An improved unified formula for $$\alpha $$-decay and cluster radioactivity of heavy and superheavy nuclei

Abstract

Improved NRDX empirical formula for $$\alpha $$ α - and cluster decay half-lives is modified by adding the effects of angular momentum, isospin asymmetry and parity. The coefficients are determined using the latest experimental data for $$\alpha $$ α -decay half-lives of 573 nuclei and the available 22 cluster decay half-lives. The modified formulas produced the $$\alpha $$ α - and cluster decay half-lives and agree with calculations of other similar formulas. We used the new formulas to calculate the half-lives of cluster emissions of the SHN with $$Z=120$$ Z = 120 , 122, 124, and 126, which have not yet been experimentally synthesized.

Cluster radioactivity in trans-lead region: A systematic study with modified empirical formulas

“…For the comparison among our modified formulas with a few of latest fitted/modified formulas [26][27][28] for cluster decay half-lives, we have calculated some other statistical parameters such as standard deviation (σ), uncertainty (u), average deviation factor (x), and mean deviation δ for 61 experimentally known cluster decay half-lives [7,9,26,29]. All these statistical parameters for these formulas are mentioned in Table 3.…”

“…(17) refers to the mean of full data set. [26] 0.81 0.10 0.03 0.68 IUF [27] 0.84 0.11 0.03 0.64 ISEF [28] 0.93 0.12 0.04 0.76…”

“…(experimental limit of half-lives of cluster emissions). For examples, 21 Na from 226−229 Np, 22 Na from 226−230 Np, 23 Na from 226−233 Np, 24 Na from 226−234 Np, 25,27 Na from 226−237 Np, 26 Na from 226−236 Np and 28 Na from 224−236 Np. Similarly, some possible clusters (Mg-isotopes) emitted from various Pu-isotopes (Z p =94) are 23 Mg from 226−231 Pu, 24,25 Mg from 226−235 Np, 26 Mg from 226−238 Np, 27 Mg from 226−239 Np, and 28,29 Mg from 226−241 Np.…”

“…For examples, 21 Na from 226−229 Np, 22 Na from 226−230 Np, 23 Na from 226−233 Np, 24 Na from 226−234 Np, 25,27 Na from 226−237 Np, 26 Na from 226−236 Np and 28 Na from 224−236 Np. Similarly, some possible clusters (Mg-isotopes) emitted from various Pu-isotopes (Z p =94) are 23 Mg from 226−231 Pu, 24,25 Mg from 226−235 Np, 26 Mg from 226−238 Np, 27 Mg from 226−239 Np, and 28,29 Mg from 226−241 Np. Among Amisotopes the potential clusters are 24 Al from 227−230 Am, 25 Al from 227−233 Am, 26 Al from 227−236 Am, 27 Al from 227−239 Am, 28 Al from 227−240 Am, 29 Al from 227−241 Am, and 30−32 Al from 227−242 Am as well as 26−33 Si from the 231−252 Cm isotopes.…”

“…In addition to this, isospin (I = (N − Z)/A) of parent nucleus is found to be pivotal for the case of α-decay in heavy and superheavy nuclei [20][21][22][23][24][25] pointing towards its significance in terms of cluster decay as well. Considering these two effects together, modified UDL formula (new UDL) by Soylu and Qi [26], and improved NRDX formula (named as improved unified formula (IUF)) by Ismail et al [27] have explained recently that angular momentum and isospin are indeed crucial quantities in determining the cluster decay half-lives. Importance of isospin effect is also probed by improving semi-empirical formula (ISEM) for the cluster radioactivity in Ref.…”