Systematical calculations on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-cluster preformation factors and decay half-lives of light nuclei near the recently observed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> emitters <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Xe</mml:mi><mml:mprescripts/><mml:none/><mml:mn>108</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Te</mml:mi><mml:mprescripts/><mml:none/><mml:mn>104</mml:mn></mml:mmultiscripts></mml:math>
Niu Wan, Jingya Fan
Abstract
In this paper, we systematically calculate the $\ensuremath{\alpha}$-cluster preformation factors and decay half-lives of light nuclei around two newly observed self-conjugate emitters $^{108}\mathrm{Xe}$ and $^{104}\mathrm{Te}$. The cluster-formation model is employed to calculate the preformation factors by using the experimental nuclear binding energies obtained from the recently updated atomic mass evaluation (AME2020). The binding energies calculated by the improved Weizs\"acker-Skyrme formula (WS4) are also used to evaluate the preformation factors. The typical behaviors are obtained that the preformation factors of even-even nuclei are larger than those of odd-$A$ (even-odd and odd-even) nuclei and the latter are generally larger than those of odd-odd nuclei. Besides, due to Pauli blocking, the preformation factors for isotopic chains are decreased with the increasing neutron number. However, it is found that, as a result of the competition between the Pauli blocking and Coulomb repulsion effects for isotonic chains, the preformation factors are generally increased with the increasing proton number. Moreover, with these obtained preformation factors, the $\ensuremath{\alpha}$-decay half-lives of these light emitters are further calculated under the density-dependent cluster model. The calculated results are compared with experimental data, especially for the two newly observed emitters.