The radioactivity of the superheavy nuclei ${}^{250−275}$Db is studied and presented using the Coulomb and proximity potentials. The half-lives corresponding to different decay modes such as α, cluster decay (${}^{12}$C, ${}^{14}$N,${}^{18,20}$O, ${}^{23}$F, ${}^{20}$Ne, ${}^{34}$S, ${}^{28}$Mg and ${}^{40}$Ca) and spontaneous fission in the superheavy nuclei ${}^{250−275}$Db are studied. The studied half-lives are compared with the available experiments. The decay modes and the branching ratios of isotopes of dubnium are presented. The isotopes of dubnium, ${}^{254−263}$Db, are identified as α emitters, whereas isotopes such as ${}^{250−253}$Db and ${}^{264−275}$Db are identified as having spontaneous fission. The identified alpha emitting isotopes of dubnium have decay energies from 6 MeV to 10 MeV and half-lives 1 ms to 100 s. The possible projectile–target combinations to synthesise the superheavy nuclei ${}^{253−263}$Db were predicted. The fusion of spherical projectile and target yields larger evaporation residue cross-sections.

We have constructed empirical formulae for the fusion and interaction barriers using a large number of experimental values chosen randomly from the literature available till date. The obtained fusion barriers have been compared with different model predictions based on the proximity, Woods–Saxon and double folding potentials along with several empirical formulas, time-dependent Hartree–Fock theories and experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for the synthesis of super heavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula (Wong,Phys. Rev. Lett. $31$:766 (1973) for the total fusion cross-sections agrees very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications incarrying out physics research near the Coulomb barrier energies. Furthermore, the present fusion barrier and radius provide us with a good nucleus–nucleus potential which is useful for numerous theoretical applications.

The cold fusion reactions with lead and bismuth as targets were used in the synthesis of superheavy elements (SHE) with mass number up to 113. Researchers ignored the cold fusion reactions in the synthesis of SHE>113. This may be due to the improper choice of projectiles. The present study focusses on cold fusion reactions leading to the formation of SHE from Z = 112 to 126. Suitable projectiles for the fusion reaction using $^{208}$Pb and $^{209}$Bi targets were identified. The fusion and evaporation residue cross-sections are evaluated usingadvance statistical model. The produced cross-sections were compared with the available experiments. Suitable projectiles for synthesising the superheavy elementswith Z = 104–126 using lead and bismuth targets are predicted.The predicted production cross-sections vary from nanobarn (nb) to picobarn (pb). The use of spherical–spherical projectile and target yields larger cross-sections than spherical–deformed or deformed–spherical projectile andtarget combination.

We have systematically studied quasifission (QF) and fusion–fission (FF) lifetimes for heavy ion fusion reactions which were used in the synthesis of superheavy elements (SHEs) 104 to 118 as well as attempted to synthesise SHEs 119 and 120 using the DNS model. The dependence of QF on energy, angular momentum, entrance channel parameters, deformation parameters and orientation angles are studied. The study reveals that QF lifetimes are larger for the successful reactions than for the unsuccessful reactions. It is also observed that the study of FF lifetimes of both successful and unsuccessful reactions will not give any clue for the reason of failure of experiments to synthesise superheavy elements. It is also observed that the QF process can be controlled by the projectile of lightly deformed or spherical nuclei. The present study finds the importance in selecting the projectile–target combination for the synthesis of SHEs with Z = 119 and 120.

The Coulomb fission may take place in a reaction if the maximum Coulomb excitation energy transfer exceeds the fission barrier of either the projectile or the target nucleus. This condition is satisfied in all the reactions used for the earlier blocking measurements of fission time-scale except for the reaction $^{208}$Pb + natural Ge crystal, where the time-scale is below the measurement limit of the blocking technique $\les$ 1 as. Inclusion of Coulomb fission in the data analysis of the blocking experiments leads us to interpret the measured time-scales longer than a few attoseconds (as) (about 1–2.2 as) due to slow Coulomb fission and those shorter than 1 as, as due to quasifission and fast Coulomb fission. Consequently, this finding resolves the critical discrepancies between the fission time-scales measured using the nuclear and blocking techniques. This, in turn, validates the fact that the quasifission and fast Coulomb fission time-scales are indeed of the order of zeptosecond (zs) in accordance with the nuclear experiment sand theories. The present results thus provide an essential input to the understanding of the fusion evaporation reaction during the formation of heavy elements.

The empirical formulae for an average total kinetic energy released during the symmetric and asymmetric fission has been estimated by considering the recently available experimental data. An empirical formulae is deduced by the systematic variation of $\langle$E$_K$$\rangle$ with Z$^2$/A$^{1/3}$. The least-square analysis of symmetricfission yields $\langle$E$_K$$\rangle$ = 0.12014(Z$^2$/A$^{1/3}$) + 5.99 MeV in the atomic number range 23 ≤ Z ≤ 120 and mass number range 46 ≤ A ≤ 302, whereas asymmetric fission yields $\langle$E$_K$$\rangle$ = 0.1367(Z$^2$/A$^{1/3}$) − 18.94 MeV in the atomic number range 78 ≤ Z ≤ 102 and mass number range 178 ≤ A ≤ 258. The root mean square error (RMSE) values are smaller than the previous systematics. The covariance of matrix and its parameters are evaluated both in symmetric and asymmetric fission of the nuclei along with the error band.