New relation for nuclear charge radius based on isotope chain

Jiao Bao-Bao

doi:10.7498/aps.71.20212343

Abstract

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:

Authors and contacts

Jiao Bao-Bao

School of Nuclear Science and Engineering, East China University of Technology, Nanchang 330013, China

Corresponding author: Jiao Bao-Bao, baobaojiao91@126.com

Funds: Project supported by the Doctoral Scientific Research Foundation of East China University of Technology, China (Grant No. DHBK2019151)

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References

[1]	Horowitz C J, Piekarewicz J 2001 Phys. Rev. Lett. 86 5647 Google Scholar
[2]	Zhang S S, Smith M S, Kang Z S, Zhao J 2014 Phys. Lett. B 730 30 Google Scholar
[3]	Abrahamyan S, Ahmed Z, Albataineh H, et al. 2012 Phys. Rev. Lett. 108 112502 Google Scholar
[4]	Engfer R, Schneuwly H, Vuilleumier J L, Walter H K, Zehnder A 1974 At. Data Nucl. Data Tables 14 509 Google Scholar
[5]	Fricke G, Bernhardt C, Heilig K, et al. 1995 At. Data Nucl. Data Tables 60 177 Google Scholar
[6]	De Vries H, De Jager C W, De Vries C 1987 At. Data Nucl. Data Tables 36 495 Google Scholar
[7]	Aufmuth P, Heilig K, Steudel A 1987 At. Data Nucl. Data Tables 37 455 Google Scholar
[8]	Heilig K, Steudel A 1974 At. Data Nucl. Data Tables 14 613 Google Scholar
[9]	Stoitsov M V, Dobaczewski J, Nazarewicz W, Pittel S, Dean D J 2003 Phys. Rev. C 68 054312 Google Scholar
[10]	Goriely S, Chamel N, Pearson J M 2010 Phys. Rev. C 82 035804 Google Scholar
[11]	Dieperink A E L, Van Isacker P 2009 Eur. Phys. J. A 42 269 Google Scholar
[12]	Wang N, Li T 2013 Phys. Rev. C 88 011301 Google Scholar
[13]	Garvey G T, Gerace W J, Jaffe R L, Talmi I, Kelson I 1969 Rev. Mod. Phys. 41 S1 Google Scholar
[14]	Sun B H, Lu Y, Peng J P, Liu C Y, Zhao Y M 2014 Phys. Rev. C 90 054318 Google Scholar
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[19]	Ma Y F, Su C, Liu J, Ren Z Z, Xu C, Gao Y H 2020 Phys. Rev. C 101 014304 Google Scholar
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[24]	Wu D, Bai C L, Sagawa H, Zhang H Q 2020 Phys. Rev. C 102 054323 Google Scholar
[25]	Bao M, Zong Y Y, Zhao Y M, Arima A 2020 Phys. Rev. C 102 014306 Google Scholar
[26]	Thakur V, Dhiman S K 2019 Nucl. Phys. A 992 121623 Google Scholar
[27]	De Groote R P, Billowes J, Binnersley C L, et al. 2020 Nat. Phys. 16 620 Google Scholar
[28]	Koszorús Á, Yang X F, Jiang W G, et al. 2021 Nat. Phys. 17 439 Google Scholar
[29]	Reinhard P G, Nazarewicz W, Garcia Ruiz R F 2020 Phys. Rev. C 101 021301(R Google Scholar
[30]	Fadeev P, Berengut J C, Flambaum V V 2020 Phys. Rev. A 102 052833 Google Scholar
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[33]	Ma C, Zong Y Y, Zhao Y M, Arima A 2021 Phys. Rev. C 104 014303 Google Scholar
[34]	Borrajo M, Egido J E 2017 Phys. Lett. B 764 328 Google Scholar
[35]	Satuła W, Dobaczewski J, Nazarewicz W 1998 Phys. Rev. Lett. 81 3599 Google Scholar
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[37]	Möller P, Nix J R, Myers W D, Swiatecki W J 1995 At. Data Nucl. Data Tables 59 185 Google Scholar
[38]	Fu G J, Lei Y, Jiang H, Zhao Y M, Sun B, Arima A 2011 Phys. Rev. C 84 034311 Google Scholar
[39]	Jiao B B 2018 Mod. Phys. Lett. A 33 1850156
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[41]	Xie L, Yang X F, Wraith C, et al. 2019 Phys. Lett. B 797 134805 Google Scholar
[42]	Gorges C, Rodríguez L V, Balabanski D L, et al. 2019 Phys. Rev. Lett. 122 192502 Google Scholar
[43]	Koszorús Á, Yang X F, Billowes J, et al. 2019 Phys. Rev. C 100 034304 Google Scholar
[44]	Marsh B A, Day Goodacre T, Sels S, et al. 2018 Nat. Phys. 14 1163 Google Scholar

Cited By

图 1 600个原子核的${\rm{d}}R_{n}(Z, N)$

Figure 1. The ${\rm{d}}R_{n}(Z, N)$ of 600 nuclei.

