Investigations on the nuclear charge radii

Sheng Zong-Qiang; Fan Guang-Wei; Qian Jian-Fa

doi:10.7498/aps.64.112101

Abstract

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.

Keywords:

Authors and contacts

1.
School of Science, Anhui University of Science and Technology, Huainan 232007, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11247001, 11447236), the Scientific Research Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2012A083), and the Natural Science Foundation of Anhui Province, China (Grant No. 1408085MA05).

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Cited By

[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 13 357]
[27]	Zeng J Y 1975 Acta Phys. Sin. 24 151 (in Chinese) [曾谨言 1975 24 151]
[28]	Chen X P, 19 N 2011 Acta Phys. Sin. 60 112101 (in Chinese) [陈兴鹏, 王楠 2011 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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Vol. 64, Issue 11 - 2015-06-05

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