Description of temperature effects on proton radioactivity

Abstract

Role of thermal effects of hot parent nuclei in the characteristics of proton emission process has been studied for the first time by analyzing the surface energy coefficient γ entering in the calculation of proximity potential for 15 experimentally detected proton emitters (67≤Z≤83) in the isomeric states. In the present work, the proton-nucleus interaction potentials are obtained by using one of the latest versions of proximity potential formalism proposed by Zhang et al. in 2013. In addition, the quantum mechanical tunneling probability and consequently the proton radioactivity half-lives are calculated within the framework of the semiclassical WKB method. We present a new temperature-dependent (TD) form of the coefficient γ based on thermal properties of hot proton emitters in the framework of the finite-temperature generalized liquid-drop model. By integrating temperature dependence into the surface energy coefficient of proximity potential Zhang 2013, a reasonable description of the experimental half-lives of proton radioactivity is achieved. We extend the modified form of the Zhang 2013 model to predict the proton radioactivity half-lives of 6 proton emitters in the isomeric states, whose proton radioactivity is energetically allowed or observed, but has not been quantified yet. The obtained results reveal that the predictions by our model are in good agreement with the other theoretical methods, namely UDLP proposed by Qi et al. (2012) [19] and NGNL proposed by Chen et al. (2019) [49]. In this work, we also attempt to introduce an empirical formula for estimating the half-lives of one-proton emission process from the excited states by taking into account both the thermal effects of all the available 15 hot proton emitters and the contribution of centrifugal potential. Our results indicate that the calculated proton radioactivity half-lives by the current formula are in good agreement with experimental data. This means that the correlation between the half-lives of proton decay processes and the nuclear temperature T of proton emitters can be suitable to deal with the proton radioactivity one-proton transition from isomeric states.