Generalizing the Liquid Drop Model (LDM) to Assess (Q_β^+-value) for Nuclei in the Range of 10≤Z≤98.

Abstract

In this research, a new formula of positive beta decay energy (𝑸 𝜷 + − 𝒗𝒂𝒍𝒖𝒆) was obtained for light, medium and heavy nuclei (eveneven, evenodd, oddeven and oddodd) for the range of nuclei (𝟏𝟎 ≤ 𝒁 ≤ 𝟗𝟖). Instead of mass differences values, this formula is expressed in the form of nuclear binding energies. After multiple mathematical derivations, the decay energy is defined using the liquid drop model (LDM) to arrive at a final equation for the positive beta decay energy. The (𝑸 𝜷 + − 𝒗𝒂𝒍𝒖𝒆) was calculated using four terms: the first term represents the symmetry energy with the opposite sign as in the liquid drop model, the second term represents the Coulomb repulsion energy, and the other two terms represent the pairing and constant (C) terms, where (C) is provided by the mass difference between the neutron and proton. In the investigation of the proposed novel formula of (𝑸 𝜷 + − 𝒗𝒂𝒍𝒖𝒆),the findings showed a good match between experimental and theoretical values, especially for heavy and medium nuclei, but a less match for light nuclei due to the presence of a magic numbers was observed. In the investigation of the novel 𝑸 𝜷 + − 𝒗𝒂𝒍𝒖𝒆 formula, the standard deviation (σ) was used to calculate the dependency of LDM.