Abstract
The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon–nucleon (N–N) scattering. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with 1/2 spin (N and \({\bar{N}}\)) fermion ones via the Yukawa-type couplings to introduce trial interactions between “bare” particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N–N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its large amount of virtual processes. We have derived the Lippmann–Schwinger type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space \({\mathcal{H}}\) of hadronic states.
Similar content being viewed by others
References
Lacombe M. et al.: Parametrization of the Paris N–N potential. Phys. Rev. C 21, 861–873 (1980)
Machleidt R., Holinde K., Elster C.: The Bonn meson exchange model for the nucleon nucleon interaction. Phys. Rep. 149, 1–89 (1987)
Stocks V.G.J. et al.: Construction of high-quality NN potential models. Phys. Rev. C 49, 2950–2962 (1994)
Wiringa R.B., Stocks V.G.J., Schiavilla R.: Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995)
Machleidt R.: High-precision, charge-dependent Bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001)
Gross F., Stadler A.: High-precision covariant one boson exchange potentials for np scattering below 350-MeV. Few-Body Syst. 44, 295–298 (2008)
Ordonez C., Ray L., van Kolck U.: Nucleon-nucleon potential from an effective chiral Lagrangian. Phys. Rev. Lett. 72, 1982–1985 (1994)
Epelbaum E., Glöckle W., Meissner U.-G.: Nuclear forces from chiral Lagrangians using the method of unitary transformations. Part 2: the two nucleon system. Nucl. Phys. A 671, 295–331 (2000)
Epelbaum E.: Few-nucleon forces and systems in chiral effective field theory. Prog. Part. Nucl. Phys. 57, 654–741 (2006)
Shebeko A.V., Shirokov M.I.: Unitary transformations in quantum field theory and bound states. Phys. Part. Nucl. 32, 31–95 (2001)
Korda V., Canton L., Shebeko A.: Relativistic interactions for the meson-two-nucleon system in the clothed-particle unitary representation. Ann. Phys. 322, 736–768 (2007)
Weinberg S.: The Quantum Theory of Fields, vol. 1. University Press, Cambridge (1995)
Machleidt R.: The meson theory of nuclear forces and nuclear structure. Adv. Nucl. Phys. 19, 189–376 (1989)
Gasiorowicz S.: Elementary Particle Physics. Wiley, New York (1966)
Schütte D.A.: A Brueckner theory including mesonic degrees of freedom. Nucl. Phys. A 221, 450–460 (1974)
Schweber S.S.: An Introduction to Relativistic Quantum Field Theory. Row, Peterson & Co., New York (1961)
Korchin A.Yu., Shebeko A.V.: The method of Okubo’s effective operators and the relativistic model of nuclear structure. Phys. At. Nucl. 56, 1663–1671 (1993)
Fuda M., Zhang Y.: Light front dynamics of one boson exchange models of the two-nucleon system. Phys. Rev. C 51, 23–37 (1995)
Shebeko, A.V.: The S-matrix within the method of unitary clothing transformations. In: Proceedings of the 16th International Baldin Seminar on High Energy Physics Problems, vol. 1, pp. 35–42 (2004)
Shebeko A.V.: The S-matrix within the method of clothing transformations. Nucl. Phys. A 737, 252–255 (2004)
Goldberger L., Watson M.: Collision Theory. Wiley, New York (1964)
Werle J.: Relativistic Theory of Reactions. PWN-Polish Scientific Publishers, Warszawa (1966)
Keister B.D., Polyzou W.N.: Relativistic Hamiltonian dynamics in nuclear and particle physics. Adv. Nucl. Phys. 20, 225–479 (1991)
Bjorken J.D., Drell S.D.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1964)
Chao C.G., Shirokov M.I.: Relativistic theory of reactions with polarized particles. JETP 34, 1230–1235 (1958)
Mel’nik Yu., Shebeko A.: Calculation of proton polarization in deuteron disintegration with longitudinally polarized electrons. Few-Body Syst. 13, 59–74 (1992)
Blatt J., Biedenharn L.: Neutron-proton scattering with spin-orbit coupling. Part I: general expressions. Phys. Rev. 86, 399–404 (1952)
Stapp H. et al.: Phase-shift analysis of 310-Mev proton-proton scattering experiments. Phys. Rev. 105, 302–310 (1957)
Brown G.E., Jackson A.D., Kuo T.T.S.: Nucleon-nucleon potentials and minimal relativity. Nucl. Phys. A 133, 481 (1969)
Haftel M.I., Tabakin F.: Nuclear saturation and the smoothness of nucleon-nucleon potentials. Nucl. Phys. A 158, 1 (1970)
Brown G.E., Jackson A.D.: Nucleon–Nucleon Interaction. North-Holland, Amsterdam (1976)
Korchin, A.Yu., Shebeko, A.V.: Application of the matrix inversion method in calculations of the cross sections of quasielastic electron scattering on atomic nuclei. Preprint. KFTI 77-35, Kharkov (1977)
Korchin A.Yu., Mel’nik Yu.P., Shebeko A.V.: Angular distributions and polarization of protons in the d(e, e-prime p)n reaction. Few-Body Syst. 9, 211–232 (1990)
Ladygina N.B., Shebeko A.V.: Reaction mechanisms of the proton deuteron breakup process at GeV energies. Few-Body Syst. 33, 49–69 (2003)
Holland J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)
Korda V.Yu.: Evolving model-free scattering matrix via evolutionary algorithm: O-16–O-16 elastic scattering at 350-MeV. Phys. Rev. C 72, 014611 (2005)
Tamura K., Niva T., Sato T., Ohtsubo H.: Exchange current due to rho meson exchange. Prog. Theor. Phys. 80, 138–150 (1988)
Melde T., Canton L., Plessas W.: Structure of meson-baryon interaction vertices. Phys. Rev. Lett. 102, 132002 (2009)
Shebeko A.V., Shirokov M.I.: Clothing procedure in relativistic quantum field theory and its applications to description of electromagnetic interactions with nuclei (bound systems). Prog. Part. Nucl. Phys. 44, 75–86 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dubovyk, I., Shebeko, O. The Method of Unitary Clothing Transformations in the Theory of Nucleon–Nucleon Scattering. Few-Body Syst 48, 109–142 (2010). https://doi.org/10.1007/s00601-010-0097-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-010-0097-5