A new empirical formula for α-decay half-life and decay chains of Z=120 isotopes

Experimental $\alpha$-decay half-life, spin, and parity of 398 nuclei in the range 50$\leq$Z$\leq$118 are utilized to propose a new formula (QF) with only 4 coefficients as well as to modify the Tagepera-Nurmia formula with just 3 coefficients (MTNF) by employing nonlinear regressions. These formulas, based on reduced mass ($\mu$) and angular momentum taken away by the $\alpha$-particle, are ascertained very effective for both favoured and unfavoured $\alpha$-decay in addition to their excellent match with all (Z, N) combinations of experimental $\alpha$-decay half-lives. After comparing with similar other empirical formulas of $\alpha$-decay half-life, QF and MTNF formulas are purported with accuracy, minimum uncertainty and deviation, dependency on least number of fitted coefficients together with less sensitivity to the uncertainties of $Q$-values. The QF formula is applied to predict $\alpha$-decay half-lives for 724 favoured and 635 unfavoured transitions having experimentally known $Q$-values. Moreover, these available $Q$-values are also employed to test various theoretical approaches viz. RMF, FRDM, WS4, RCHB, etc. along with machine learning method XGBoost for determining theoretical $Q$-values, incisively. Thereafter, using $Q$-values from the most precise theoretical treatment mentioned above along with the proposed formulas, probable $\alpha$-decay chains for Z$=$120 isotopes are identified.