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Chinese Physics C> 1983, Vol. 7> Issue(2) : 203-216 

CALCULATION OF MUON FINAL PROBABILITIES AFTER THE PROMPT FISSION OF MUONIC ATOM

  • Based on the variational method and using two classes (exponential and square) nuclear charge distributions and two classes (Gaussian and exponential) trial wave functions the 1s and 2p energy levels of muonic atoms are calculated and compared with the accurate calculation[1]. Then we use the LCAO (Linear Combination of Atomic Orbitals) to calculate the foure energy levels of Muon in the two centre nuclear extended coulombian potential, and use the PSS (Purterbation of Stationary States) to solve the time-dependent Schrödinger equation and obtain the final Muon probabilities for these four states. We find that after the prompt fission of Muonic atom. Muon is mainly attached on the 1s state of the heavy fragment, only 3.8—5.1% of the probabilities are attached on 1s state of the light fragment, and 0.7—0.9% and ~0.1% on the 2p states of the heavy fragment and the light fragment respectively. These results are in agreement with those of references [2], [3], and also in accordance with the experimental results within the experimental errors.
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    [1] G. A. Rinker et al., At. Data and Nucl. Data Table, 20(1977), 143.[2] 马中玉等,原子核物理,4(1982), 97.[3] J. O. Raemussen et al, 原子核物理，2 (1980), 107; Z. Y. Ma et al., Nucl. Phys., A348 (1980), 446.[4] J. A. wheeler, Rev. Mod. Phys., 21 (1949), 133.[5] D. F. Zaretsky et al., Proc. Second United Nations Int. Conf. on Peaceful Usea of Atomic Energy (Geneva 1985) Vol. 15, p. 175.[6] D. F. Zaretsky et al., Nucl. Phys., 14 (1960), 540; 28(1961), 177.[7] Dz. Ganzoring et al., European Organization for Nuclear Research Preprint CERN-EP/80-86 (3 June 1980).[8] W. V. Schroder et al., Phys. Rev. Lett., 43 (1979),672.[9] S. Polikanov, IAEA SM-241/El, Symp. on Physics and Chemistry of Fission, Jülick, FRG, 1979, Vol. 2, p. 3.[10] D. Goulard and H. Primakoff, Phys. Rev., C10 (1974), 2034.[11] P. Olanders et al., Phys. Lett., 90B (1980), 193.[12] J. R. Nix, Private Comunication.

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CAI Chong-Hai and ZHUO Yi-Zhong. CALCULATION OF MUON FINAL PROBABILITIES AFTER THE PROMPT FISSION OF MUONIC ATOM[J]. Chinese Physics C, 1983, 7(2): 203-216.
CAI Chong-Hai and ZHUO Yi-Zhong. CALCULATION OF MUON FINAL PROBABILITIES AFTER THE PROMPT FISSION OF MUONIC ATOM[J]. Chinese Physics C, 1983, 7(2): 203-216. shu
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Received: 1900-01-01
Revised: 1900-01-01
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CALCULATION OF MUON FINAL PROBABILITIES AFTER THE PROMPT FISSION OF MUONIC ATOM

    Corresponding author: CAI Chong-Hai,
  • Received Date: 1900-01-01
  • Accepted Date: 1900-01-01
  • Available Online: 1983-04-05

Abstract: Based on the variational method and using two classes (exponential and square) nuclear charge distributions and two classes (Gaussian and exponential) trial wave functions the 1s and 2p energy levels of muonic atoms are calculated and compared with the accurate calculation[1]. Then we use the LCAO (Linear Combination of Atomic Orbitals) to calculate the foure energy levels of Muon in the two centre nuclear extended coulombian potential, and use the PSS (Purterbation of Stationary States) to solve the time-dependent Schrödinger equation and obtain the final Muon probabilities for these four states. We find that after the prompt fission of Muonic atom. Muon is mainly attached on the 1s state of the heavy fragment, only 3.8—5.1% of the probabilities are attached on 1s state of the light fragment, and 0.7—0.9% and ~0.1% on the 2p states of the heavy fragment and the light fragment respectively. These results are in agreement with those of references [2], [3], and also in accordance with the experimental results within the experimental errors.

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