DownLoad: Full-Size Img PowerPoint

图 2 (a) Rb (Z = 37), Sr (Z = 38), Y (Z = 39), Zr (Z = 40)和 Nb (Z = 41)同位素链核电荷半径的实验值; (b) Eu (Z = 63), Tb (Z = 65)和Ho (Z = 67)同位素链核电荷半径的实验值

Figure 2. (a) Nuclear charge radii of Rb (Z = 37), Sr (Z = 38), Y (Z = 39), Zr (Z = 40) and Nb (Z = 41) elements; (b) nuclear charge radii of Eu (Z = 63), Tb (Z = 65) and Ho (Z = 67) elements

DownLoad: Full-Size Img PowerPoint

图 3 (a) Au (Z = 79)同位素链核电荷半径的实验值; (b) Hg (Z = 80)同位素链核电荷半径的实验值

Figure 3. (a) Nuclear charge radii of Au (Z = 79) elements; (b) nuclear charge radii of Hg (Z = 80) elements

DownLoad: Full-Size Img PowerPoint

图 4 573个原子核的$ {\rm{d}}R_{n}(Z, N) $

Figure 4. The $ {\rm{d}}R_{n}(Z, N) $ of 573 nuclei

DownLoad: Full-Size Img PowerPoint

图 5 基于CR2013数据库得到的预言值与其他模型^[25,33]得到的预言值对比图

Figure 5. Difference for predicted values of nuclear charge radius between in our paper (obtained by the CR2013 database) and others’ papers^[25,33]

DownLoad: Full-Size Img PowerPoint

表 1 基于CR1999数据库得到的预言值与CR2013数据库中的实验值进行对比

Table 1. Difference between the predicted values of nuclear charge radius (obtained by the CR1999 database) and experimental values in the CR2013 database

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

DownLoad: CSV

表 2 基于CR2004数据库得到的预言值与CR2013数据库中的实验值进行对比

Table 2. Difference between the predicted values of nuclear charge radius (obtained by the CR2004 database) and experimental values in the CR2013 database

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

DownLoad: CSV

表 3 基于CR2013数据库得到的预言值与近几年测得的实验值^{[27,28,40,41]}进行对比

Table 3. Difference between the predicted values of nuclear charge radius (obtained by the CR2013 database) and experimental values in recent years

Nucleus	$R_{{\rm{th}}3}$/fm	$R_{{\rm{exp}}}$/fm	dev3/fm
$^{37}{\rm{K}}$	3.4179	3.419^[28]	–0.0011
$^{48}{\rm{K}}$	3.4510	3.4825^[28]	–0.0315
$^{64}{\rm{Cu}}$	3.8923	3.8873^[27,40]	0.005
$^{65}{\rm{Zn}}$	3.9420	3.9164^[41]	0.0256
$^{69}{\rm{Zn}}$	3.9769	3.9524^[41]	0.0245

