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本文通过考虑原子核的形变效应和引入α粒子预形成因子的解析表达式对统一裂变模型(unified fission model, UFM)进行改进. 通过考虑原子核形变效应得到了改进的UFM (improved UFM-1, IMUFM1), 在IMUFM1基础上引入α粒子预形成因子的解析表达式得到了进一步改进的UFM (improved UFM-2, IMUFM2). 利用UFM, IMUFM1和IMUFM2三个版本分别对$ Z \geqslant 92 $重核和超重核的α衰变半衰期进行了系统地计算. 通过计算理论值和实验值之间的平均偏差和标准偏差, 发现IMUFM1的精度比UFM的精度仅提高了2.45%, 而IMUFM2的精度却提高了32.09%. 接着, 通过有限力程小液滴模型(finite-range Droplet model-2012, FRDM2012), Weizsäcker-Skyrme-4 (WS4)和Koura-Tachibana-Uno-Yamada (KTUY) 3种质量模型分别提取了Z = 118—120同位素链的α衰变能, 并利用IMUFM1和IMUFM2计算了相应的α衰变半衰期. 通过观察半衰期随同位素链的演化, 发现不同质量模型预言的演化趋势是一致的, 而且在N = 178和N = 184处会出现转折点, 但不同的质量模型预言的α衰变半衰期会出现数量级的差异. 另外, 通过讨论α衰变和自发裂变之间的竞争, 发现N<186质量核区的超重核以α衰变为主. 最后, 结合上述3种核质量模型, 利用IMUFM1和IMUFM2讨论了296Og, 297119和298120 α衰变链的衰变模式, 发现WS4和KTUY两种质量模型的预言结果与实验结果一致. 尽管FRDM2012质量模型预言的288Fl, 285Nh 和 286Fl的衰变模式与实验结果有所差别, 但对于288Fl, IMUFM2的预言结果比IMUFM1更符合实验测量结果, 再次验证了IMUFM2的合理性和可靠性. 上述研究结果可为将来实验鉴别新核素提供理论依据.An unified fission model (UFM) has been improved by considering the nuclear deformation effect and introducing an analytical expression of preformation factor. The improved version of the UFM by taking into consideration the nuclear deformation effect is named IMUFM1. Based on the IMUFM1, the further improved version is termed IMUFM2, which incorporates an analytical expression of the preformation factor. Within the UFM, the IMUFM1 and the IMUFM2, the α decay half-lives of heavy and superheavy nuclei with $ Z \geqslant 92 $are systematically calculated. The calculated standard deviation between the calculation results and the experimental data shows that the accuracy of the IMUFM1 is improved by 2.45% compared with that of the UFM. The accuracy of the IMUFM2 will be further improved by 32.09% compared with that of the IMUFM1, which implies that the nuclear deformation effect and the preformation factor are both important in prediction. Then, the α decay half-lives of Z = 118–120 isotopes are predicted from the IMUFM1 and the IMUFM2 by inputting the α decay energy values that are extracted from the sinite-range droplet model (FRDM), the Weizsäcker-Skyrme-4 (WS4) model and the Koura-Tachibaba-Uno-Yamads (KTUY) formula, respectively. The observed evolution of the α decay half-lives indicates that the evolution trends obtained from the above-mentioned three mass models are consistent with each other and the shell effects occur at N = 178 and 184, but their orders of magnitude, obtained from different mass models, are different from each other. Meanwhile, the comparison of half-lives between α decay and spontaneous fission shows that the dominant decay modes of the superheavy nuclei with N < 186 are α decay. Finally, the decay modes of 296Og, 297119 and 298120 α decay chains are predicted within the IMUFM1 and the IMUFM2 by using these three mass models, showing that the predictions from the WS4 mass model and KTUY mass model are more consistent with the experimental measurements. Form the FRDM2012 mass model, the predictions of 288Fl, 285Nh and 286Fl within the IMUFM1 mass model are not consistent with the experimental measurements, however, the prediction of 288Fl from the IMUFM2 is good agreement with the experimental measurement, which once again verifies the rationality and reliability of the IMUFM2. This study may be helpful for identifying new nuclide in future experiments.
