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Prog. Theor. Phys. Vol. 25 No. 6 (1961) pp. 1035-1042

[ Full Text PDF : FREE ACCESS (406K) ]

Note on the Pairing Correlation in Nuclear Matter

Toshio Marumori, Toshiyuki Murota,* Shuji Takagi,** Hajime Tanaka*** and Masaru Yasuno****

Department of Physics, Kyoto University, Kyoto
*Department of Physics, Osak City University, Osaka
**Research Institute for Fundamental Physics, Kyoto University, Kyoto
***Department of Physics, Hokkaido University, Sapporo
****Kobayashi Institute for Physical Research, Kokubunji, Kitatamagun, Tokyo

(Received March 6, 1961)

Abstract:

A difficulty in literally applying the BCS-Bogoliubov formalism to the nuclear system with singular interaction is pointed out. A prescription to overcome this difficulty is proposed. According to this method, it is possible to consistently join the BCS-Bogoliubov formalism with the “reaction matrix” formalism in a unified manner. The results obtained verify the validity of the basic conjecture underlying Cooper-Mills-Sessler's procedure.


URL : http://ptp.ipap.jp/link?PTP/25/1035/
DOI : 10.1143/PTP.25.1035

[ Full Text PDF : FREE ACCESS (406K) ] Citation:

References:

  1. A. Bohr, B. R. Mottelson and D. Pines, Phys. Rev. 110 (1958), 936[APS].
    C. DeDominicis and P. C. Martin, Bull. Am. Phys. Soc. 3 (1958), 224.
    L. N. Cooper, R. L. Mills and A. M. Sessler, Phys. Rev. 114 (1959), 1377[APS].
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  2. T. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108 (1957), 1175[APS]. (We refer to this as BCS.)
  3. N. N. Bogoliubov, JETP USSR 34 (1958), 58; ibid. 34 (1958), 73.
    See also N. N. Bogoliubov, V. V. Tolmachev and D. V. Shirkov, A new method in the theory of superconductivity, Izv. Akad. Nauk USSR (1958).
  4. A. Bohr, Proceedings of the Paris Conference on Nuclear Structure 1958.
    B. R. Mottelson, Many-Body Problems, editted by DeWitt (John Wiley and Sons, N. Y., 1959), p. 283.
    S. T. Belyaev, Kgl. Danske Videnskab. Selskab, Mat. -fys. Medd. 31 (1959), No. 11.
  5. See K. A. Brueckner and J. L. Gammel, Phys. Rev. 109 (1958), 1023, [APS]for a complete list of reference.
  6. K. Sawada, Phys. Rev. 119 (1960), 2090[APS].
  7. H. A. Bethe and J. Goldstone, Proc. R. Soc. A 238 (1957), 551.
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    F. Iwamoto, Prog. Theor. Phys. 23 (1960), 871[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 26 No. 3 (1961) pp. 321-336 :
    Nuclear Matter at Low Density with Attractive and Singular Interactions
    Yasushi Wada
  2. Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 221-234 :
    Effective Hamiltonian and Energy Gap in Finite Nuclei
    Hiroharu Bandō, Toshiyuki Murota and Sinobu Nagata
  3. Progress of Theoretical Physics Vol. 29 No. 6 (1963) pp. 940-942 :
    Energy Gap in Nuclear Matter
    Masaru Yasuno and Takeshi Ishihara
  4. Progress of Theoretical Physics Vol. 29 No. 6 (1963) pp. 942-944 :
    Energy Gap in Nuclear Matter
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  5. Progress of Theoretical Physics Vol. 30 No. 5 (1963) pp. 601-614 :
    Energy Gap in Nuclear Matter
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  6. Progress of Theoretical Physics Vol. 35 No. 6 (1966) pp. 1026-1042 :
    Nuclear Force and Energy Gap in Finite Nuclei
    Hiroharu Bandō and Sinobu Nagata
  7. Progress of Theoretical Physics Vol. 46 No. 1 (1971) pp. 114-134 :
    Superfluid State in Neutron Star Matter. II
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  8. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 2107-2127 :
    Neutron 3P2-Dominant Superfluidity with Two-Dimensional Character under Well-Developed π0 Condensation
    Ryozo Tamagaki, Tatsuyuki Takatsuka and Hiroaki Frukawa
  9. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1432-1435 :
    Energy Gaps in Crust-Phase of Neutron Stars
    Tatsuyuki Takatsuka
  10. Progress of Theoretical Physics Vol. 102 No. 4 (1999) pp. 897-902 :
    Constructing Effective Pair Wave Function from Relativistic Mean Field Theory with a Cutoff
    Tomonori Tanigawa and Masayuki Matsuzaki
  11. Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 127-142 :
    Liquid-Gas Instability and Superfluidity in Nuclear Matter
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  12. Progress of Theoretical Physics Supplement No.112 (1993) pp. 27-65 :
    Chapter II. Superfluidity in Neutron Star Matter and Symmetric Nuclear Matter
    Tatsuyuki Takatsuka and Ryozo Tamagaki

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