强磁场对中子星转动惯量与表面引力红移的影响

赵诗艺; 刘承志; 黄修林; 王夷博; 许妍

doi:10.7498/aps.70.20211051

摘要

开展强磁场环境下中子星物质性质的研究对约束中子星物态方程, 揭示星体内部磁场分布形式等有重要意义. 本文基于相对论平均场理论利用GL91参数组研究了处于β平衡条件下传统中子星物质在强磁场作用下的主要宏观性质. 结果表明, 强磁场的引入使传统中子星物态方程变硬, 星体质量上限由2.111 M_⊙增大到3.081 M_⊙, 相同质量星体对应的半径变大使星体变得不那么致密; 强磁场对传统中子星表面引力红移有抑制作用, 对转动惯量有促进作用. 此外, 给出了目前已观测到的四颗大质量脉冲星—PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135, 以及双星合并事件GW190814中质量在2.50 M_⊙—2.67 M_⊙的致密星体表面引力红移和转动惯量的理论值范围. 结果表明, 随着中子星内部磁场的增强, 这五颗星的表面引力红移值范围变窄, 而转动惯量的范围变宽.

关键词:

Abstract

Research on the properties of neutron stars with strong magnetic fields is of great significance in constraining the equation of state and revealing the real distribution of magnetic fields in neutron stars. The main macroscopic properties of the traditional neutron star matter under β equilibrium condition are studied within the relativistic mean field theory through using the GL91 parameter set by considering the strong magnetic field. It is found that the onset of the strong magnetic field leads to the stiffened equation of state of the traditional neutron star matter. The maximum mass of the traditional neutron star grows from 2.111 M_⊙ to 3.081 M_⊙, the radius of the fixed mass traditional neutron star grows larger with the increase of internal magnetic field, which makes traditional neutron star become less dense. The strong magnetic field can also reduce the surface gravitational redshift and strengthen the moment of inertia of the traditional neutron star matter. In addition, the theoretical ranges of the surface gravitational redshift and the moment of inertia for the four massive PSRs J1614-2230, J0348+0432, J0740+6620 and J2215-5135, and the 2.50 M_⊙ − 2.67 M_⊙ compact object in the binary merger event GW190814 are also given. The results show that the ranges of the surface redshift become narrower, while the scopes of the moment of inertia widen as the magnetizing field increases in the five stars.

Keywords:

作者及机构信息

1.
中国科学院国家天文台长春人造卫星观测站, 长春　130117

2.
中国科学院大学天文与空间科学学院, 北京　100049

通信作者: 刘承志, lcz@cho.ac.cn ; 王夷博, wangyb@cho.ac.cn ; 许妍, xuy@cho.ac.cn

基金项目: 国家自然科学基金(批准号: 11805022, 11803057)资助的课题.

Authors and contacts

1.
Changchun Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Changchun 130117, China

2.
School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Liu Cheng-Zhi, lcz@cho.ac.cn ; Wang Yi-Bo, wangyb@cho.ac.cn ; Xu Yan, xuy@cho.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11805022, 11803057).