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Keywords:
- superheavy nuclei /
- unified fission model /
- α decay /
- spontaneous fission
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图 1 $ {\log _{10}}r $值随中子数N的演化
Fig. 1. The values of log10r as functions of the neutron number N.
图 2 294Og发生α衰变时的核-核相互作用势
Fig. 2. The nuclear-nuclear interaction potential in α decay of 294Og.
图 3 α衰变和自发裂变的对数半衰期随中子数N的演化
Fig. 3. The logarithm half-lives of α decay and spontaneous fission as functions of the neutron number N.
偶-偶 其他 系数 126 < N < 152 N > 152 126 < N < 152 N > 152 a –0.3583 0 5.2940 0 b 0.0298 –0.0099 0.0388 –0.0606 c 0.0022 0.0382 8.7843×10–4 0.0214 d 0.0017 0.0102 –0.0241 0.0042 
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表 2 $ Z \geqslant 92 $重核和超重核α衰变半衰期的理论值与实验值之间的平均偏差$ \overline \sigma $和标准偏差$ \sqrt {\overline {{\sigma ^2}} } $
Table 2. The average deviation $ \overline \sigma $and the standard deviation $ \sqrt {\overline {{\sigma ^2}} } $ between the calculated ones and the experimental data of the heavy and superheavy nuclei with $ Z \geqslant 92 $.
模型 $ \overline \sigma $ $ \sqrt {\overline {{\sigma ^2}} } $ 总值(n = 178) 偶-偶(n = 56) 其他(n = 122) 总值(n = 178) 偶-偶(n = 56) 其他(n = 122) UFM 0.5760 0.6617 0.5367 0.7066 0.7292 0.6960 IMUFM1 0.5619 0.6822 0.5067 0.6855 0.7434 0.6572 IMUFM2 0.3816 0.2232 0.4544 0.5320 0.3390 0.6002
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表 3 $ Z \geqslant 110 $超重核α衰变半衰期的实验值与理论值, 其中Qα值取自于文献[76], 实验半衰期和原子核的自旋宇称取自文献[77]
Table 3. The experimental and calculated α decay half-lives of superheavy nuclei with $ Z \geqslant 110 $. Here the Qα values taken from Ref. [76], and the experimental α decay half-lives and the nuclear spin parity taken from Ref. [77], respectively.
母核 子核 Qα/MeV $ J_i^{\text{π}} $ $ J_j^{\text{π}} $ l $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Expt}}{.}}{\text{/s}} $ $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ UFM IMUFM1 IMUFM2 267Ds 263Hs 11.78 3/2+# 3/2+# 0 –5.00 –4.956 –4.764 –4.295 269Ds 265Hs 11.51 — 3/2+# 0 –3.638 –4.384 –4.194 –3.777 270Ds 266Hs 11.117 0+ 0+ 0 –3.688 –3.479 –3.340 –3.602 273Ds 269Hs 11.37 — 9/2+# 0 –3.620 –4.105 –3.934 –3.620 272Rg 268Mt 11.197 — — 0 –2.377 –3.377 –3.205 –2.783 278Rg 274Mt 10.85 — — 0 –2.097 –2.596 –2.403 –2.134 279Rg 275Mt 10.53 — — 0 –0.77 –1.794 –1.616 –1.373 280Rg 276Mt 10.149 — — 0 0.633 –0.786 –0.623 –0.405 277Cn 273Ds 11.62 — — 0 –3.102 –4.095 –3.910 –3.534 281Cn 277Ds 10.43 — — 0 –0.745 –1.212 –1.121 –0.847 282Nh 278Rg 10.78 — — 0 –0.854 –1.800 –1.753 –1.422 284Nh 280Rg 10.28 — — 0 –0.013 –0.492 –0.422 –0.142 285Nh 281Rg 10.01 — — 0 0.663 0.258 0.328 0.581 286Nh 282Rg 9.79 — — 0 1.079 0.891 0.911 1.139 285Fl 281Cn 10.56 — — 0 –0.678 –0.932 –0.883 –0.547 286Fl 282Cn 10.36 0+ 0+ 0 –0.657 –0.390 –0.351 –0.836 287Fl 283Cn 10.17 0+ — 0 –0.292 0.130 0.168 0.453 288Fl 284Cn 10.076 0+ 0+ 0 –0.185 0.386 0.272 –0.309 289Fl 285Cn 9.95 — — 0 0.322 0.731 0.627 0.860 287Mc 283Nh 10.76 — — 0 –1.222 –1.140 –1.107 –0.741 288Mc 284Nh 10.65 — — 0 –0.752 –0.861 –0.828 –0.487 289Mc 285Nh 10.49 — — 0 –0.387 –0.442 –0.408 –0.093 290Mc 286Nh 10.41 — — 0 –0.076 –0.232 –0.200 0.090 290Lv 286Fl 11 0+ 0+ 0 –2.046 –1.458 –1.444 –1.846 291Lv 287Fl 10.89 — — 0 –1.585 –1.186 –1.172 –0.826 292Lv 288Fl 10.791 0+ 0+ 0 –1.796 –0.940 –1.052 –1.551 293Lv 289Fl 10.68 — — 0 –1.155 –0.667 –0.737 –0.442 293Ts 289Mc 11.32 — — 0 –1.602 –1.973 –2.238 –1.861 294Ts 290Mc 11.18 — — 0 –1.155 –1.636 –1.881 –1.530 294Og 290Lv 11.87 0+ 0+ 0 –3.155 –2.985 –3.110 –3.430
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表 4 利用IMUFM2预言的Z = 118—120同位素链α衰变半衰期, Qα值分别取自FRDM2012[79], WS4[80]和KTUY[81]质量模型
Table 4. The predicted α decay half-lives of superheavy nuclei with Z = 118–120 isotopes within the IMUFM2 by inputting the Qα values that extracted from FRDM2012[79], WS4[80], and KTUY[81] mass tables, respectively.
母核 FRDM2012 WS4 KTUY Qα/MeV $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ Qα/MeV $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ Qα/MeV $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ 282Og 13.115 –5.234 13.494 –5.960 12.935 –4.877 284Og 13.565 –6.311 13.227 –5.673 12.745 –4.711 286Og 13.045 –5.346 12.915 –5.087 12.335 –3.873 288Og 12.855 –5.081 12.616 –4.591 11.905 –3.035 290Og 12.665 –4.786 12.601 –4.653 11.645 –2.523 292Og 12.385 –4.301 12.240 –3.987 11.465 –2.194 294Og 12.365 –4.382 12.198 –4.017 11.165 –1.571 296Og 12.275 –4.335 11.752 –3.151 10.945 –1.148 298Og 12.485 –4.901 12.182 –4.243 11.115 –1.705 300Og 12.505 –5.062 11.956 –3.852 11.035 –1.617 302Og 12.615 –5.407 12.041 –4.168 10.945 –1.504 304Og 13.395 –7.080 13.122 –6.557 12.435 –5.146 285119 14.055 –6.359 13.612 –5.553 13.085 –4.451 287119 13.365 –5.366 13.278 –5.195 12.705 –4.041 289119 13.465 –5.311 13.157 –4.716 12.455 –3.268 291119 13.235 –4.941 13.048 –4.573 12.165 –2.705 293119 12.915 –4.362 12.715 –3.949 11.985 –2.355 295119 12.935 –4.477 12.758 –4.113 11.705 –1.774 297119 12.895 –4.501 12.424 –3.512 11.285 –0.853 299119 13.075 –4.929 12.764 –4.298 11.475 –1.389 301119 13.075 –5.012 12.426 –3.664 