A new empirical formula for <i>α</i> -decay half-life and decay chains of Z = 120 isotopes
G Saxena, A Jain, P K Sharma
Abstract
Abstract Experimental α -decay half-life, spin, and parity of 398 nuclei in the range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>50</mml:mn> <mml:mo>≤</mml:mo> </mml:math> Z <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≤</mml:mo> <mml:mn>118</mml:mn> </mml:math> 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 ( μ ) and angular momentum taken away by the α -particle, are ascertained very effective for both favoured and unfavoured α -decay in addition to their excellent match with all (Z, N) combinations of experimental α -decay half-lives. After comparing with similar other empirical formulas of α -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 α -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 α -decay chains for Z = 120 isotopes are identified.