文章全文 : translate this paragraph

参考文献

[1]	Riley T E, Watts A L, Bogdanov S, et al. 2019 Astrophys. J. Lett. 887 21 Google Scholar
[2]	Shao D H, Tang S P, Jiang J L, et al. 2020 Phys. Rev. D 102 063006 Google Scholar
[3]	Zhao X F 2020 Chin. J. Phys. 63 240 Google Scholar
[4]	喻传赞 1980 科学通报 16 50 Google Scholar Yu C Z 1980 Chin. Sci. Bull. 16 50 Google Scholar
[5]	陈家麟, 季沛勇 2013 上海大学学报(自然科学版) 19 176 Google Scholar Chen J L, Ji P Y 2013 Journal of Shanghai University (Natural science Edition) 19 176 Google Scholar
[6]	彭芳, 彭秋和, 张丰收 2001 天文学报 42 1 Google Scholar Peng F, Peng Q H, Zhang F S 2001 Acta Astronomica Sinica 42 1 Google Scholar
[7]	赵先锋, 张华 2010 四川大学学报(自然科学版) 4 28 Google Scholar Zhao X F, Zhang H 2010 Journal of Sichuan University (Natural Science Edition) 4 28 Google Scholar
[8]	Zhao X F 2020 Chin. J. Physics 63 240
[9]	Lim Y, Holt J W, Stahulak R J 2019 Phys. Rev. C 3 035802 Google Scholar
[10]	Sen D 2021 J. Phys. G 48 025201 Google Scholar
[11]	Wang W, Tang Y M, Tuo Y L 2021 J. High. Energy Astrophys. 30 1 Google Scholar
[12]	Kouvelioton C 1998 Nature 393 253 Google Scholar
[13]	Kaspi V M 2003 Astrophys. J. 588 93 Google Scholar
[14]	Shapiro S L 1983 Black Holes, White Dwarfs and neutron Stars (New York: Wiley - Insterscience) pp277−282
[15]	Lai D, Shapiro S L 1991 Astrophys. J. 383 745 Google Scholar
[16]	孙晓辉, 韩金林 2002 天文学进展 20 130 Google Scholar Sun X H, Han J L 2002 Prog. Astron. 20 130 Google Scholar
[17]	Chakrabarty S, Debades B, Subrata P 1997 Phys. Rev. Lett. 78 2898 Google Scholar
[18]	Broderick A, Prakash M, Lattimer J M 2000 Astrophys. J. 537 351 Google Scholar
[19]	Broderick A E, Prakash M, Lattimer J M 2002 Phys. Lett. B 531 167 Google Scholar
[20]	Bednarek I, Brzezina A, Manka R 2003 Nucl. Phys. A 24 245 Google Scholar
[21]	Mao G J, Akira 2003 Chin. J. Astron. Astrophys. 3 359 Google Scholar
[22]	张洁, 刘门全, 魏丙涛, 罗志全 2008 物理学报 57 5448 Google Scholar Zhang J, Liu M Q, Wei B T, Luo Z Q 2008 Acta Phys. Sin. 57 5448 Google Scholar
[23]	Dong J M, Lombardo U, Zuo W 2013 Nucl. Phys. A 898 32 Google Scholar
[24]	Dong J M, Zuo W, Gu J Z 2016 Sci. China Phys. Mech. 59 642003 Google Scholar
[25]	鲍世绍, 胡金牛, 申虹 2018 科学通报 63 828 Google Scholar Bao S S, Hu J N, Shen H 2018 Chin. Sci. Bull. 63 828 Google Scholar
[26]	Boguta J, Bodmer A R 1977 Nucl. Phys. 292 413 Google Scholar
[27]	Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414 Google Scholar
[28]	Glendenning N K 1992 Phys. Rev. D 46 1274 Google Scholar
[29]	朗道著 (周奇译)1 963 连续媒介电动力学 (北京: 人民教育出版社) 第179—182页 Landau L D, Lifshitz E M, Pitaevskii L P (translated by Zhou Q) 1963 Electrodynamics of Continuous Media (Beijing: People’s Education Press) pp179−182 (in Chinese)
[30]	Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 55 374 Google Scholar
[31]	Tolman R C 1939 Phys. Rev. 55 364 Google Scholar
[32]	Worley A, Krastev P G, Li B A 2008 Astronphys. J. 685 390 Google Scholar
[33]	Lattimer J M, Schutz B F 2005 Astrophys. J. 629 979 Google Scholar
[34]	Glendenning N K 1997 Compact Stars: Nuclear Physics, Particle Physics, and General Relativity (New York: Springer-Verlag) pp75−78
[35]	Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys. Rev. Lett. 79 2176 Google Scholar
[36]	Wiringa R B, Fiks V, Fabroeini A 1988 Phys. Rev. 38 1010 Google Scholar
[37]	Manchester R N 2004 Science 304 542 Google Scholar
[38]	Gao Z F, Shan H, Wang H 2021 Astron. Nachr. 342 369 Google Scholar
[39]	Krotscheck E, Kundt W 1978 Commun. Math. Phys. 60 171 Google Scholar
[40]	Demorest P B, Pennucci T, Ransom S M 2010 Nature 467 1081 Google Scholar
[41]	Fonseca E, Pennucci T T, Ellis J A 2016 Astrophys. J. 832 167 Google Scholar
[42]	Antoniadis J, Freire, P C C, Wex N 2013 Science 340 448 Google Scholar
[43]	Cromartie H T, Fonseca E, Ransom S M 2020 Nat. Astron. 4 72 Google Scholar
[44]	Kandel D, Romani R W 2020 Astrophys. J. 892 101 Google Scholar
[45]	Godzieba D A, Radice D, Bernuzzi S 2021 Astrophys. J. 908 122 Google Scholar
[46]	Fattoyev F J, Horowitz C J, Piekarewicz J 2020 Phys. Rev. C 102 065805 Google Scholar
[47]	Liang E P 1986 Astrophys. J. 304 682 Google Scholar

