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Chinese Physics C> 2000, Vol. 24> Issue(5) : 400-407 

Lamb Shift Calculated by a Semiquantitative Method

  •  Department of Physics,Fudan University,Shanghai 200433,China

  • The radiative correction of self-energy of an electron moving with momentum p and emitting-absorbing the virtual photon is calculated by the noncovariant quantum perturbation theory to have the form being b2p4. After adding modifications arising from the vacuum polarization and finite nucleus size,we find the Lamb shift (LS) of 2S1/2-2P1/2 states in Hydrogen atom being 1056.522 MHz,smaller than the experimental value 1057.845 MHz by 0.13%. Taking the relativistic modification by Dirac equation into account,the energy differences of 4D5/24S1/2 states, the so-called Hyper LS and absolute LS of 1S state in Hydrogen are also calculated with maximum discrepancy up to 6.7%. The reasons are analyzed.For dealing with the divergence,we propose a simple but effective regularization renormalization method,showing that we have to reconfirm the reduced mass first before bringing a finite and fixed modification to it via radiative corrections.
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    [1] Weitz M,Schmidt-Kaler F,Hansch T W. Phys. Rev. Lett. ,1992,68(8):1120-1123[2] Weitz M,Huder A,Schmidt-Kaler F et al. Phys.Rev. Lett. ,1994,72(3):328-331[3] Weitz M et al. Phys. Rev.，1995,A52(4):2664-2681[4] De Beauvoir B et al. Phy. Rev. Lett. ,1997,78(3) :440443[5] Jentschura U D, Mohr P J , Soff G. Phys. Rev, Lett. ,1999 , 82(1) : 53-56[6] YANG JiFeng,Thesis for PhD,Fudan University 1994 (in Chinese);Preprint,hep-th/9708104;hep-th/9801005,hep-th/9807037 ; YANG JiFeng, Ni Gj. Acts Physics Situca (Overseas Edition) ,1995, 4(1) :88-98 (杨继锋，博士论文，复旦大学,1994)[7] NI G J,CHEN S Q. Acts Physics Sinica (Overseas Edition),1998,7(6):401-413; (hep-th/9708155)[8] NI G J , LOU S Y, LU W F et al. Science in China ( Series A) ,1998 , 41(11) :1206-1215 ( hep-ph/9801264 )[9] NI G].Kexue (Science)(in Chinese),1998,50(3):36-40(quant-ph9806009) (倪光炯.科学,1998,50(3):36-40)[10] NI G J, WANG HaiBin. Why We Enoourtter Infinity in Quantum Field Theory and How to Dcal with it? Physics Since Parity Symmetry Breaking in Memory of Professor C. S. Wu Edit: F. Wang. World Scienti6c,1998. 436442[11] ZENG J Y. Quantum Mechanics,Vol I,Beijing:Scienoe Press(in Chineae),1995,Chapt 6 (曾谨言.量子力学，卷I，北京:科学出版社，1995,第六章)[12] Bjorken 1 D, Drell S D. Relativistic Quantum Mechanics, McGraw-I-Till Book Canpany,1964. 55 ,158[13] 5akurai J J. Advanced Quantum Mechanics,Addiam-Wesley Publishing Cornpany,1967.127,280[14] QIAN B C, ZENG J Y. Selection and Analysis of Problems in Quantum Mechanics, Beijing;Science Press(in Chinese),1995,391 (钱伯初，曾谨言.量子力学习厄精选与剖析，北京:科学出版社，1995.391)[15] N1 G J,ZHOU W M,YAN J.Ptoca9ding of International Workshop0L.orentz Group. CPT,and Neutrinos", World Sci-entific. to be published

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NI GuangJiong, WANG HaiBin, YAN Jun and LI HaiLong. Lamb Shift Calculated by a Semiquantitative Method[J]. Chinese Physics C, 2000, 24(5): 400-407.
NI GuangJiong, WANG HaiBin, YAN Jun and LI HaiLong. Lamb Shift Calculated by a Semiquantitative Method[J]. Chinese Physics C, 2000, 24(5): 400-407. shu
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Received: 1999-06-09
Revised: 1900-01-01
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Lamb Shift Calculated by a Semiquantitative Method

    Corresponding author: NI GuangJiong,
  • Department of Physics,Fudan University,Shanghai 200433,China
  • Received Date: 1999-06-09
  • Accepted Date: 1900-01-01
  • Available Online: 2000-04-05

Abstract: The radiative correction of self-energy of an electron moving with momentum p and emitting-absorbing the virtual photon is calculated by the noncovariant quantum perturbation theory to have the form being b2p4. After adding modifications arising from the vacuum polarization and finite nucleus size,we find the Lamb shift (LS) of 2S1/2-2P1/2 states in Hydrogen atom being 1056.522 MHz,smaller than the experimental value 1057.845 MHz by 0.13%. Taking the relativistic modification by Dirac equation into account,the energy differences of 4D5/24S1/2 states, the so-called Hyper LS and absolute LS of 1S state in Hydrogen are also calculated with maximum discrepancy up to 6.7%. The reasons are analyzed.For dealing with the divergence,we propose a simple but effective regularization renormalization method,showing that we have to reconfirm the reduced mass first before bringing a finite and fixed modification to it via radiative corrections.

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