ⁹⁰Rb and ⁹¹Rb. The second maximum yield value was achieved in the cases of ²⁹⁸119 with combination [¹³⁵I (N=82) + ¹⁶³Dy] and ²⁹⁹119 with combination [¹³⁶Xe (N=82) + ¹⁶³Tb]. For ³⁰⁰119, the first and second yield peaks occurred for decay combinations [⁹⁴Sr + ²⁰⁶Tl (N=125)] and [¹³⁶Xe (N=82) + ¹⁶⁴Tb], respectively. Based on these observations, we can infer that if the cluster or daughter nuclei involved in the decay possess a magic number of neutrons, the probability of the reaction occurring is higher, leading to an increased yield for that specific decay combination. Magic numbers are known to provide greater stability to atomic nuclei, and their presence in decay products enhances the probability of decay combinations.

Fig. 5Full-screen View

(Color online) Plot showing log₁₀[Y] vs. mass number of clusters for all the possible decay combinations from ²⁹⁷119

Fig. 6Full-screen View

(Color online) Plot showing log₁₀[Y] vs. mass number of clusters for all the possible decay combinations from ²⁹⁸119

Fig. 7Full-screen View

(Color online) Plot showing log₁₀[Y] vs. mass number of clusters for all the possible decay combinations from ²⁹⁹119

Fig. 8Full-screen View

(Color online) Plot showing log₁₀[Y] vs. mass number of clusters for all the possible decay combinations from ³⁰⁰119

Table 7 lists the decay modes of ^297–300119, which were determined by comparing the $T_{1/2}$ values of the α decay with the $T_{1/2}$ values of the spontaneous fission. Columns 1–4 indicate the parent nuclei, Qvalues, SF half-lives, and α-decay half-lives, respectively. The mass inertia-dependent expression [26] was employed to calculate the SF half-life, while the MGLDM method was utilized to obtain the α-decay half-life. The equation for the SF half-life is as follows: ${\text{log}}_{10}\left[T_{1/2}\left(\text{yr}\right)\right]=c_1+c_2\left(\frac{Z^2}{\left(1-k{I}^2\right)A}\right)+c_3{\left(\frac{Z^2}{\left(1-k{I}^2\right)}\right)}^2+c_4{E}_{\text{shell}}+c_5{I}_{\text{rigid}}+h_i,$ (12) where $I_{\text{rigid}}=B_{\text{rigid}}\left[1+0.31{\beta }_2+0.44{\beta }_2^2+\dots \right]$ is the mass inertia of a rigid nucleus [42, 43], with mass inertia parameter $B_{\text{rigid}}=\frac{2}{5} M{R}^2=0.0138A^{5/3}\left(\raisebox{1ex}{${\hslash }^2$}\!\left/ \!\raisebox{-1ex}{$\text{MeV}$}\right.\right)$ and $R=1.2A^{1/3}$ (fm). M represents the mass of the nucleus, while ${\beta }_2$ stands for the quadrupole deformation of the nucleus. The given constants have specific values:c₁ = 1208.763104, c₂ = -49.26439288, c₃ = 0.486222575, c₄ = 3.557962857, and c₅ = 0.04292571494. Additionally, the value of k is set at 2.6 [44], and h_i represents the blocking effect for a nucleon that is unpaired. For heavy and SHN with even numbers of both protons and neutrons, h_i is set to 0. However, for nuclei with an odd number of neutrons (odd-N nuclei), h_eo is equal to 2.749814, and for nuclei with an odd number of protons (odd-Z nuclei), h_oe is equal to 2.490760. The experimental half-lives reported in Ref. [45] are listed in the 5^th column. The theoretical and experimental decay modes are presented in columns 6 and 7, respectively. The daughter nuclei resulting from the decay of ²⁹⁷119, namely ²⁹³Ts, ²⁸⁹Mc, and ²⁸⁵Nh, possess half-lives shorter than the spontaneous fission half-life. Consequently, they are capable of enduring the fission process. Spontaneous fission takes place in daughter nuclei ²⁸¹Rg and ²⁷⁷Mt because their spontaneous fission half-life is shorter than their α half-life.

Hence, this work implies that the decay of ²⁹⁷119 includes four α decay chains and two spontaneous fissions. The decay of parent nucleus ²⁹⁸119 involves seven α decay chains only because of the significantly shorter α half-lives compared to the SF half-lives. In the context of parent nucleus ²⁹⁹119, the α half-life is shorter than the SF half-life for the initial four decays. Subsequently, for daughter nuclei ²⁸³Rg and ²⁷⁹Mt, spontaneous fission takes place due to the α half-lives being longer than the SF half-lives. Consequently, the decay of ²⁹⁹119 involves a sequence of four α decay chains followed by two instances of spontaneous fission. Similarly, ³⁰⁰119 experiences a series of six α decays, followed by two occurrences of spontaneous fission. The currently obtainable experimental half-life, as well as the predicted decay mode based on the accessible experimental data, provide additional validation of our predictions. We would like to mention that the isotopes of Z = 119 are the most promising candidates for synthesis in the future. The present study determined the most favorable heavy cluster emissions from these nuclei and provided suitable projectile target combinations (obtained from the cold reaction valley) for their synthesis, depending on the availability and lifetimes of the projectiles and targets.

Summary

We investigated all of the possible cluster–daughter combinations for isotopes ^297–300119 and computed the heavy-cluster decay half-lives using the MGLDM, including the decay energy-dependent preformation probabilities. The expected half-life of any heavy cluster within experimentally detectable limits had a Z_c ≥ 32, and these results were in line with the predictions of Poenaru et al. that SHN with Z >110 will produce heavy particles with penetrability comparable to or greater than that of the α-decay. The isotopes of heavy clusters of Kr, Rb, Sr, Pa, In, and Cd have half-lives comparable to the α half-lives; and the isotopes of clusters of I, Xe, and Cs have a minimum half-life (10^-14 s), indicating the role of shell closure (Z = 82, N = 82, and N = 126) for cluster and daughter nuclei in heavy-cluster radioactivity. We anticipate that isotopes ^297,299119 will decay in 4α chains, isotope ³⁰⁰119 will decay in 6α chains, and isotope ²⁹⁸119 will decay in continuous α chains. The predicted half-lives (α and SF) and modes of decay of nuclei in the disintegration chains of ^297–300119 agree with the experimental data, which verifies the reliability of our findings.