施引文献

图 1 不同磁场强度下(α = 0, 20, 40, 60)中子星物质的(a)压强-核子密度、(b)质量-半径关系. 本文中, 黑红绿蓝四条线表示α = 0, 20, 40, 60四种情况; 不同颜色条纹区域分别表示PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135以及GW190814中致密星的质量测量值范围; 橙色误差棒表示NICER公布的PSR J0030+0415的质量-半径测量值对中子星质量-半径关系的约束. 各曲线上黑色圆点表示中子星最大质量所处位置, 三角形点表示最大半径所处位置

Fig. 1. Relationship of (a) the pressure - density and (b) the mass - radius in neutron star (NS) matter. In the paper the black, red, green, and blue lines represent the four cases of α = 0, 20, 40 and 60, respectively. The different colored areas stand for the recent constraints inferred from PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135 and GW190814 respectively. The orange error bar represents the constraints on the mass-radius limits of PSR J0030+0451 obtained from NICER observations. The dots and the triangle points show the maximum masses and radii of NSs for the four cases, respectively.

下载: 全尺寸图片幻灯片

图 2 不同磁场强度下(α = 0, 20, 40, 60), 中子星内声速-核子密度关系

Fig. 2. Relationships of the speed of sound and the nucleon density with α = 0, 20, 40, 60 in NS matter.

下载: 全尺寸图片幻灯片

图 3 不同磁场强度下(α = 0, 20, 40, 60), 中子星转动惯量-质量关系

Fig. 3. Relationships of the moment of inertia and the mass with α = 0, 20, 40, 60 in NS matter.

下载: 全尺寸图片幻灯片

图 4 不同磁场强度下(α = 0, 20, 40, 60), 中子星表面引力红移-质量的关系

Fig. 4. Relationships of the gravitational redshift and mass with α = 0, 20, 40, 60 in NS matter.

下载: 全尺寸图片幻灯片

表 1 不同磁场强度下(α = 0, 20, 40, 60), 中子星最大质量及其对应半径和中心密度, 最大半径及其对应质量和中心密度

Table 1. Table 1. Values of the maximum NS masses M_max and the corresponding radii R as well as the center densities ρ_c/ρ₀, values of the maximum NS radii R_max and the corresponding masses M as well as the center densities ρ_c/ρ₀ with α = 0, 20, 40, 60 in npeμ matter.

α	中子星最大质量处			中子星最大半径处
α	M /M_⊙	R /km	ρ_c/ρ₀	M /M_⊙	R/km	ρ_c/ρ₀
0	2.111	11.648	7.013	0.971	14.014	2.102
20	2.574	12.496	3.977	1.520	14.306	2.227
40	2.877	13.601	2.960	2.066	15.060	2.031
60	3.081	14.375	2.478	2.415	15.765	1.734

下载: 导出CSV

表 2 不同磁场强度下(α = 0, 20, 40, 60), PSRs J1614-2230, J0348+0432, J0740+6620, J2215-5135以及GW190814中致密星的半径、转动惯量、引力红移理论值范围

Table 2. Ranges of the theoretical values for the radius, the moment of inertia and the gravitational redshift corresponding to PSRS J1614-2230, J0348+0432, J0740+6620, J2215-5135 and the compact star in GW190814 with α = 0, 20, 40, 60.

