Half-lives for One-proton Radioactivity within the Deformed Gamow-like Model

In this work, the Gamow-like model for calculating the one-proton radioactivity half-life is improved by introducing the deformation of the nucleus. The calculations show that the deformed Gamow-like model can reproduce the experimental data better than the Gamow-like model. In addition, the reliability of the deformed Gamow-like model is confirmed by studying the linear relationship between the logarithmic form of the experimental half-life and the logarithmic form of the theoretical penetration probability. As an application, the one-proton radioactivity half-life of the deformed nucleus is predicted using the deformed Gamow-like model, and the predictions are able to comply well with the Geiger-Nuttall law. Finally, by studying the relationship between the orbital angular momentum and the calculated half-life, the reference values of the orbital angular momentum of ¹⁰⁹I and ¹³¹Eu are given to obtain a more accurate theoretical half-life for one-proton radioactivity.