Bethe-logarithm calculation using the B-spline method

被引：15
|
作者：
Tang, Yongbo [1 ,2 ]
Zhong, Zhenxiang [2 ]
Li, Chengbin [2 ]
Qiao, Haoxue [1 ]
Shi, Tingyun [2 ]
机构：
[1] Wuhan Univ, Dept Phys, Wuhan 430072, Peoples R China
[2] Chinese Acad Sci, State Key Lab Magnet Resonance & Atom & Mol Phys, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China
来源：
PHYSICAL REVIEW A | 2013年 / 87卷 / 02期
基金：
中国国家自然科学基金;
关键词：
HYDROGEN;
D O I：
10.1103/PhysRevA.87.022510
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
A method based on the B-spline basis set is developed that significantly simplifies the Bethe-logarithm calculations for the atomic hydrogen. Without any auxiliary optimization and extrapolation, this method not only can calculate the Bethe logarithms of low-lying states to high precision using relatively small basis sets, but can also calculate high-lying Rydberg states efficiently. For the ground state, the Bethe logarithm is calculated to 24 significant figures using 450 B-spline functions. For high-lying Rydberg states, we can reproduce all the results of Jentschura and Mohr [Phys. Rev. A 72, 012110 (2005)]. DOI: 10.1103/PhysRevA.87.022510
引用
收藏
页数：6
相关论文
共 50 条
  • [1] Two-loop Bethe-logarithm correction in hydrogenlike atoms
    Pachucki, K
    Jentschura, UD
    [J]. PHYSICAL REVIEW LETTERS, 2003, 91 (11)
  • [2] Digital Curve Length Calculation by Using B-spline
    Suhadolnik, Alojz
    Petrisic, Joze
    Kosel, Franc
    [J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2010, 38 (02) : 132 - 138
  • [3] Digital Curve Length Calculation by Using B-spline
    Alojz Suhadolnik
    Jože Petrišič
    Franc Kosel
    [J]. Journal of Mathematical Imaging and Vision, 2010, 38 : 132 - 138
  • [4] Calculation of coefficients of a cardinal B-spline
    Milovanovic, Gradimir V.
    Udovicic, Zlatko
    [J]. APPLIED MATHEMATICS LETTERS, 2010, 23 (11) : 1346 - 1350
  • [5] A Simplified Method of B-spline Curve Back Calculation in Reverse Engineering
    Li, Kangmei
    Luo, Lei
    Yo, Zhenqiang
    [J]. 2009 IEEE INTERNATIONAL CONFERENCE ON MECHATRONICS AND AUTOMATION, VOLS 1-7, CONFERENCE PROCEEDINGS, 2009, : 2229 - 2233
  • [6] Computational aeroacoustics using the B-spline collocation method
    Widjaja, R
    Ooi, A
    Chen, L
    Manasseh, R
    [J]. COMPTES RENDUS MECANIQUE, 2005, 333 (09): : 726 - 731
  • [7] Extending Ball B-spline by B-spline
    Liu, Xinyue
    Wang, Xingce
    Wu, Zhongke
    Zhang, Dan
    Liu, Xiangyuan
    [J]. COMPUTER AIDED GEOMETRIC DESIGN, 2020, 82
  • [8] Parameterization Method on B-Spline Curve
    Haron, H.
    Rehman, A.
    Adi, D. I. S.
    Lim, S. P.
    Saba, T.
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
  • [9] METHOD FOR FAIRING B-SPLINE SURFACES
    LOTT, NJ
    PULLIN, DI
    [J]. COMPUTER-AIDED DESIGN, 1988, 20 (10) : 597 - &
  • [10] Collocation method using quadratic B-spline for the RLW equation
    Soliman, AA
    Raslan, KR
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2001, 78 (03) : 399 - 412
12345