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Model with Coupled Internal and External Channels for 2N and 3N Systems

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Abstract

A Faddeev-type formalism for a three-body problem with two-body interactions containing internal degrees of freedom is introduced. The Faddeev equations for the basic objects such as total resolvent, scattering wave function and transition operators are derived explicitly. As a particular example, the dibaryon model for NN interaction with internal channel corresponding to a six-quark bag is considered. It is shown that this interaction model allows to reproduce both real and imaginary parts of some NN partial phase shifts at energies up to 600 MeV. The developed formalism can be also applied to other quantum systems.

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Notes

  1. From a mathematical point of view, an operator depending on the spectral parameter is not the operator at all, because its domain depends on this spectral parameter. Thus, this object should not be called as a Hamiltonian. However, physicists do not turn their attention to the fact and use energy-dependent interactions very widely.

  2. In terms the dibaryon model the case (a) corresponds to including a single six-quark state in internal channel, while in the case (b) the internal channel includes also the motion of a meson inside the cloud of the dressed six-quark bag and \(t^\mathrm{in}\) is a kinetic energy of the meson [28].

  3. It was referred to as a “dressed bag model” in our previous papers [27,28,29,30].

  4. The parameter \(\rho \) reflects the inelasticity of the S-matrix above the pion-production threshold and is related to the Arndt parametrization of the K-matrix [52]. For the partial NN channels without tensor couplings, \(K=\tan \delta +i \tan ^2\rho \).

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Acknowledgements

Authors thank Prof. S.A. Moszkowski for useful comments and suggestions. Also, we are grateful to Dr. M.N. Platonova, the results presented in Sect. 4 have been obtained in collaboration with her. The work has been partially supported by the RFBR Grants Nos. 19-02-00011 and 19-02-00014.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Leninskie gory 1(2), Moscow, Russia

    V. N. Pomerantsev, V. I. Kukulin & O. A. Rubtsova

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  1. V. N. Pomerantsev
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  2. V. I. Kukulin
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  3. O. A. Rubtsova
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Correspondence to O. A. Rubtsova.

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This paper is dedicated to the memory of the brilliant Russian theorist Ludwig Faddeev who believed that an accurate treatment of few-body dynamics in few-nucleon systems should shed light on a proper form of the NN interaction

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Pomerantsev, V.N., Kukulin, V.I. & Rubtsova, O.A. Model with Coupled Internal and External Channels for 2N and 3N Systems. Few-Body Syst 60, 48 (2019). https://doi.org/10.1007/s00601-019-1516-x

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