Source	α	R/km	I/M_⊙·km²	Z
PSR J1614-2230	0	[13.067, 13.158]	[131.615, 133.926]	[0.317, 0.329]
	20	[14.179, 14.220]	[148.276, 152.485]	[0.283, 0.291]
	40	[15.037, 15.048]	[161.795, 166.371]	[0.261, 0.269]
	60	[15.450, 15.670]	[172.197, 175.693]	[0.244, 0.253]
PSR J0348-0432	0	[12.548, 12.954]	[135.781, 138.653]	[0.348, 0.388]
	20	[14.108, 14.179]	[155.490, 164.997]	[0.305, 0.323]
	40	[15.048, 15.068]	[171.237, 182.428]	[0.277, 0.291]
	60	[15.690, 15.722]	[182.428, 195.897]	[0.260, 0.276]
PSR J0740+6620	0	[11.648, 12.965]	[119.641, 138.653]	[0.344, 0.462]
	20	[13.782, 14.170]	[155.490, 194.213]	[0.300, 0.416]
	40	[14.976, 15.060]	[171.237, 220.062]	[0.273, 0.361]
	60	[15.670, 15.783]	[182.428, 238.087]	[0.259, 0.334]
PSR J2215-5135	0	—	—	—
	20	[13.679, 13.986]	[180.150, 198.670]	[0.362, 0.429]
	40	[14.987, 15.037]	[199.859, 226.797]	[0.325, 0.371]
	60	[15.742, 15.783]	[215.606, 244.822]	[0.300, 0.343]
GW190814	0	—	—	—
	20	[12.496, 13.291]	[203.820, 206.593]	[0.496, 0.591]
	40	[14.670, 14.905]	[242.544, 264.431]	[0.407, 0.470]
	60	[15.670, 15.752]	[262.153, 288.002]	[0.370, 0.418]

