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结合原子核电荷半径实验数据, 对885个中子数N8和质子数Z8的核电荷半径做了系统的研究. 对于单参数核电荷半径公式, Z1/3律公式计算的结果优于A1/3律的结果, 而对于两参数和三参数公式, Z1/3律和A1/3律的结果基本相当. 考虑到壳效应及奇偶摆动现象, 在原有的三参数公式基础上提出了加入Casten因子项和项的核电荷半径新公式. 利用该公式计算得到的核电荷半径理论值和实验值符合得非常好, 均方根偏差仅为=0.0266 fm, 此值比常用的三参数公式的结果下降了近50%, 理论计算值能更好地反映出壳效应及核电荷半径奇偶摆动的变化趋势.Experimental nuclear charge radii for 885 nuclei with N8 and Z8 have been systematically investigated. Results show that the formula for single parameter Z1/3 law is superior to that for the A1/3 law in describing nuclear charge radii. For two-parameter and three-parameter formulae, the Z1/3 law is as good as the A1/3 law. Considering the importance of shell effect and deformations for nuclear charge radii, we add a term including the Casten factor P into the conventional three-parameter formula and thus obtain very good results. The corresponding root-mean-square deviation falls to =0.0273 fm, i.e. reduced by about 50% when compared with the result obtained with the old three-parameter formula. Shell effect can be well reproduced for some elements by adding the Casten factor term. It is shown that the Casten factor plays a key role for nuclear charge radii. The odd-even staggering is a common phenomenon in many nuclear fields. This phenomenon can be observed with nuclear charge radii for most elements. For this reason, we add a term into the formula (10) in this paper. The root-mean-square deviation falls to =0.0266 fm. A five-parameter formula can well reproduce the variation of the nuclear charge radii for most elements. Calculated results are well consistent with the experimental data available. The differences between the experimental nuclear charge radii and the results calculated using the conventional three-parameter formula and the present five-parameter formula for the 885 selected nuclei are presented. A comparison of the formulae mentioned in this paper is given. The present five-parameter formula including the Casten factor P and the odd-even staggering is the best formula to fit available RC data and gives the smallest root-mean-square deviation . Our calculated results may be useful for future experiments.
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Keywords:
- nuclear charge radius /
- the Casten factor /
- odd-even staggering
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[13] Angeli I, Marinova K P 2013 At. Data Nucl. Data Tables 99 69
[14] Angeli I 2004 At. Data Nucl. Data Tables 87 185
[15] Nerlo-Pomorska B, Pomorski K 1993 Z. Phys. A 344 359
[16] Nerlo-Pomorska B, Pomorski K 1994 Z. Phys. A 348 169
[17] Royer G, Rousseau R 2009 Eur. Phys. J. A 42 541
[18] Iimura H, Buchinger F 2009 Eur. Phys. J. A 42 559
[19] Wang N, Li T 2013 Phys. Rev. C 88 011301
[20] Zhang S Q, Meng J, Zhou S G, Zeng J Y 2002 Eur. Phys. J. A 13 285
[21] Buchinger F, Pearson J M, Goriely S 2001 Phys. Rev. C 64 067303
[22] Sakakihara S, Tanaka Y 2001 Nucl. Phys. A 691 649
[23] Ni D D, Ren Z Z, Dong T K, Qian Y B 2013 Phys. Rev. C 87 024310
[24] Qian Y B, Ren Z Z, Ni D D 2013 Phys. Rev. C 87 054323
[25] Qian Y B, Ren Z Z, Ni D D 2014 Phys. Rev. C 89 024318
[26] Zeng J Y 1957 Acta Phys. Sin. 13 357 (in Chinese) [曾谨言 1957 物理学报 13 357]
[27] Zeng J Y 1975 Acta Phys. Sin. 24 151 (in Chinese) [曾谨言 1975 物理学报 24 151]
[28] Chen X P, 19 N 2011 Acta Phys. Sin. 60 112101 (in Chinese) [陈兴鹏, 王楠 2011 物理学报 60 112101]
[29] Casten R F 1985 Phys. Rev. Lett. 54 1991
[30] Casten R F, Brenner D S, Haustein P E 1987 Phys. Rev. Lett. 58 658
[31] Casten R F, Zamfir N V 1993 Phys. Rev. Lett. 70 402
[32] Foy B D, Casten R F, Zamfir N V, Brenner D S 1994 Phys. Rev.C 49 1224
[33] Saha M, Sen S 1994 Phys. Rev. C 49 2460
[34] Zhao Y M, Casten R F, Arima A 2000 Phys. Rev. Lett. 85 720
