Theoretical Study of the Quadruple Gamma Transitions of Radioactive Radon and Radium Isotopes Based on Half-Life

Background: This study investigated multiple aspects of radon and radium’s nuclear properties since they are heavy, radioactive elements that may emit alpha, beta, and gamma radiation, which is connected to cancer and poses a risk to the environment. The purpose of this study is to investigate the significance of quadruple gamma transitions with |M(E2)|2w.u↓ as a valuable probe of the internal structure, deformations, and energy levels of atomic nuclei. Objective: By studying these gamma transitions, we hope to get more insight into the behavior of protons and neutrons within the nucleus as well as the fundamental forces governing their interactions. Methods: We applied MATLAB software to compute the probability of quadruple gamma transitions while accounting for the isotope energy characteristics and nuclei half-lives. Results: Our study’s important results about the transition forces for particular isotopes are as follows: Ra-226 was reported to have the lowest transition force value, measuring 9.6623×10−17, with a half-life of 1600 years. Furthermore, several transition force values were observed for Rn-214, the greatest values being 1.0248×104 and 1.5666×10−15. On the other hand, Rn-216 has the highest recorded transition force value (1.70305×10−4). Conclusions: The widths of Weisskopf transitions, gamma-gamma transitions, and gamma transitions were found by gathering and evaluating previously studied globally publicly available information. In the end, we successfully determined a relationship between the decay constant and the half-life of a decay event, which let us determine the probability that such events will occur within a certain time frame. Our study provides important insights into the transition probability within the examined nuclides and is in excellent agreement with global results and experimental data.