Released energy formula for proton radioactivity based on the liquid-drop model* *Supported by National Natural Science Foundation of China (Grant No. 11205083 and No. 11975132 ), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 18A237), the Innovation Group of Nuclear and Particle Physics in USC, the

Abstract

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity (Q p ). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 MeV. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51 ≤ Z ≤ 83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q p is inferior to WS4 while better than HFB-29.