Released energy formula for proton radioactivity based on the liquid-drop model*

Xiao Pan(潘霄),You-Tian Zou(邹有 甜),Hong-Ming Liu(刘宏 铭),Biao He(何彪),Xiao-Hua Li(李小 华),Dong Xiang(向东)

Table 2. The experimental data and calculated Qp values of this work, the WS4 model and the HFB-29 model. Δ1, Δ2 and Δ3 are the deviation between experimental data and calculated value for equation (6), the WS4 model and the HFB-29 model.

Nuclei Qp(MeV) Δ(MeV) Expt. This work WS4 [46] HFB-29 [47] Δ1 Δ2 Δ3 103 Sb 1.469 0.984 1.389 1.729 0.485 0.080 −0.260 104 Sb 0.519 0.763 0.787 0.779 −0.244 −0.268 −0.260 107 I 1.510 1.113 1.965 1.940 0.397 −0.455 −0.430 108 I 0.610 0.900 1.298 1.070 −0.29 −0.688 −0.460 111 Cs 1.820 1.246 1.927 2.220 0.574 −0.107 −0.400 114 Cs 0.244 0.629 0.423 0.360 −0.385 −0.179 −0.116 115 Cs 0.106 0.423 0.181 0.060 −0.317 −0.075 0.046 116 La 1.091 1.184 1.412 1.601 −0.093 −0.321 −0.510 119 La 0.281 0.588 0.093 −0.139 −0.307 0.188 0.420 123 Pr 0.361 0.754 0.221 0.361 −0.393 0.140 0.000 127 Pm 0.922 0.921 0.828 0.342 0.001 0.094 0.580 128 Pm 0.472 0.741 0.304 0.082 −0.269 0.168 0.390 129 Pm 0.152 0.558 0.140 −0.448 −0.406 0.012 0.600 131 Eu 0.963 1.090 1.155 1.133 −0.127 −0.192 −0.170 133 Eu 0.563 0.737 0.441 0.583 −0.174 0.122 −0.020 137 Tb 0.843 0.917 0.774 0.703 −0.074 0.069 0.140 142Ho 0.854 0.935 0.692 0.464 −0.081 0.162 0.390 143 Ho 0.794 1.244 0.542 0.294 −0.45 0.252 0.500 144 Ho 0.283 0.610 0.048 0.134 −0.327 0.235 0.149 145 Ho 0.174 0.447 −0.218 −0.186 −0.273 0.392 0.360 148 Tm 0.569 0.803 0.268 0.774 −0.234 0.301 −0.205 149 Tm 0.323 0.645 0.163 0.824 −0.322 0.160 −0.501 152 Lu 0.845 0.997 0.679 1.005 −0.152 0.166 −0.160 153 Lu 0.625 0.842 0.460 0.485 −0.217 0.165 0.140 154 Lu 0.215 0.692 −0.007 2.005 −0.477 0.222 −1.790 155 Lu 0.112 0.539 −0.089 0.035 −0.427 0.201 0.077 158 Ta 0.456 0.892 0.254 0.286 −0.436 0.202 0.170 159 Ta 0.389 0.743 0.141 0.316 −0.354 0.248 0.073 165 Ir 1.557 1.430 1.636 1.087 0.127 −0.079 0.470 168 Ir 0.557 1.011 0.721 0.237 −0.454 −0.164 0.320 169 Ir 0.628 0.870 0.673 0.217 −0.242 −0.045 0.411 170 Ir 0.090 0.734 0.260 0.067 −0.644 −0.170 0.023 171 Ir 0.243 0.596 0.249 −0.353 −0.353 −0.006 0.596 169 Au 1.948 1.626 2.011 1.428 0.322 −0.063 0.520 173 Au 1.003 1.078 1.028 0.608 −0.075 −0.025 0.395 175 Au 0.646 0.809 0.673 0.508 −0.163 −0.027 0.138 177 Au 0.117 0.544 0.152 −0.412 −0.427 −0.035 0.529 178 Tl 0.718 1.154 0.963 1.388 −0.436 −0.245 −0.670 179 Tl 0.774 1.021 1.080 0.708 −0.247 −0.306 0.066 180 Tl 0.266 0.892 0.677 0.308 −0.626 −0.411 −0.042 181 Tl 0.179 0.762 0.677 0.258 −0.583 −0.498 −0.079 182 Tl 0.061 0.634 0.182 −0.062 −0.573 −0.121 0.123 184 Bi 1.364 1.106 1.519 0.669 0.258 −0.155 0.695 186 Bi 1.124 0.853 0.938 0.259 0.271 0.186 0.865 187 Bi 1.028 0.726 0.845 0.159 0.302 0.183 0.869 188 Bi 0.521 0.603 0.300 −0.311 −0.082 0.221 0.832 189 Bi 0.479 0.478 0.266 −0.571 0.001 0.213 1.050 162 Re 0.786 1.092 0.616 0.896 −0.306 0.170 −0.110 163 Re 0.723 0.946 0.556 0.536 −0.223 0.167 0.187 164 Re 0.166 0.805 0.083 0.286 −0.639 0.083 −0.120 165 Re 0.302 0.662 −0.005 0.146 −0.36 0.307 0.156