11.345 –1.150 303119 13.105 –5.141 12.416 –3.707 11.215 –0.887 305119 13.855 –6.639 13.424 –5.828 12.815 –4.628 288120 13.845 –6.523 13.725 –6.303 13.105 –5.110 290120 13.745 –6.571 13.700 –6.488 12.835 –4.796 292120 13.775 –6.215 13.467 –5.634 12.715 –4.125 294120 13.485 –5.788 13.242 –5.315 12.495 –3.774 296120 13.585 –6.103 13.343 –5.640 12.225 –3.306 298120 13.235 –5.804 13.007 –5.345 11.625 –2.280 300120 13.695 –6.572 13.319 –5.854 11.885 –2.784 302120 13.545 –6.421 12.890 –5.125 11.795 –2.704 304120 13.545 –6.529 12.763 –4.970 11.515 –2.135 306120 14.275 –7.977 13.787 –7.108 13.225 –6.028
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表 5 296Og, 297119和298120 α衰变链的衰变模式, 其中Qα值分别取自FRDM2012[79], WS4[80]和 KTUY[81]质量表
Table 5. Decay modes of 296Og, 297119 and 298120 α decay chains, here the Qα values taken from FRDM2012[79], WS4[80] , and KTUY[81] mass tables, respectively.
母核 $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ FRDM2012 $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ WS4 $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ KTUY $ {\log _{10}}T_{{\text{1/2}}}^{{\text{Cal}}{.}}{\text{/s}} $ 衰变模式 SF Qα/MeV IMUFM1 IMUFM2 Qα/MeV IMUFM1 IMUFM2 Qα/MeV IMUFM1 IMUFM2 FRDM2012 WS4 KTUY Expt. 296Og 5.39 12.275 –3.919 –4.335 11.752 –2.735 –3.151 10.945 –0.732 –1.148 α(α) α(α) α(α) — 292Lv 5.34 10.815 –1.115 –1.614 11.127 –1.911 –2.410 10.335 0.195 –0.304 α(α) α(α) α(α) α 288Fl 3.02 9.165 3.100 2.519 9.645 1.561 0.980 9.465 2.123 1.542 SF(α) α(α) α(α) α 284Cn –2.15 8.955 3.281 2.617 9.544 1.375 0.712 9.225 2.385 1.721 SF(SF) SF(SF) SF(SF) SF 297119 8.53 12.895 –4.940 –4.501 12.424 –3.951 –3.512 11.285 –1.291 –0.853 α(α) α(α) α(α) — 293Ts 8.28 11.395 –2.396 –2.019 11.622 –2.963 –2.586 10.725 –0.708 –0.331 α(α) α(α) α(α) α 289Mc 7.12 10.085 0.731 1.046 10.296 0.129 0.444 10.005 0.966 1.281 α(α) α(α) α(α) α 285Nh 3.04 9.125 3.075 3.328 9.810 0.917 1.171 9.555 1.693 1.946 SF(SF) α(α) α(α) α 281Rg –1.89 9.215 2.128 2.320 9.758 0.455 0.647 9.785 0.374 0.566 SF(SF) SF(SF) SF(SF) SF 298120 4.68 13.235 –5.567 –5.804 13.007 –5.108 –5.345 11.625 –2.043 –2.280 α(α) α(α) α(α) — 294Og 4.67 12.365 –4.062 –4.382 12.198 –3.698 –4.017 11.165 –1.252 –1.571 α(α) α(α) α(α) α 290Lv 3.71 11.065 –1.610 –2.011 11.084 –1.657 –2.059 10.575 –0.323 –0.725 α(α) α(α) α(α) α 286Fl 1.54 9.465 2.30 1.815 9.970 0.756 0.272 9.725 1.489 1.004 SF(SF) α(α) α(α) α 282Cn –3.78 9.425 1.788 1.221 10.140 –0.331 –0.898 10.135 –0.317 –0.884 SF(SF) SF(SF) SF(SF) SF
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