Studies on α and cluster radioactivity using the improved universal (UNIV) curve

Abstract In this article, we modified the universal (UNIV) formula of Poenaru et al [Phys. Rev. C 83 , 014601 (2011)] by including the disintegration energy-dependent formula as a preformation factor. The improved universal formula (Imp UNIV) is applied to α decay of 309 heavy nuclei in the region Z = 74–93 and found that the standard deviation, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> of decimal logarithmic half-life decreased from 0.64312 (UNIV) to 0.56467 (Imp UNIV). It is also observed that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> value decreased from 0.70502 (UNIV) to 0.68189 (Imp UNIV) in the case of cluster radioactivity showing improvement of present formalism Imp UNIV over UNIV in reproducing experimental half-lives of α and cluster radioactivity of heavy nuclei. The α decay half-lives of 80 superheavy nuclei (SHN) with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Z</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>104</mml:mn> </mml:math> have also been investigated by UNIV and Imp UNIV formula and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> value is found as 1.10681 and 0.69399 respectively, which shows that experimental α half-lives of SHN can be reproduced well by using Imp UNIV formula. The plot connecting the sum of the decimal logarithm of half-life and preformation factor, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:mi>S</mml:mi> </mml:math> versus the decimal logarithm of external penetrability, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:math> for Imp UNIV is found linear for both α and cluster radioactivity with the same slope and intercept showing the universal nature of the curve. The good agreement between our predictions on α decay of Og (Z = 118) isotopes with the generalized liquid drop model (GLDM) and Royer formula reveals our formalism's reliability. The neutron shell closure at N = 184 and N ≈ 200 are evident in our study. The prediction of the unobserved α and cluster radioactivity performed in this study will be helpful for future experiments.