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The proton-proton reaction and related reactions in an intense magnetic field

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Abstract

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH q =m 2 c 3/eħ=4.414×1013G. For fields greater thanH q , the proton-proton reaction rates are enhanced linearly with Θ (Θ=H/H q ).

The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T 9≳5) and low fields (Θ≲1). For instance, ℛpep(H)=0.04 ℛpep(O) at Θ=10−3,T 9=10. For relatively high fields (Θ>1) and low temperatures (T 9≲2), the reaction rates are enhanced approximately linearly with Θ. In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (ϱ6/μe≲10). At high densities (ϱ6/μe≳10) the reaction rates are unaffected by the magnetic field.

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References

  • Bahcall, J. N. and May, R. M.: 1968, ‘The Rate of the Proton-Proton Reaction’,Astrophys. J. 152, L17.

    Google Scholar 

  • Bahcall, J. N. and May, R. M.: 1969, ‘The Rate of the Proton-Proton Reaction and Some Related Reactions’,Astrophys. J. 155, 501.

    Google Scholar 

  • Bethe, H. A.: 1939, ‘Energy Production in Stars’,Phys. Rev. 55, 434.

    Google Scholar 

  • Bethe, H. A. and Critchfield, C. L.: 1938, ‘The Formation of Deuterons by Proton Combination’,Phys. Rev. 54, 248.

    Google Scholar 

  • Cameron, A. G. W.: 1966,Nuclear Astrophysics, 2nd ed. (compiled by S. Edelstein, W. Langer and D. W. Watkins), based on lectures given at Yale University 1965–1966.

  • Canuto, V. and Chiu, H. Y.: 1968a, ‘Quantum Theory of an Electron Gas in Intense Magnetic Field’,Phys. Rev. 173, 1210.

    Google Scholar 

  • Canuto, V. and Chiu, H. Y.: 1968b, ‘Thermodynamic Properties of a Magnetized Fermi Gas’,Phys. Rev. 173, 1220.

    Google Scholar 

  • Canuto, V. and Chiu, H. Y.: 1968c, ‘The Magnetic Moment of a Magnetized Fermi Gas’,Phys. Rev. 173, 1229.

    Google Scholar 

  • Canuto, V., Chiu, H. Y., Chou, C. K., and Fassio-Canuto, L.: 1970, ‘Neutrino Bremsstrahlung in an Intense Magnetic Field’,Phys. Rev., in press.

  • Canuto, V., Chiuderi, C., and Chou, C. K.: 1970a, ‘Plasmon Neutrinos Emission in a Strong Magnetic Field. I: Transverse Plasmons’,Astrophys. Space Sci. 7, 407.

    Google Scholar 

  • Canuto, V., Chiuderi, C., and Chou, C. K.: 1970b, ‘Plasmon Neutrinos Emission in a Strong Magnetic Field. II: Longitudinal Plasmons’,Astrophys. Space Sci., in press.

  • Canuto, V. and Chou, C. K.: 1970, ‘Neutrino Luminosity by the Ordinary URCA Process in an Intense Magnetic Field’, to be published.

  • Chiu, H. Y.: 1968,Stellar Physics, Vol. I, Blaisdell Publishing Company, Waltham, Mass., Chapter 6.

    Google Scholar 

  • Chiu, H. Y. and Canuto, V.: 1969, ‘Radio Emission from Magnetic Neutron Stars’,Phys. Rev. Letters 22, 415.

    Google Scholar 

  • Chiu, H. Y. and Canuto, V.: 1970, ‘Theory of Radiation Mechanisms for Pulsars I’,Astrophys. J., to be published.

  • Cox, J. P. and Giuli, R. T.: 1968,Principles of Stellar Structure, Vol. 2, Gordon & Breach, New York, Chapter 24.

    Google Scholar 

  • Fassio-Canuto, L.: 1969, ‘Neutron Beta Decay in a Strong Magnetic Field’,Phys. Rev. 187, 2141.

    Google Scholar 

  • Hansen, C. J.: 1966, Ph. D. Thesis, Yale University, unpublished.

  • Hansen, C. J.: 1968, ‘Some Weak Interaction Processes in Highly Evolved Stars’,Astrophys. Space Sci. 1, 499.

    Google Scholar 

  • Lee, H. J., Canuto, V., Chiu, H. Y., and Chiuderi, C.: 1969, ‘New State of Ferromagnetism in Degenerate Electron Gas and Magnetic Fields in Collapsed Bodies’,Phys. Rev. Letters 23, 390.

    Google Scholar 

  • McGee, I. J.: 1966,Phys. Rev. 151, 772.

    Google Scholar 

  • Ostriker, J. P. and Hartwick, F. D. A.: 1968, ‘Rapidly Rotaning Stars. IV.: Magnetic White Dwarfs’,Astrophys. J. 153, 797.

    Google Scholar 

  • Salpeter, E. E.: 1952, ‘Nuclear Reactions in the Stars. I: Proton-Proton Chain’,Phys. Rev. 88, 547.

    Google Scholar 

  • Schatzman, E.: 1958,White Dwarfs, Interscience Publishers, New York, p. 141.

    Google Scholar 

  • Tsuruta, S. and Cameron, A. G. W.: 1970, ‘URCA Shells in Dense Stellar Interiors’,Astrophys. Space Sci. 7, 374.

    Google Scholar 

  • Woltjer, L.: 1964,Astrophys. J. 140, 1309.

    Google Scholar 

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  1. Institute for Space Studies, Goddard Space Flight Center, NASA, New York, N.Y., USA

    Chih Kang Chou

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  1. Chih Kang Chou
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Chou, C.K. The proton-proton reaction and related reactions in an intense magnetic field. Astrophys Space Sci 10, 291–308 (1971). https://doi.org/10.1007/BF00704088

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  • DOI: https://doi.org/10.1007/BF00704088

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