下载: 导出CSV

[1]	Riley T E, Watts A L, Bogdanov S, et al. 2019 Astrophys. J. Lett. 887 21 Google Scholar
[2]	Shao D H, Tang S P, Jiang J L, et al. 2020 Phys. Rev. D 102 063006 Google Scholar
[3]	Zhao X F 2020 Chin. J. Phys. 63 240 Google Scholar
[4]	喻传赞 1980 科学通报 16 50 Google Scholar Yu C Z 1980 Chin. Sci. Bull. 16 50 Google Scholar
[5]	陈家麟, 季沛勇 2013 上海大学学报(自然科学版) 19 176 Google Scholar Chen J L, Ji P Y 2013 Journal of Shanghai University (Natural science Edition) 19 176 Google Scholar
[6]	彭芳, 彭秋和, 张丰收 2001 天文学报 42 1 Google Scholar Peng F, Peng Q H, Zhang F S 2001 Acta Astronomica Sinica 42 1 Google Scholar
[7]	赵先锋, 张华 2010 四川大学学报(自然科学版) 4 28 Google Scholar Zhao X F, Zhang H 2010 Journal of Sichuan University (Natural Science Edition) 4 28 Google Scholar
[8]	Zhao X F 2020 Chin. J. Physics 63 240
[9]	Lim Y, Holt J W, Stahulak R J 2019 Phys. Rev. C 3 035802 Google Scholar
[10]	Sen D 2021 J. Phys. G 48 025201 Google Scholar
[11]	Wang W, Tang Y M, Tuo Y L 2021 J. High. Energy Astrophys. 30 1 Google Scholar
[12]	Kouvelioton C 1998 Nature 393 253 Google Scholar
[13]	Kaspi V M 2003 Astrophys. J. 588 93 Google Scholar
[14]	Shapiro S L 1983 Black Holes, White Dwarfs and neutron Stars (New York: Wiley - Insterscience) pp277−282
[15]	Lai D, Shapiro S L 1991 Astrophys. J. 383 745 Google Scholar
[16]	孙晓辉, 韩金林 2002 天文学进展 20 130 Google Scholar Sun X H, Han J L 2002 Prog. Astron. 20 130 Google Scholar
[17]	Chakrabarty S, Debades B, Subrata P 1997 Phys. Rev. Lett. 78 2898 Google Scholar
[18]	Broderick A, Prakash M, Lattimer J M 2000 Astrophys. J. 537 351 Google Scholar
[19]	Broderick A E, Prakash M, Lattimer J M 2002 Phys. Lett. B 531 167 Google Scholar
[20]	Bednarek I, Brzezina A, Manka R 2003 Nucl. Phys. A 24 245 Google Scholar
[21]	Mao G J, Akira 2003 Chin. J. Astron. Astrophys. 3 359 Google Scholar
[22]	张洁, 刘门全, 魏丙涛, 罗志全 2008 物理学报 57 5448 Google Scholar Zhang J, Liu M Q, Wei B T, Luo Z Q 2008 Acta Phys. Sin. 57 5448 Google Scholar
[23]	Dong J M, Lombardo U, Zuo W 2013 Nucl. Phys. A 898 32 Google Scholar
[24]	Dong J M, Zuo W, Gu J Z 2016 Sci. China Phys. Mech. 59 642003 Google Scholar
[25]	鲍世绍, 胡金牛, 申虹 2018 科学通报 63 828 Google Scholar Bao S S, Hu J N, Shen H 2018 Chin. Sci. Bull. 63 828 Google Scholar
[26]	Boguta J, Bodmer A R 1977 Nucl. Phys. 292 413 Google Scholar
[27]	Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414 Google Scholar
[28]	Glendenning N K 1992 Phys. Rev. D 46 1274 Google Scholar
[29]	朗道著 (周奇译)1 963 连续媒介电动力学 (北京: 人民教育出版社) 第179—182页 Landau L D, Lifshitz E M, Pitaevskii L P (translated by Zhou Q) 1963 Electrodynamics of Continuous Media (Beijing: People’s Education Press) pp179−182 (in Chinese)
[30]	Oppenheimer J R, Volkoff G M 1939 Phys. Rev. 55 374 Google Scholar
[31]	Tolman R C 1939 Phys. Rev. 55 364 Google Scholar
[32]	Worley A, Krastev P G, Li B A 2008 Astronphys. J. 685 390 Google Scholar
[33]	Lattimer J M, Schutz B F 2005 Astrophys. J. 629 979 Google Scholar
[34]	Glendenning N K 1997 Compact Stars: Nuclear Physics, Particle Physics, and General Relativity (New York: Springer-Verlag) pp75−78
[35]	Bandyopadhyay D, Chakrabarty S, Pal S 1997 Phys. Rev. Lett. 79 2176 Google Scholar
[36]	Wiringa R B, Fiks V, Fabroeini A 1988 Phys. Rev. 38 1010 Google Scholar
[37]	Manchester R N 2004 Science 304 542 Google Scholar
[38]	Gao Z F, Shan H, Wang H 2021 Astron. Nachr. 342 369 Google Scholar
[39]	Krotscheck E, Kundt W 1978 Commun. Math. Phys. 60 171 Google Scholar
[40]	Demorest P B, Pennucci T, Ransom S M 2010 Nature 467 1081 Google Scholar
[41]	Fonseca E, Pennucci T T, Ellis J A 2016 Astrophys. J. 832 167 Google Scholar
[42]	Antoniadis J, Freire, P C C, Wex N 2013 Science 340 448 Google Scholar
[43]	Cromartie H T, Fonseca E, Ransom S M 2020 Nat. Astron. 4 72 Google Scholar
[44]	Kandel D, Romani R W 2020 Astrophys. J. 892 101 Google Scholar
[45]	Godzieba D A, Radice D, Bernuzzi S 2021 Astrophys. J. 908 122 Google Scholar
[46]	Fattoyev F J, Horowitz C J, Piekarewicz J 2020 Phys. Rev. C 102 065805 Google Scholar
[47]	Liang E P 1986 Astrophys. J. 304 682 Google Scholar