[35] Zhao Y M, Arima A, Casten R F 2001 Phys. Rev. C 63 067302
[36] Bhattacharya M, Gangopadhyay G 2009 Phys. Lett. B 672 182
[37] Gangopadhyay G 2009 J. Phys. G:Nucl. Part. Phys. 36 095105
[38] Angeli I 1991 J. Phys. G:Nucl. Part. Phys. 11 439
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[1] De Vries H, De Jager C W, De Vries C 1987 At. Data Nucl. Data Tables 36 495
[2] Engfer R, Schneuwly H, Vuilleumier J L, Walter H K, Zehnder A 1974 At. Data Nucl. Data Tables 14 509
[3] Fricke G, Bernhardt C, Heilig K, Schaller L A, Schellenberg L, Shera E B, De Jager C W 1995 At. Data Nucl. Data Tables 60 177
[4] Heilig K, Steudel A 1974 At. Data Nucl. Data Tables 14 613
[5] Aufmuth P, Heilig K, Steudel A 1987 At. Data Nucl. Data Tables 37 455
[6] Boehm F, Lee P L 1974 At. Data Nucl. Data Tables 14 605
[7] Mané E, Voss A, Behr J A, Billowes J, Brunner T, Buchinger F, Crawford J E, Dilling J, Ettenauer S, Levy C D P, Shelbaya O, Pearson M R 2011 Phys. Rev. Lett. 107 212502
[8] Yordanov D T, Bissell M L, Blaum K, De Rydt M, Geppert Ch, Kowalska M, Krämer J, Kreim K, Krieger A, Lievens P, Neff T, Neugart R, Neyens G, Nörtershäuser W, Sánchez R, Vingerhoets P 2012 Phys. Rev. Lett. 108 042504
[9] Krieger A, Blaum K, Bissell M L, Frömmgen N, Geppert Ch, Hammen M, Kreim K, Kowalska M, Krämer J, Neff T, Neugart R, Neyens G, Nörtershäuser W, Novotny Ch, Sánchez R, Yordanov D T 2012 Phys. Rev. Lett. 108 142501
[10] Procter T J, Billowes J, Bissell M L, Blaum K, Charlwood F C, Cheal B, Flanagan K T, Forest D H, Fritzsche S, Geppert Ch, Heylen H, Kowalska M, Kreim K, Krieger A, Krämer J, Lynch K M, Mané E, Moore I D, Neugart R, Neyens G, Nörtershäuser W, Papuga J, Rajabali M M, Stroke H H, Vingerhoets P, Yordanov D T, Žáková M 2012 Phys. Rev. C 86 034329
[11] Schuessler H A, Alousi A, Evans R M, Brieger M, Buchinger F, Li Y F 1990 Phys. Rev. Lett. 65 1332
[12] Levins J M G, Benton D M, Billowes J, Campbell P, Cooper T G, Dendooven P, Evans D E, Forest D H, Grant I S, Griffith J A R, Huikari J, Jokinen A, Peräjärvi K, Tungate G, Yeandle G, Äystö J 1999 Phys. Rev. Lett. 82 2476
[13] Angeli I, Marinova K P 2013 At. Data Nucl. Data Tables 99 69
[14] Angeli I 2004 At. Data Nucl. Data Tables 87 185
[15] Nerlo-Pomorska B, Pomorski K 1993 Z. Phys. A 344 359
[16] Nerlo-Pomorska B, Pomorski K 1994 Z. Phys. A 348 169
[17] Royer G, Rousseau R 2009 Eur. Phys. J. A 42 541
[18] Iimura H, Buchinger F 2009 Eur. Phys. J. A 42 559
[19] Wang N, Li T 2013 Phys. Rev. C 88 011301
[20] Zhang S Q, Meng J, Zhou S G, Zeng J Y 2002 Eur. Phys. J. A 13 285
[21] Buchinger F, Pearson J M, Goriely S 2001 Phys. Rev. C 64 067303
[22] Sakakihara S, Tanaka Y 2001 Nucl. Phys. A 691 649
[23] Ni D D, Ren Z Z, Dong T K, Qian Y B 2013 Phys. Rev. C 87 024310
[24] Qian Y B, Ren Z Z, Ni D D 2013 Phys. Rev. C 87 054323
[25] Qian Y B, Ren Z Z, Ni D D 2014 Phys. Rev. C 89 024318
[26] Zeng J Y 1957 Acta Phys. Sin. 13 357 (in Chinese) [曾谨言 1957 物理学报 13 357]
[27] Zeng J Y 1975 Acta Phys. Sin. 24 151 (in Chinese) [曾谨言 1975 物理学报 24 151]
[28] Chen X P, 19 N 2011 Acta Phys. Sin. 60 112101 (in Chinese) [陈兴鹏, 王楠 2011 物理学报 60 112101]
[29] Casten R F 1985 Phys. Rev. Lett. 54 1991
[30] Casten R F, Brenner D S, Haustein P E 1987 Phys. Rev. Lett. 58 658
[31] Casten R F, Zamfir N V 1993 Phys. Rev. Lett. 70 402
[32] Foy B D, Casten R F, Zamfir N V, Brenner D S 1994 Phys. Rev.C 49 1224
[33] Saha M, Sen S 1994 Phys. Rev. C 49 2460
[34] Zhao Y M, Casten R F, Arima A 2000 Phys. Rev. Lett. 85 720
[35] Zhao Y M, Arima A, Casten R F 2001 Phys. Rev. C 63 067302
[36] Bhattacharya M, Gangopadhyay G 2009 Phys. Lett. B 672 182
[37] Gangopadhyay G 2009 J. Phys. G:Nucl. Part. Phys. 36 095105
[38] Angeli I 1991 J. Phys. G:Nucl. Part. Phys. 11 439
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