A systematic study on α-decay chains of superheavy nuclei, Z=126 & 138

The alpha-decay chain of (314-340)126 and (350-400)138 is studied using cubic plus proximity potential with improved transfer matrix (CPP-ITM) model. The nuclear mass models DD-PC1, WS4, WS3.3 are employed to evaluate the alpha-decay energies. Thus calculated a-decay half-lives and decay chain lengths are found to be in good agreement with other theoretical formalisms. The spontaneous fission (SF) half-lives are calculated using the formalism of Xu et al. [Phys. Rev. C 71 (2005) 014309; Phys. Rev. C 78 (2008) 044329] to have a vision on the possible decay modes and decay chain lengths, and the most probable decay chains associated with the isotopes of Z = 126 & 138. This paper unveils the mass region that survives fission and also predict the long alpha-decay chains of Z = 126 & 138 with (314)126 emitting 6 alpha, (316&318)126 emit 5 alpha & (320)126 4 alpha particles, while for (350,352,354,356&358)138 chains will have 8, 7, 6, 5 alpha emission. The SF for Z = 126 & 138 occur at A >= 330 and A >= 372. These current predictions may pave way to detect/synthesize the most probable isotopes of the superheavy elements Z = 126 & 138 in the laboratory through future experiments.