[1]	刁彬, 许妍, 黄修林, 王夷博. 利用含δ介子的相对论平均场理论研究中子星潮汐形变性质. 物理学报, 2023, 72(2): 022601. doi: 10.7498/aps.72.20221599
[2]	高朋林, 郑皓, 孙光爱. 中子星对自旋相关轴矢量新相互作用的约束. 物理学报, 2019, 68(18): 181102. doi: 10.7498/aps.68.20190477
[3]	宋冬灵, 明亮, 单昊, 廖天河. 超强磁场下电子朗道能级稳定性及对电子费米能的影响. 物理学报, 2016, 65(2): 027102. doi: 10.7498/aps.65.027102
[4]	门福殿, 田青松, 陈新龙. 强磁场中弱相互作用费米气体的稳定性. 物理学报, 2014, 63(12): 120504. doi: 10.7498/aps.63.120504
[5]	苑轶, 李英龙, 王强, 刘铁, 高鹏飞, 赫冀成. 强磁场对Mn-Sb包晶合金相变及凝固组织的影响. 物理学报, 2013, 62(20): 208106. doi: 10.7498/aps.62.208106
[6]	孙旭东, 陈菊华, 王永久. 磁荷对中子星质量半径比的约束. 物理学报, 2013, 62(16): 160401. doi: 10.7498/aps.62.160401
[7]	门福殿, 王海堂, 何晓刚. 强磁场中Fermi气体的稳定性及顺磁性. 物理学报, 2012, 61(10): 100503. doi: 10.7498/aps.61.100503
[8]	门福殿, 王炳福, 何晓刚, 隗群梅. 强磁场中弱相互作用费米气体的热力学性质. 物理学报, 2011, 60(8): 080501. doi: 10.7498/aps.60.080501
[9]	曾思良, 倪飞飞, 何建锋, 邹士阳, 颜君. 强磁场中氢原子的能级结构. 物理学报, 2011, 60(4): 043201. doi: 10.7498/aps.60.043201
[10]	王兆军, 吕国梁, 朱春花, 张军. 中子星中简并电子气体的临界磁化. 物理学报, 2011, 60(4): 049702. doi: 10.7498/aps.60.049702
[11]	王春江, 苑轶, 王强, 刘铁, 娄长胜, 赫冀成. 强磁场条件下金属凝固过程中第二相的迁移行为. 物理学报, 2010, 59(5): 3116-3122. doi: 10.7498/aps.59.3116
[12]	刘晶晶. 超强磁场对中子星外壳层核素56Fe,56Co,56Ni,56Mn和56Cr电子俘获过程中微子能量损失的影响. 物理学报, 2010, 59(7): 5169-5174. doi: 10.7498/aps.59.5169
[13]	任树洋, 任忠鸣, 任维丽, 操光辉. 3 T强磁场对真空蒸发Zn薄膜晶体结构的影响. 物理学报, 2009, 58(8): 5567-5571. doi: 10.7498/aps.58.5567
[14]	赵安昆, 任忠鸣, 任树洋, 操光辉, 任维丽. 强磁场对真空蒸镀制取Te薄膜的影响. 物理学报, 2009, 58(10): 7101-7107. doi: 10.7498/aps.58.7101
[15]	高翱, 王强, 王春江, 刘铁, 张超, 赫冀成. 强磁场条件下Mn-Sb梯度复合材料的制备. 物理学报, 2008, 57(2): 767-771. doi: 10.7498/aps.57.767
[16]	施德恒, 孙金锋, 朱遵略, 马恒, 杨向东. 7Li2(X1Σ+g)分子的振动能级、转动惯量及离心畸变常数. 物理学报, 2008, 57(1): 165-171. doi: 10.7498/aps.57.165
[17]	张洁, 刘门全, 魏丙涛, 罗志全. 强磁场中修正URCA过程的中微子产能率. 物理学报, 2008, 57(9): 5448-5451. doi: 10.7498/aps.57.5448
[18]	施德恒, 孙金锋, 刘玉芳, 马恒, 朱遵略, 杨向东. 7Li2分子23Πu激发态的解析势能函数、振动能级及其转动惯量. 物理学报, 2007, 56(8): 4454-4460. doi: 10.7498/aps.56.4454
[19]	庞雪君, 王强, 王春江, 王亚勤, 李亚彬, 赫冀成. 强磁场对铝合金中溶质组元分布状态的影响效果. 物理学报, 2006, 55(10): 5129-5134. doi: 10.7498/aps.55.5129
[20]	王春江, 王强, 王亚勤, 黄剑, 赫冀成. 强磁场对Al-Si合金凝固组织中硅分布的影响. 物理学报, 2006, 55(2): 648-654. doi: 10.7498/aps.55.648

计量

文章访问数: 5474
PDF下载量: 70
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板