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系统研究了2013年发表的核电荷半径数据库中的实验值, 基于这个数据库中大量的同位素链核电核半径实验值, 对相邻3个同位素核电荷半径之间的关系进行分析, 进而得到一个新的核电荷半径关系: 一个原子核的电荷半径等于其左右相邻的两个同位素核电荷半径之和的一半. 运用该关系对质量数
$ A\geqslant20 $ (质子数$ Z\geqslant10 $ 和中子数$ N\geqslant10 $ )的核电荷半径进行拟合, 结果发现核电荷半径的理论值与实验值符合得较好, 均方根偏差(RMSD)仅为0.00471 fm; 对质量数$ A\geqslant54 $ 的核电荷半径进行拟合时, 得到理论值和实验值的RMSD仅为0.00337 fm. 同时还添加了奇偶摆动修正来提高核电荷半径的精确度. 此外, 利用这个新的核电荷关系, 结合1999年和2004年发表的数据库对一些核电荷半径进行预言, 得到核电荷半径的预言值与2013年发表的数据库中的实验值符合得较好; 基于CR2013数据库得到的预言值与近几年新测得的核电荷半径的实验值也较接近. 研究结果表明新的核电荷半径关系对电荷半径的描述和预言具有一定的精确性和可靠性.In this paper, experimental values of nuclear charge radii in database published in 2013 (CR2013 database) are systematically investigated. We analyze the relationship among the three neighboring nuclei based on the nuclear charge radius of isotope chain in the database. Then we obtain a new nuclear charge radius relation for atomic nuclei: the charge radius of a given nucleus is equal to the average of the charge radii of its two neighboring nuclei. We calculate the nuclear charge radius by combining the new relation with CR2013 database, the root-mean-squared deviation (RMSD) between our calculated values and the experimental values in CR2013 database is small: for nuclei with A$\geqslant$ 20 (proton number Z$\geqslant$ 10 and neutron number N$\geqslant$ 10), the RMSD$\approx$ 0.00471 fm; for nuclei with A$\geqslant$ 54, the RMSD reaches an accuracy of RMSD$\approx$ 0.00337 fm. The systematicness of nuclear charge radius in heavy nucleus region is better than that in the light nucleus region, so that the values are more precise in the heavy nucleus region. In the meantime, we also use the odd-even staggering to improve the accuracy of nuclear charge radius: the accuracy increases by about 6.8%. In addition, according to the CR1999 and CR2004 database and the new relation, we make some predictions about some nuclear charge radii, and we find that our predicted values only slightly deviate from the experimental values in CR2013 database. The difference between our predicted value based on CR2013 database and experimental value measured in recent years is small. These results show that the proposed new relation used to study nuclear charge radius is feasible and accurate. The predicted values can provide a valuable reference for future experiments.-
Keywords:
- nuclear charge radius/
- isotope chain/
- odd-even staggering
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Nucleus $2013^{{\rm{Exp}}}$/fm $R_{\rm{{th1}} }$/fm dev1/fm Nucleus $2013^{{\rm{Exp}}}$/fm $R_{\rm{{th1}} }$/fm dev1/fm $^{23}$Ne 2.9104 2.9355 –0.0251 $^{126}$Sn 4.6833 4.6795 0.0038 $^{37}$Ar 3.3908 3.3967 –0.0059 $^{127}$Xe 4.7747 4.7761 –0.0014 $^{39}$Ar 3.4093 3.4151 –0.0058 $^{133}$Xe 4.7831 4.7895 –0.0064 $^{40}$K 3.4381 3.4434 –0.0053 $^{133}$Ba 4.8286 4.835 –0.0064 $^{41}$Ca 3.478 3.5068 –0.0288 $^{139}$Ba 4.8513 4.8442 0.0071 $^{45}$Ca 3.4944 3.5235 –0.0291 $^{141}$Nd 4.9057 4.8992 0.0065 $^{45}$Ti 3.5939 3.6178 –0.0239 $^{146}$Sm 4.9808 4.9742 0.0066 $^{47}$Ca 3.4783 3.4862 –0.0079 $^{151}$Sm 5.055 5.0622 –0.0072 $^{67}$Zn 3.953 3.9575 –0.0045 $^{153}$Sm 5.0925 5.0936 –0.0011 $^{79}$Kr 4.2034 4.2004 0.003 $^{160}$Dy 5.1951 5.185 0.0101 $^{81}$Kr 4.1952 4.1956 –0.0004 $^{169}$Yb 5.2771 5.28 –0.0029 $^{85}$Kr 4.1846 4.1878 –0.0032 $^{175}$Yb 5.3135 5.3166 –0.0031 $^{85}$Sr 4.2304 4.2358 –0.0054 $^{175}$Hf 5.3191 5.3263 –0.0072 $^{86}$Rb 4.2025 4.2013 0.0012 $^{187}$Os 5.3933 5.3961 –0.0028 $^{89}$Sr 4.2407 4.2231 0.0176 $^{193}$Pt 5.4191 5.4202 –0.0011 $^{89}$Zr 4.2706 4.2543 0.0163 $^{195}$Pb 5.4389 5.4442 –0.0053 $^{107}$Cd 4.5466 4.548 –0.0014 $^{197}$Hg 5.4412 5.4452 –0.004 $^{109}$Cd 4.5601 4.5678 –0.0077 $^{201}$Hg 5.4581 5.4614 –0.0033 $^{109}$Sn 4.5679 4.5734 –0.0055 $^{203}$Hg 5.4679 5.4696 –0.0017 $^{114}$In 4.6056 4.6083 –0.0027 $^{204}$Tl 5.4704 5.4712 –0.0008 $^{115}$Cd 4.6114 4.6153 –0.0039 $^{236}$U 5.8431 5.8383 0.0048 
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Nucleus $ 2013^{ {\rm{Exp} }} $/fm $R_{\rm th2}$/fm dev2/fm $^{39}$Ga 3.4595 3.4772 –0.0177 $^{41}$Ar 3.4251 3.4455 –0.0204 $^{45}$Ti 3.5939 3.6178 –0.0239 $^{67}$Zn 3.953 3.9575 –0.0045 $^{77}$Sr 4.2569 4.2536 0.0033 $^{117}$Cd 4.6136 4.6258 –0.0122 $^{126}$Sn 4.6833 4.6795 0.0038 $^{127}$Xe 4.7747 4.7761 –0.0014 $^{133}$Xe 4.7831 4.7895 –0.0064 $^{137}$Eu 4.9762 4.9798 –0.0036 $^{155}$Yb 5.104 5.1047 –0.0007 $^{157}$Yb 5.1324 5.1358 –0.0034 $^{159}$Yb 5.1629 5.1656 –0.0027 $^{169}$Yb 5.2771 5.2787 –0.0016 $^{171}$Hf 5.3041 5.2986 0.0055 $^{175}$Yb 5.3135 5.3166 –0.0031 $^{189}$Pb 5.4177 5.4215 –0.0038 $^{195}$Pb 5.4389 5.4428 –0.0039 $^{204}$Tl 5.4704 5.4725 –0.0021 下载:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]
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