Search for long lived heaviest nuclei beyond the valley of stability

The existence of long lived superheavy nuclei (SHN) is controlled mainly by spontaneous fission and α-decay processes. According to microscopic nuclear theory, spherical shell effects at $Z=114$, 120, 126 and $N=184$ provide the extra stability to such SHN to have long enough lifetime to be observed. To investigate whether the so-called “stability island” could really exist around the above $Z$, $N$ values, the α-decay half-lives along with the spontaneous fission and β-decay half-lives of such nuclei are studied. The α-decay half-lives of SHN with $Z=102$–120 are calculated in a quantum tunneling model with DDM3Y effective nuclear interaction using $Q_{\alpha }$ values from three different mass formulas prescribed by Koura-Uno-Tachibana-Yamada (KUTY), Myers-Swiatecki (MS), and Muntian-Hofmann-Patyk-Sobiczewski (MMM). Calculation of spontaneous fission (SF) half-lives for the same SHN are carried out using a phenomenological formula and compared with SF half-lives predicted by Smolanczuk et al. A possible source of discrepancy between the calculated α-decay half-lives of some nuclei and the experimental data of GSI, JINR-FLNR, RIKEN, is discussed. In the region of $Z=106$–108 with $N~$ 160–164, the β-stable SHN ${}_{106}^{268}{\text{Sg}}_{162}$ is predicted to have highest α-decay half-life ($T_{\alpha }~3.2$ h) using $Q_{\alpha }$ value from MMM. Interestingly, it is much greater than the recently measured $T_{\alpha }$ ($~22$ s) of deformed doubly magic ${}_{108}^{270}{\text{Hs}}_{162}$ nucleus. A few fission-survived long-lived SHN which are either β-stable or having large β-decay half-lives are predicted to exist near ${}^{294}{110}_{184}$, ${}^{293}{110}_{183}$, ${}^{296}{112}_{184}$, and ${}^{298}{114}_{184}$. These nuclei might decay predominantly through α-particle emission.

Figure 1

Plots of α decay half-life [$\log {}_{10}(T_{1/2}/\sec )$] in logarithmic scale versus proton number Z for different mass number A (indicated on top of each coloumn) using zero angular momentum transfer ($\ell =0$). (a) bar coded columns are theoretical half lives ($T_{\alpha }$ M3Y Q-MS) in WKB frame work with DDM3Y interaction and [$Q_{\mathrm{th}}^{\mathrm{MS}}$] from Myers-Swiatecki mass formula, (b) columns filled with dots ($T_{\alpha }$ M3Y Q-K) are in the same framework but with [$Q_{\mathrm{th}}^{\mathrm{KUTY}}$] from Koura-Tachibana-Uno-Yamada mass estimates, (c) solid columns are theoretical half lives ($T_{\alpha }$ M3Y Q-M) in WKB frame work with DDM3Y interaction and [$Q_{\mathrm{th}}^M$] from Muntian-Patyk-Hofmann-Sobiczewski mass formula, (d) hollow columns are experimental α decay half lives ($T_{\alpha }$ Expt). Experimental errors are given in Table .

Figure 2

Variation of α decay and fission half-lives with neutron number for elements (a) $Z=102$, (b) $Z=104$, (c) $Z=106$, (d) $Z=108$ are shown. For all plots the following symbols are used: Dash-dotted line ($T_{\alpha }$ M3Y Q-K) and continuous line with square symbols ($T_{\alpha }$ M3Y Q-M) represent α decay half-lives calculation using Q-values from KUTY (Q-K) and Muntian et al. (Q-M) respectively in this work. Triangle symbol ($T_{\alpha }$ SM) represents α-decay half-lives predicted within a microscopic framework [61, 62]. Hexagon symbol ($T_{\alpha }$ Expt) represents measured α decay half-lives. Solid circle (Tsf SM) represents fission half-lives predicted by microscopic calculation. Diamond symbol (Tsf expt) represents measured fission half-lives for some nuclei. Line-inverted triangle ($T_{\beta }$) shows β decay half-lives predicted in Ref. [63].

Figure 3

Same as Fig. 2 for elements (a) $Z=110$, (b) $Z=112$, (c) $Z=114$, (d) $Z=116$, (e) $Z=118$, (f) $Z=120$.

Figure 4

Plots for variation of phenomenological [64, 65] and microscopically [61, 62] calculated fission half lives with neutron numbers for (a) $Z=102$, (b) $Z=104$, (c) $Z=106$, (d) $Z=108$, (e) $Z=110$, (f) $Z=112$. The corresponding α decay half-lives from the present calculation are also shown for comparison. Continuous line with solid circle ($T_{\alpha }$ M3Y Q-M) represents α decay half-lives predicted by this work using Q value from Muntian et al. [7, 68, 69]. Continuous line with solid triangle (Tsf Ph) represents spontaneous fission half-lives predicted by phenomenological calculation. Solid dark circle (Tsf SM) shows the spontaneous fission half-lives predicted by microscopic calculation.

Figure 5

Same as Fig. 4 for (a) $Z=114$, (b) $Z=116$, (c) $Z=118$, (d) $Z=120$.

Figure 6

Variation of α decay half-lives ($T_{\alpha }$) predicted by present calculation with neutron number for (a) odd-Z and (b) even-Z elements from $Z=102$–120. Each graphs show the abrupt reduction of $T_{\alpha }$ after $N=162$ as the possible signature of shell effect. Similar reductions of $T_{\alpha }$ after $N=184$ are also shown by the elements for which $Q_{\alpha }$ values are available from MMM calculation.