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Angular momentum reduction in the four-body problem

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Czechoslovak Journal of Physics B Aims and scope

Abstract

A complete angular momentum analysis of the integral equations of motion for four identical spinless particles is given. After separation of the variables associated with rotation, the equations of motion take the form of an infinite set of coupled integral equations in three continuous variables. In general, the four-particle kinematic factors in the integral kernels are expressed as bilinear combinations of factors of the three-particle kinematic factors type. For the case of a separable two-particle interaction the equations obtained are simplified so that they are reduced to coupled integral equations in two continuous variables.

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References

  1. Faddeev L. D., ZhETF 39 (1960), 1459, Mathematical problems of the quantum scattering theory for a three-particle system, vol. 69 (Steklov Mathematical Institute, Leningrad, 1963).

    Google Scholar 

  2. Omnes R. L., Phys. Rev.134B (1964), 1358.

    Google Scholar 

  3. Osborn T., Noyes H. P., Phys. Rev. Lett.17 (1966), 215.

    Google Scholar 

  4. Ahmadzadeh A., Tjon J. A., Phys. Rev.139 (1965), B 1085.

    Google Scholar 

  5. Balian R., Brezin E., Nuovo Cimento61B (1969), 403.

    Google Scholar 

  6. El Baz E., Fayard C., Lamot G.-H., Pigeon J., Acta Physica Hungarica33 (1973), 243.

    Google Scholar 

  7. Bolle D., Osborn T. A., Phys. Rev.C9 (1974), 441.

    Google Scholar 

  8. Malfliet R. A., Tjon J. A., Annals of Physics61 (1970), 425.

    Google Scholar 

  9. Harper E. P., Kim Y. E., Tubis A., Phys. Rev.C2 (1970), 877, 2455 (E);C6 (1972), 126.

    Google Scholar 

  10. Kharchenko V. F., Kuzmichev V. E., Nucl. Phys.A183 (1972), 606;A196 (1972), 636.

    Google Scholar 

  11. Faddeev L. D., Proc. problem Symp. on Nuclear Physics, vol. 1, Tbilisi, Moscow 1967, p. 43; Three-body problem in nuclear and particle physics, (ed. J.S.C. McKee and P. M. Rolph, North-Holland, Amsterdam 1970) p. 154.

    Google Scholar 

  12. Yacubovsky O. A., Sov. J. Nucl. Phys.5 (1967), 1312.

    Google Scholar 

  13. Rose M. E., Multipole Fields, John Wiley and Sons, inc., New York 1955;Baldin A. M.,Goldansky V. I.,Rosental I. L., Kinematic of Nuclear Reactions, Fizmatgiz, Moscow 1959.

    Google Scholar 

  14. Kharchenko V. F., Kuzmichev V. E., Sov. J. Nucl. Phys.17 (1973), 975; Czech. J. Phys.B24 (1974), 1071.

    Google Scholar 

  15. Kharchenko V. F., Kuzmichev V. E., Shadchin S. A., Nucl. Phys.A226 (1974), 71.

    Google Scholar 

  16. Kharchenko V. F., Kuzmichev V. E., Sov. J. Nucl. Phys.20 (1974), 334.

    Google Scholar 

  17. Narodetsky I. M., Galpern E. S., Lyakhovitsky V. N., ZhETF Letters18 (1973), 136

    Google Scholar 

  18. Narodetsky I. M., Sov. J. Nucl. Phys.19 (1974), 552.

    Google Scholar 

  19. Sitenko A. G., Kharchenko V. F., Uspekhi Fiz. Nauk103 (1971), 469.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kiev, Metrologicheskaya St. 14- b, Kiev-130, Ukr. SSR, USSR

    V. F. Kharchenko & S. A. Shadchin

Authors
  1. V. F. Kharchenko
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  2. S. A. Shadchin
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Kharchenko, V.F., Shadchin, S.A. Angular momentum reduction in the four-body problem. Czech J Phys 27, 255–279 (1977). https://doi.org/10.1007/BF01587359

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  • DOI: https://doi.org/10.1007/BF01587359

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