DownLoad: CSV

map

[1]	Horowitz C J, Piekarewicz J 2001 Phys. Rev. Lett. 86 5647 Google Scholar
[2]	Zhang S S, Smith M S, Kang Z S, Zhao J 2014 Phys. Lett. B 730 30 Google Scholar
[3]	Abrahamyan S, Ahmed Z, Albataineh H, et al. 2012 Phys. Rev. Lett. 108 112502 Google Scholar
[4]	Engfer R, Schneuwly H, Vuilleumier J L, Walter H K, Zehnder A 1974 At. Data Nucl. Data Tables 14 509 Google Scholar
[5]	Fricke G, Bernhardt C, Heilig K, et al. 1995 At. Data Nucl. Data Tables 60 177 Google Scholar
[6]	De Vries H, De Jager C W, De Vries C 1987 At. Data Nucl. Data Tables 36 495 Google Scholar
[7]	Aufmuth P, Heilig K, Steudel A 1987 At. Data Nucl. Data Tables 37 455 Google Scholar
[8]	Heilig K, Steudel A 1974 At. Data Nucl. Data Tables 14 613 Google Scholar
[9]	Stoitsov M V, Dobaczewski J, Nazarewicz W, Pittel S, Dean D J 2003 Phys. Rev. C 68 054312 Google Scholar
[10]	Goriely S, Chamel N, Pearson J M 2010 Phys. Rev. C 82 035804 Google Scholar
[11]	Dieperink A E L, Van Isacker P 2009 Eur. Phys. J. A 42 269 Google Scholar
[12]	Wang N, Li T 2013 Phys. Rev. C 88 011301 Google Scholar
[13]	Garvey G T, Gerace W J, Jaffe R L, Talmi I, Kelson I 1969 Rev. Mod. Phys. 41 S1 Google Scholar
[14]	Sun B H, Lu Y, Peng J P, Liu C Y, Zhao Y M 2014 Phys. Rev. C 90 054318 Google Scholar
[15]	Bao M, Lu Y, Zhao Y M, Arima A 2016 Phys. Rev. C 94 064315 Google Scholar
[16]	Nerlo-Pomorska B, Pomorski K 1993 Z Phys. A 344 359 Google Scholar
[17]	Nerlo-Pomorska B, Pomorski K 1994 Z Phys. A 348 169 Google Scholar
[18]	圣宗强, 樊广伟, 钱建发 2015 64 112101 Google Scholar Sheng Z Q, Fan G W, Qian J F 2015 Acta Phys. Sin. 64 112101 Google Scholar
[19]	Ma Y F, Su C, Liu J, Ren Z Z, Xu C, Gao Y H 2020 Phys. Rev. C 101 014304 Google Scholar
[20]	Angeli I, Marinova K P 2013 At. Data Nucl. Data Tables 99 69 Google Scholar
[21]	Angeli I 2004 At. Data Nucl. Data Tables 87 185 Google Scholar
[22]	Angeli I 1999 Table of Nuclear Root Mean Square Charge Radii (Appendix IV) (Vienna: International Nuclear Data Committee) INDC(HUN)-033 IAEA Nuclear Data Section
[23]	Reinhard P G, Nazarewicz W 2021 Phys. Rev. C 103 054310 Google Scholar
[24]	Wu D, Bai C L, Sagawa H, Zhang H Q 2020 Phys. Rev. C 102 054323 Google Scholar
[25]	Bao M, Zong Y Y, Zhao Y M, Arima A 2020 Phys. Rev. C 102 014306 Google Scholar
[26]	Thakur V, Dhiman S K 2019 Nucl. Phys. A 992 121623 Google Scholar
[27]	De Groote R P, Billowes J, Binnersley C L, et al. 2020 Nat. Phys. 16 620 Google Scholar
[28]	Koszorús Á, Yang X F, Jiang W G, et al. 2021 Nat. Phys. 17 439 Google Scholar
[29]	Reinhard P G, Nazarewicz W, Garcia Ruiz R F 2020 Phys. Rev. C 101 021301(R Google Scholar
[30]	Fadeev P, Berengut J C, Flambaum V V 2020 Phys. Rev. A 102 052833 Google Scholar
[31]	曾谨言 1957 13 357 Google Scholar Zeng J Y 1957 Acta Phys. Sin. 13 357 Google Scholar
[32]	张双全, 孟杰, 周善贵, 曾谨言 2002 高能物理与核物理 26 252 Google Scholar Zhang S Q, Meng J, Zhou S G, Zeng J Y 2002 High Energy Physics and Nuclear Physics 26 252 Google Scholar
[33]	Ma C, Zong Y Y, Zhao Y M, Arima A 2021 Phys. Rev. C 104 014303 Google Scholar
[34]	Borrajo M, Egido J E 2017 Phys. Lett. B 764 328 Google Scholar
[35]	Satuła W, Dobaczewski J, Nazarewicz W 1998 Phys. Rev. Lett. 81 3599 Google Scholar
[36]	Qi C, Wyss R 2016 Phys. Scr. 91 013009 Google Scholar
[37]	Möller P, Nix J R, Myers W D, Swiatecki W J 1995 At. Data Nucl. Data Tables 59 185 Google Scholar
[38]	Fu G J, Lei Y, Jiang H, Zhao Y M, Sun B, Arima A 2011 Phys. Rev. C 84 034311 Google Scholar
[39]	Jiao B B 2018 Mod. Phys. Lett. A 33 1850156
[40]	Bissell M L, Carette T, Flanagan K T, et al. 2016 Phys. Rev. C 93 064318 Google Scholar
[41]	Xie L, Yang X F, Wraith C, et al. 2019 Phys. Lett. B 797 134805 Google Scholar
[42]	Gorges C, Rodríguez L V, Balabanski D L, et al. 2019 Phys. Rev. Lett. 122 192502 Google Scholar
[43]	Koszorús Á, Yang X F, Billowes J, et al. 2019 Phys. Rev. C 100 034304 Google Scholar
[44]	Marsh B A, Day Goodacre T, Sels S, et al. 2018 Nat. Phys. 14 1163 Google Scholar

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